{"id":13310,"date":"2022-04-04T17:52:56","date_gmt":"2022-04-04T12:22:56","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=13310"},"modified":"2022-04-07T11:08:24","modified_gmt":"2022-04-07T05:38:24","slug":"big-ideas-math-answers-grade-4-chapter-10","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-10\/","title":{"rendered":"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals"},"content":{"rendered":"<p>Do you want to become proficient in Math? Then, must follow our Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals. <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4\/\">Big Ideas Math Answers Grade 4<\/a> Chapter 10 Relate Fractions and Decimals is the one-stop destination for all your practice. You can get the topic-wise Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals PDF for free of cost. Test your knowledge on the complete concepts by solving from the Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals and identify the knowledge gap accordingly.<\/p>\n<h2>Big Ideas 4th Grade Chapter 10 Relate Fractions and Decimals Math Book Answer Key<\/h2>\n<p>Use our ultimate guide Big Ideas Math Book 4th Grade Answer Key Chapter 10 Relate Fractions and Decimals over here to clear all your doubts. How to grab the best source of BIM 4th grade Chapter 10 Answer Key? All you have to do is simply tap on the below quick links to get the respective topic from the 4th grade Chapter 10 Solution Key. Start your preparation right away by taking the help of the Relate Fractions and Decimals Big Ideas Math Grade 4 Solutions and clear the exam with flying colors.<\/p>\n<p><strong>Lesson: 1 Understand Tenths<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.1_Understand_Tenths\">Lesson 10.1 Understand Tenths<\/a><\/li>\n<li><a href=\"#Understand_Tenths_Homework_&amp;_Practice_10.1\">Understand Tenths Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Understand Hundredths<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.2_Understand_Hundredths\">Lesson 10.2 Understand Hundredths<\/a><\/li>\n<li><a href=\"#Understand_Hundredths_Homework_&amp;_Practice_10.2\">Understand Hundredths Homework &amp; Practice 10.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Fractions and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.3_Fractions_and_Decimals\">Lesson 10.3 Fractions and Decimals<\/a><\/li>\n<li><a href=\"#Fractions_and_Decimals_Homework_&amp;_Practice_10.3\">Fractions and Decimals Homework &amp; Practice 10.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Compare Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.4_Compare_Decimals\">Lesson 10.4 Compare Decimals<\/a><\/li>\n<li><a href=\"#Compare_Decimals_Homework_&amp;_Practice_10.4\">Compare Decimals Homework &amp; Practice 10.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Add Decimal Fractions and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.5_Add_Decimal_Fractions_and_Decimals\">Lesson 10.5 Add Decimal Fractions and Decimals<\/a><\/li>\n<li><a href=\"#Add_Decimal_Fractions_and_Decimals_Homework_&amp;_Practice_10.5\">Add Decimal Fractions and Decimals Homework &amp; Practice 10.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Fractions, Decimals and Money<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.6_Fractions,_Decimals_and_Money\">Lesson 10.6 Fractions, Decimals and Money<\/a><\/li>\n<li><a href=\"#Fractions,_Decimals_and_Money_Homework_&amp;_Practice_10.6\">Fractions, Decimals and Money Homework &amp; Practice 10.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Operations with Money<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.7_Operations_with_Money\">Lesson 10.7 Operations with Money<\/a><\/li>\n<li><a href=\"#Operations_with_Money_Homework_&amp;_Practice_10.7\">Operations with Money Homework &amp; Practice 10.7<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Relate_Fractions_and_Decimals_Performance_Task_10\">Relate Fractions and Decimals Performance Task 10<\/a><\/li>\n<li><a href=\"#Relate_Fractions_and_Decimals_Activity\">Relate Fractions and Decimals Activity<\/a><\/li>\n<li><a href=\"#Relate_Fractions_and_Decimals_Chapter_Practice_10\">Relate Fractions and Decimals Chapter Practice 10<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_10.1_Understand_Tenths\"><\/a>Lesson 10.1 Understand Tenths<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>How many dimes have a total value of one dollar? Draw a model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 1\" width=\"162\" height=\"86\" \/><\/p>\n<p>One dime is what fraction of one dollar? Write your answer in words and as a fraction.<\/p>\n<p>Answer:<br \/>\nWe know that,<br \/>\n1 dollar = 10 dimes<br \/>\nSo,<br \/>\nThe representation of one dime in the fraction of 1 dollar is: \\(\\frac{1}{10}\\)<br \/>\nIn terms of words, one Dime is equal to one-tenth of the Dollar<\/p>\n<p>Explanation:<br \/>\nThe given note is &#8220;Dollar note&#8221;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 1\" width=\"162\" height=\"86\" \/><br \/>\nWe know that,<br \/>\n1 Dollar = 10 Dimes<br \/>\nSo,<br \/>\nThe representation of one Dime in the fraction of 1 dollar is: \\(\\frac{1}{10}\\)<\/p>\n<p>So,<br \/>\nThe representation of a Dime in the model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10.jpg\" alt=\"\" width=\"477\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10.jpg 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-300x69.jpg 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that one Dime is equal to one-tenth of one Dollar.<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow is one whole related to one-tenth? How do you think you can write \\(\\frac{1}{10}\\) in a place value chart?<br \/>\nAnswer:<br \/>\nThe representation of one-tenth in a place value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-2.jpg\" alt=\"\" width=\"226\" height=\"89\" \/><\/p>\n<p>Explanation:<br \/>\nThe one-tenth is the fraction value which is less than one whole. When we divide the one whole into ten parts,<br \/>\nthen each divided part represents one-tenth of the 10 parts.<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{1}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-2.jpg\" alt=\"\" width=\"226\" height=\"89\" \/><\/p>\n<p><strong>Think and Grow: Understand Tenths<\/strong><\/p>\n<p>A decimal is a number with one or more digits to the right of the decimal point. The first place to the right of the decimal point is the tenths place.<br \/>\nYou can write tenths as fractions or decimals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 2\" width=\"242\" height=\"183\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nWrite \\(\\frac{3}{10}\\) as a decimal.<br \/>\nShade the model. Use a place value chart.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-3.jpg\" alt=\"\" width=\"711\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-3.jpg 711w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-3-300x88.jpg 300w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nWrite 2\\(\\frac{8}{10}\\) as a decimal.<br \/>\nShade the model. Use a place value chart.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-5.jpg\" alt=\"\" width=\"691\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-5.jpg 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-5-300x105.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Write the fraction or mixed number as a decimal.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 5\" width=\"140\" height=\"111\" \/><br \/>\nAnswer: The representation of \\(\\frac{5}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-6.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-6.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-6-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nExplanation:<br \/>\nThe given fraction is: \\(\\frac{5}{10}\\)<br \/>\nThe given model fro \\(\\frac{5}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 5\" width=\"140\" height=\"111\" \/><br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 6\" width=\"246\" height=\"116\" \/><\/p>\n<p>Answer: The representation of 1\\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-7.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-7.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-7-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{7}{10}\\) is: \\(\\frac{17}{10}\\)<br \/>\nThe given model for 1\\(\\frac{7}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 6\" width=\"246\" height=\"116\" \/><br \/>\nHere,<br \/>\nIn 1\\(\\frac{7}{10}\\),<br \/>\n1 represents the one&#8217;s place and 7 represents the tenths place<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 1\\(\\frac{7}{10}\\) in the decimal form is: 1.7<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Shade the model to represent the fraction or mixed number. Then write the fraction or mixed number as a decimal.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 7\" width=\"143\" height=\"122\" \/><br \/>\nAnswer: The representation of\u00a0 \\(\\frac{2}{10}\\) in the place- value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-8.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-8.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-8-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{2}{10}\\)<br \/>\nThe model representing the \\(\\frac{2}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-9.jpg\" alt=\"\" width=\"142\" height=\"111\" \/><br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 8\" width=\"251\" height=\"113\" \/><br \/>\nAnswer: The representation of 1\\(\\frac{9}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-10.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-10.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-10-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{9}{10}\\) is: \\(\\frac{19}{10}\\)<br \/>\nThe model representiong 1\\(\\frac{9}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-11.jpg\" alt=\"\" width=\"253\" height=\"113\" \/><br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{9}{10}\\) in the decimal form is: 1.9<\/p>\n<p>Write the fraction or mixed number as a decimal.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 9\" width=\"35\" height=\"47\" \/><br \/>\nAnswer: The representation of \\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-12.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-12.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-12-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{7}{10}\\)<br \/>\nThe model representing the \\(\\frac{7}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-13.jpg\" alt=\"\" width=\"142\" height=\"111\" \/><br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{7}{10}\\) in the decimal form is: 0.7<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 10\" width=\"30\" height=\"46\" \/><br \/>\nAnswer: The representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-14.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-14.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-14-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{4}{10}\\)<br \/>\nThe model representing the \\(\\frac{4}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-15.jpg\" alt=\"\" width=\"245\" height=\"219\" \/><br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the decimal form is: 0.4<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 11\" width=\"51\" height=\"55\" \/><br \/>\nAnswer: The representation of 5\\(\\frac{1}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-16.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-16.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-16-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is:5\\(\\frac{1}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 5\\(\\frac{1}{10}\\) is: \\(\\frac{51}{10}\\)<br \/>\nIn 5\\(\\frac{1}{10}\\),<br \/>\n5 represents the ones position and 1 represents the tenths position.<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 5\\(\\frac{1}{10}\\) in the decimal form is: 5.1<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 12\" width=\"65\" height=\"55\" \/><br \/>\nAnswer: The representation of 24\\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-17.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-17.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-17-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 24\\(\\frac{3}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 24\\(\\frac{3}{10}\\) is: \\(\\frac{243}{10}\\)<br \/>\nIn 24\\(\\frac{3}{10}\\),<br \/>\n2 represents the tens position<br \/>\n4 represents the one&#8217;s position<br \/>\n3 represents the tenths position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 24\\(\\frac{3}{10}\\) in the decimal form is: 24.3<\/p>\n<p><strong>Write the number as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 9.<br \/>\nsix tenths<br \/>\nAnswer: The representation of six tenths in the fraction form is: \\(\\frac{6}{10}\\)<br \/>\nThe representation of \\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-18.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-18.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-18-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{6}{10}\\)<br \/>\nIn \\(\\frac{6}{10}\\),<br \/>\n6 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{6}{10}\\) in the Decimal form is: 0.6<\/p>\n<p>Question 10.<br \/>\neleven and five-tenths<br \/>\nAnswer: The representation of eleven and five-tenths in the fraction form is: 11\\(\\frac{5}{10}\\)<br \/>\nThe representation of 11\\(\\frac{5}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-19.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-19.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-19-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 11\\(\\frac{5}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 11\\(\\frac{5}{10}\\) is: \\(\\frac{115}{10}\\)<br \/>\nIn 11\\(\\frac{5}{10}\\),<br \/>\n1 represents Ten&#8217;s and 1 represents the one&#8217;s position<br \/>\n5 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nthe representation of 11\\(\\frac{5}{10}\\) in the decimal form is: 11.5<\/p>\n<p>Question 11.<br \/>\nNewton passes 8 out of 10 obedience classes. What portion of the classes does Newton pass? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 13\" width=\"147\" height=\"154\" \/><br \/>\nAnswer: The portion of the classes does Newton pass is: 0.8<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton passes 8 out of 10 obedience classes.<br \/>\nThe representation of the portion of the classes that Newton passed in the fraction form = \\(\\frac{The number of classes that Newton passed} {The total number of classes}\\) = \\(\\frac{8}{10}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-20.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-20.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-20-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{8}{10}\\),<br \/>\n8 represents the Tenth&#8217;s position.<br \/>\nSo, the representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nWe can conclude that the representation of the portion of the classes that Newton passed in the decimal form is: 0.8<\/p>\n<p>Question 12.<br \/>\nYou move a game piece around a game board 3\\(\\frac{2}{10}\\) times before you lose a turn. Write this number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-14..png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 14.\" width=\"92\" height=\"108\" \/><br \/>\nAnswer: The representation of 3\\(\\frac{2}{10}\\) in the decimal form is: 3.2<\/p>\n<p>Explanation:<br \/>\nIt is given that you move a game piece around a game board 3\\(\\frac{2}{10}\\) times before you lose a sum.<br \/>\nSo,<br \/>\nThe representation of 3\\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-21.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-21.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-21-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 3\\(\\frac{2}{10}\\),<br \/>\n3 represents one&#8217;s position<br \/>\n2 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 3\\(\\frac{2}{10}\\) in the decimal form is: 3.2<\/p>\n<p>Question 13.<br \/>\n<strong>Writing<\/strong><br \/>\nDo 0.5 and 5.0 have the same value? Explain.<br \/>\nAnswer: 0.5 and 5.0 does not have the same value because the place-value of 5 is different in both 0.5 and 5.0<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.5 and 5.0<br \/>\nThe position of 5 in 0.5 according to the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-22.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-22.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-22-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nThe position of 5 in 5.0 according to the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-23.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-23.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-23-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 0.5, the position of 5 is: tenth&#8217;s position<br \/>\nIn 5.0, the position of 5 is: One&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.5 and 5.0 do not have the same value.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou have a collection of dinosaur figurines. What portion of the dinosaurs in your collection are carnivores? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 15\" width=\"352\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15-232x300.png 232w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nDraw a model to represent the collection. Shade the same number of parts as there are carnivore dinosaurs in the collection.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 15.1\" width=\"119\" height=\"117\" \/><br \/>\nWrite the decimal shown by the model.<br \/>\nAnswer:<br \/>\nFrom the above table, 3 of the dinosaurs in the collection are carnivores.<br \/>\nThe total number of dinosaurs in the collection is: 10<br \/>\nSo,<br \/>\nThe representation of carnivores in the collection of dinosaurs is: \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 15\" width=\"352\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15-232x300.png 232w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nFrom the above table,<br \/>\nThe total number of dinosaurs are: 10<br \/>\nThe number of carnivores in the total number of dinosaurs is: 3<br \/>\nSo,<br \/>\nThe representation of carnivores in the total number of dinosaurs in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-24.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-24.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-24-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{3}{10}\\),<br \/>\n3 represents tenth&#8217;s position.<br \/>\nThe formula for converting a fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of carnivores from the total number of dinosaurs in the decimal form is: 0.3<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nUse the table above. What portion of the dinosaurs in your collection are herbivores? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-16.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 16\" width=\"168\" height=\"103\" \/><br \/>\nAnswer: The portion of dinosaurs in your collection that are herbivores is: 0.5<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 15\" width=\"352\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-15-232x300.png 232w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nFrom the above table,<br \/>\nThe total number of dinosaurs are: 10<br \/>\nThe number of herbivores from the collection of dinosaurs is: 5<br \/>\nSo,<br \/>\nThe representation of the number of herbivores from the total dinosaurs in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-25.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-25.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-25-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{3}{10}\\),<br \/>\n3 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of the herbivores from the total number of dinosaurs in the decimal form is: 0.5<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 10 apps on your tablet. Six of the apps are games. What portion of the apps on your tablet are not games? Write your answer as a decimal.<br \/>\nAnswer: The portion of the apps on your tablet that is not games in the fraction form is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 10 apps on your tablet out of which 6 of the apps are games.<br \/>\nSo,<br \/>\nThe total number of apps on your tablet are: 10<br \/>\nThe number of apps that are games on your tablet is: 6<br \/>\nSo,<br \/>\nThe number of apps that are not games on your tablet is: 4<br \/>\nSo,<br \/>\nThe representation of the apps that are not games out of the total apps in the fraction form is: \\(\\frac{4}{10}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-26.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-26.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-26-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{4}{10}\\),<br \/>\n4 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe portion of the apps that are not games out of the total number of apps in the decimal form is: 0.4<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou make 3 pans of lasagna for a party. You cut each pan of lasagna into10 equal pieces. The guests eat 22 pieces. Write the fraction and decimal that represent how many pans of lasagna the guests eat.<br \/>\nAnswer: The representation of the pans of lasagna the guests eat in the fraction form is: \\(\\frac{22}{30}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 3 pans of lasagna for a party and each pan of lasagna cut into 10 equal parts.<br \/>\nSo,<br \/>\nThe total number of pieces of Lasagna = The total number of pans \u00d7 The number of parts that each Lasagna is cut<br \/>\n= 3 \u00d7 10 = 30 pieces<br \/>\nIt is also given that the guests eat 22 pieces out of 30 pieces.<br \/>\nSo,<br \/>\nThe representation of the number of pieces that the guests eat is: \\(\\frac{22}{30}\\)<br \/>\nThe representation of \\(\\frac{22}{30}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-27.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-27.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-27-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{22}{30}\\),<br \/>\n22 represents the ten&#8217;s and one&#8217;s position<br \/>\n30 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of the number of pieces out of the total number of pieces in the decimal form is: 22.30<\/p>\n<h3><a id=\"Understand_Tenths_Homework_&amp;_Practice_10.1\"><\/a>Understand Tenths Homework &amp; Practice 10.1<\/h3>\n<p>Question 1<br \/>\nWrite \\(\\frac{6}{10}\\) as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 17\" width=\"113\" height=\"110\" \/><br \/>\nAnswer: The representation of \\(\\frac{6}{10}\\) in the decimal form is: 0.6<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{6}{10}\\)<br \/>\nThe given model for \\(\\frac{6}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 17\" width=\"113\" height=\"110\" \/><br \/>\nThe representation of \\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-28.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-28.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-28-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{6}{10}\\),<br \/>\n6 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{6}{10}\\) in the decimal form is: 0.6<\/p>\n<p>Question 2.<br \/>\nShade the model to represent 1\\(\\frac{8}{10}\\). Then write the mixed number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-18.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 18\" width=\"214\" height=\"112\" \/><\/p>\n<p>Write the fraction or mixed number as a decimal.<br \/>\nAnswer: The representation of 1\\(\\frac{8}{10}\\) in the decimal form is: 1.8<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{8}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{8}{10}\\) is: \\(\\frac{18}{10}\\)<br \/>\nThe model given for 1\\(\\frac{8}{10}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-29.jpg\" alt=\"\" width=\"217\" height=\"106\" \/><br \/>\nSo,<br \/>\nThe representation of 1\\(\\frac{8}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-30.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-30.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-30-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 1\\(\\frac{8}{10}\\),<br \/>\n1 represents the one&#8217;s position<br \/>\n8 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nTh representation of 1\\(\\frac{8}{10}\\) in the decimal form is: 1.8<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{1}{10}\\) in the decimal form is: 0.1<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{1}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{1}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-31.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-31.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-31-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{1}{10}\\),<br \/>\n1 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{1}{10}\\) in the decimal form is: 0.1<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{5}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-32.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-32.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-32-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{5}{10}\\),<br \/>\n5 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{2}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{2}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-33.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-33.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-33-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{2}{10}\\),<br \/>\n2 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{8}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{8}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-34.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-34.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-34-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{8}{10}\\),<br \/>\n8 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Question 7.<br \/>\n4\\(\\frac{3}{10}\\)<br \/>\nAnswer: The representation of 4\\(\\frac{3}{10}\\) in the decimal form is: 4.3<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 4\\(\\frac{3}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 4\\(\\frac{3}{10}\\) is: \\(\\frac{43}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 4\\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-35.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-35.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-35-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 4\\(\\frac{3}{10}\\),<br \/>\n4 represents the one&#8217;s position<br \/>\n3 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 4\\(\\frac{3}{10}\\) in the decimal form is: 4.3<\/p>\n<p>Question 8.<br \/>\n1\\(\\frac{4}{10}\\)<br \/>\nAnswer: The representation of 1\\(\\frac{4}{10}\\) in the decimal form is: 1.4<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{4}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{4}{10}\\) is: \\(\\frac{14}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 1\\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-36.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-36.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-36-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 1\\(\\frac{4}{10}\\),<br \/>\n1 represents the one&#8217;s position<br \/>\n4 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{4}{10}\\) in the decimal form is: 1.4<\/p>\n<p>Question 9.<br \/>\n31\\(\\frac{7}{10}\\)<br \/>\nAnswer: The representation of 31\\(\\frac{7}{10}\\) in the decimal form is: 31.7<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 31\\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 31\\(\\frac{7}{10}\\) is: \\(\\frac{317}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 31\\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-37.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-37.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-37-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 31\\(\\frac{7}{10}\\),<br \/>\n3 represents the ten&#8217;s position<br \/>\n1 represents the one&#8217;s position<br \/>\n7 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 31\\(\\frac{7}{10}\\) in the decimal form is: 31.7<\/p>\n<p>Question 10.<br \/>\n40\\(\\frac{6}{10}\\)<br \/>\nAnswer: The representation of 40\\(\\frac{6}{10}\\) in the decimal form is: 40.6<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 40\\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 40\\(\\frac{6}{10}\\) is: \\(\\frac{406}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 40\\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-38.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-38.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-38-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 40\\(\\frac{6}{10}\\),<br \/>\n4 represents the ten&#8217;s position<br \/>\n0 represents the one&#8217;s position<br \/>\n6 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 40\\(\\frac{6}{10}\\) in the decimal form is: 40.6<\/p>\n<p><strong>Write the number as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 11.<br \/>\nthree tenths<br \/>\nAnswer: The representation of the three-tenths in the decimal form is: 0.3<\/p>\n<p>Explanation:<br \/>\nThe given fraction in the word form is: Three-tenths<br \/>\nThe representation of the three-tenths in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-39.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-39.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-39-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{3}{10}\\),<br \/>\n3 represents the tenth&#8217;s place<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Question 12.<br \/>\nfourteen and nine-tenths<br \/>\nAnswer: The representation of fourteen and nine-tenths in the decimal form is: 14.9<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction in Word form is: fourteen and nine-tenths<br \/>\nThe representation of fourteen and nine-tenths in the fraction form is: 14\\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 14\\(\\frac{9}{10}\\) is: \\(\\frac{149}{10}\\)<br \/>\nSo,<br \/>\nThe representation of 14\\(\\frac{9}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-40.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-40.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-40-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 14\\(\\frac{9}{10}\\),<br \/>\n1 represents the ten&#8217;s place<br \/>\n4 represents the one&#8217;s place<br \/>\n9 represents the tenth&#8217;s place<br \/>\nHence,<br \/>\nThe representation of 14\\(\\frac{9}{10}\\) in the decimal form is: 14.9<\/p>\n<p>Question 13.<br \/>\nYou knock down 5 out of 10 bowling pins. What portion of the bowling pins do you knockdown? Write your answer as a decimal.<br \/>\nAnswer: The portion the bowling pins did you knockdown is: \\(\\frac{5}{10}\\) = 0.6<\/p>\n<p>Explanation:<br \/>\nIt is given that you knock down 5 bowling pins out of 10 bowling pins.<br \/>\nSo,<br \/>\nThe representation of the portion of bowling pins you knock down is: \\(\\frac{5}{10}\\)<br \/>\nso,<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-41.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-41.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-41-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{5}{10}\\),<br \/>\n5 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of the portion of the bowling pins that you knockdown in the decimal form is: \\(\\frac{5}{10}\\) = 0.5<\/p>\n<p>Question 14.<br \/>\nYou drive a go-kart around a track 8\\(\\frac{7}{10}\\) times before you spin out. Write this number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-19.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 19\" width=\"176\" height=\"105\" \/><\/p>\n<p>Answer:\u00a0 The representation of 8\\(\\frac{7}{10}\\) in the decimal form is: 8.7<\/p>\n<p>Explanation:<br \/>\nIt is given that you drive a go-kart around a track 8\\(\\frac{7}{10}\\) before you spin out.<br \/>\nSo,<br \/>\nThe given mixed fraction is: 8\\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 8\\(\\frac{7}{10}\\) is: \\(\\frac{87}{10}\\)<br \/>\nSo,<br \/>\nThe representation of 8\\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-42.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-42.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-42-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn 8\\(\\frac{7}{10}\\),<br \/>\n8 represents the one&#8217;s position<br \/>\n7 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of 8\\(\\frac{7}{10}\\) in the decimal form is: 8.7<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhich number-cards are represented by the model?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 20\" width=\"586\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20-300x57.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Use the table.<br \/>\nAnswer: The number- cards represented by the model are: 1\\(\\frac{3}{10}\\) and 1.3<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 20\" width=\"586\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-20-300x57.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><br \/>\nIn the given model, the tables are represented by:<br \/>\nA) 1\\(\\frac{3}{10}\\) B) 13 C) 0.13 D) 1.3<br \/>\nIn the given model,<br \/>\nConsider the fully colored model as one whole unit.<br \/>\nSo,<br \/>\nThe total number of colored units is: 10<br \/>\nNow, in another model,<br \/>\nThe number of colored parts is: 3<br \/>\nThe number of total parts is: 10<br \/>\nSo,<br \/>\nThe portion of the colored part from the total number of parts is: \\(\\frac{3}{10}\\)<br \/>\nSo, by combining the 2 models,<br \/>\nThe total number of colored parts = 1 + \\(\\frac{3}{10}\\)<br \/>\n= 1 + 0.3<br \/>\n= 1.3<br \/>\nSo,<br \/>\nThe representation of the total number of colored parts in the mixed fraction form is: 1\\(\\frac{3}{10}\\)<br \/>\nThe representation of the total number of colored parts in the decimal form is: 1.3<\/p>\n<p>Question 16.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA photographer frames her photographs from a safari trip. What portion of the framed photographs are of mammals? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 21\" width=\"249\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21-215x300.png 215w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 21.1\" width=\"258\" height=\"142\" \/><\/p>\n<p>Answer: The portion of the framed photographs that are of mammals in the decimal form is: 0.6<\/p>\n<p>Explanation:<br \/>\nIt is given that a photographer frames photos from a safari trip and the framed photos are all categorized according to the table given below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 21\" width=\"249\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21-215x300.png 215w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><br \/>\nSo,<br \/>\nFrom the table,<br \/>\nThe total number of framed photographs are: 10<br \/>\nThe number of framed photographs that are mammals is: 6<br \/>\nSo,<br \/>\nThe portion of the mammals from the total number of framed photographs in the fraction form is: \\(\\frac{6}{10}\\)<br \/>\nThe representation of the \\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-43.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-43.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-43-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{6}{10}\\),<br \/>\n6 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe portion of the mammals from the\u00a0 framed photographs in the decimal form is:\u00a0 0.6<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat portion of the framed not photographs are of mammals? Write your answer as a decimal.<br \/>\nAnswer: THe portion of the photographs that are not mammals in the decimal form is: 0.4<\/p>\n<p>Explanation:<br \/>\nThe table for all the framed photographs is given below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 21\" width=\"249\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-21-215x300.png 215w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><br \/>\nFrom the table,<br \/>\nThe total number of framed photographs are: 10<br \/>\nThe number of framed photographs that are not mammals is: 4<br \/>\nSo,<br \/>\nThe portion of the photographs that are not mammals in the fraction form is: \\(\\frac{4}{10}\\)<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-44.jpg\" alt=\"\" width=\"353\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-44.jpg 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-44-300x105.jpg 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nIn \\(\\frac{4}{10}\\),<br \/>\n4 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe number of framed photographs that are not mammals in the decimal form is: 0.4<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-22.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 22\" width=\"61\" height=\"56\" \/><br \/>\nAnswer: 47 \u00d7 6 = 282<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n47 \u00d7 6 = ( 40 + 7 ) \u00d7 6<br \/>\n= ( 40 \u00d7 6 ) + ( 7 \u00d7 6 )<br \/>\n= 240 + 42<br \/>\n= 282<br \/>\nHence, 47 \u00d7 6 = 282<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-23.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 23\" width=\"66\" height=\"59\" \/><br \/>\nAnswer: 961 \u00d7 3 = 2,883<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n961 \u00d7 3 = ( 900 + 60 + 1 ) \u00d7 3<br \/>\n= ( 900 \u00d7 3 ) + ( 60 \u00d7 3 ) + ( 1 \u00d7 3 )<br \/>\n= 2,700 + 180 + 3<br \/>\n= 2,883<br \/>\nHence, 961 \u00d7 3 = 2,883<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-24.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 24\" width=\"84\" height=\"58\" \/><br \/>\nAnswer: 2,405 \u00d7 8 = 19,240<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n2,405 \u00d7 8 = ( 2,400 + 5 ) \u00d7 8<br \/>\n= ( 2,400 \u00d7 8 ) + ( 5 \u00d7 8 )<br \/>\n= 19,200 + 40<br \/>\n= 19,240<br \/>\nHence, 2,405 \u00d7 8 = 19,240<\/p>\n<h3><a id=\"Lesson_10.2_Understand_Hundredths\"><\/a>Lesson 10.2 Understand Hundredths<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>How many pennies have a total value of one dollar? Draw a model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-25.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 25\" width=\"166\" height=\"79\" \/><\/p>\n<p>One penny is what fraction of one dollar? Write your answer in words and as a fraction.<\/p>\n<p>Answer: The representation of one penny into the dollar in the fraction form is: 0.01<\/p>\n<p>Explanation:<br \/>\nThe given note is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-25.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 25\" width=\"166\" height=\"79\" \/><br \/>\nWe know that,<br \/>\n1 Dollar = 100 pennies<br \/>\nSo,<br \/>\nThe representation of\u00a0 1 penny into the dollar is: \\(\\frac{1}{100}\\) dollars<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-45.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-45.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-45-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nHence, one dollar is equal to 100 pennies and 1 penny is equal to 0.01 dollars<\/p>\n<p>Structure<br \/>\nHow is one-tenth related to one hundredth? How do you think you can write \\(\\frac{1}{100}\\) in a place value chart?<\/p>\n<p>Answer: The one-tenth is related to the one-hundredth as: \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\none-hundredth = \\(\\frac{1}{10}\\) \u00d7 \\(\\frac{1}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{1}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-90.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-90.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-90-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{1}{100}\\),<br \/>\n1 represents the hundredth&#8217;s position<\/p>\n<p><strong>Think and Grow: Understand Hundredths<\/strong><\/p>\n<p>In decimal, the second place to the right of the decimal point is the hundredths place. You can write hundredths as fractions or decimals. A fraction with a denominator of 10 or 100 is called a decimal fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-26.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 26\" width=\"387\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-26.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-26-300x95.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-48.jpg\" alt=\"\" width=\"697\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-48.jpg 697w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-48-300x126.jpg 300w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-47.jpg\" alt=\"\" width=\"702\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-47.jpg 702w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-47-300x119.jpg 300w\" sizes=\"(max-width: 702px) 100vw, 702px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Write the fraction or mixed number as a decimal.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-29.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 29\" width=\"173\" height=\"109\" \/><br \/>\nAnswer: The representation of \\(\\frac{45}{100}\\) in the decimal form is: 0.45<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{45}{100}\\)<br \/>\nThe model given for \\(\\frac{45}{100}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-29.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 29\" width=\"173\" height=\"109\" \/><\/p>\n<p>So,<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-91.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-91.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-91-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{45}{100}\\),<br \/>\n5 represents the hundredth&#8217;s position<br \/>\n4 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the decimal form is: 0.45<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-30.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 30\" width=\"289\" height=\"108\" \/><br \/>\nAnswer: The representation of 1\\(\\frac{90}{100}\\) in the decimal form is: 1.90<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 1\\(\\frac{90}{100}\\)<br \/>\nThe model given for 1\\(\\frac{90}{100}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-30.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 30\" width=\"289\" height=\"108\" \/><\/p>\n<p>So,<br \/>\nThe representation of 1\\(\\frac{90}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-92.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-92.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-92-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 1\\(\\frac{90}{100}\\),<br \/>\n1 represents the one&#8217;s position<br \/>\n0 represents the hundredth&#8217;s position<br \/>\n9 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{90}{100}\\) in the decimal form is: 1.90<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Shade the model to represent the fraction or mixed number. Then write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-31.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 31\" width=\"173\" height=\"108\" \/><br \/>\nAnswer: The representation of \\(\\frac{98}{100}\\) in the decimal form is: 0.98<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{98}{100}\\)<br \/>\nThe model given for \\(\\frac{98}{100}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-31.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 31\" width=\"173\" height=\"108\" \/><\/p>\n<p>So,<br \/>\nThe representation of \\(\\frac{98}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-93.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-93.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-93-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{98}{100}\\),<br \/>\n8 represents the hundredth&#8217;s position<br \/>\n9 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{98}{100}\\) in the decimal form is: 0.98<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-32.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 32\" width=\"283\" height=\"119\" \/><br \/>\nAnswer:<\/p>\n<p>The representation of 1\\(\\frac{34}{100}\\) in the decimal form is: 1.34<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{34}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{34}{100}\\) is: \\(\\frac{134}{100}\\)<br \/>\nThe model given for 1\\(\\frac{34}{100}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-32.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 32\" width=\"283\" height=\"119\" \/><\/p>\n<p>So,<br \/>\nThe representation of 1\\(\\frac{34}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-94.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-94.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-94-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 1\\(\\frac{34}{100}\\),<br \/>\n1 represents the one&#8217;s position<br \/>\n4 represents the hundredth&#8217;s position<br \/>\n3 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{34}{100}\\) in the decimal form is: 1.34<\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{42}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{42}{100}\\) in the form of decimal number is: 0.42<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{42}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{42}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-95.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-95.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-95-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{42}{100}\\),<br \/>\n2 represents the hundredth position<br \/>\n4 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{42}{100}\\) in the decimal form is: 0.42<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{7}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{7}{100}\\) in the form of decimal number is: 0.07<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{7}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{7}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-97.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-97.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-97-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{7}{100}\\),<br \/>\n7 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{7}{100}\\) in the decimal form is: 0.07<\/p>\n<p>Question 7.<br \/>\n4\\(\\frac{56}{100}\\)<br \/>\nAnswer: The representation of 4\\(\\frac{56}{100}\\) in the form of a decimal number is: 4.56<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 4\\(\\frac{56}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 4\\(\\frac{56}{100}\\) is: \\(\\frac{456}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 4\\(\\frac{56}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-98.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-98.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-98-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 4\\(\\frac{56}{100}\\),<br \/>\n4 represents the one&#8217;s position<br \/>\n6 represents the hundredth position<br \/>\n5 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 4\\(\\frac{56}{100}\\) in the decimal form is: 4.56<\/p>\n<p>Question 8.<br \/>\n23\\(\\frac{9}{100}\\)<br \/>\nAnswer: The representation of 23\\(\\frac{9}{100}\\) in the form of a decimal number is: 23.09<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 23\\(\\frac{9}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 23\\(\\frac{9}{100}\\) is: \\(\\frac{2,309}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 23\\(\\frac{9}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-99.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-99.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-99-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 23\\(\\frac{9}{100}\\),<br \/>\n2 represents the ten&#8217;s position<br \/>\n3 represents the one&#8217;s position<br \/>\n9 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 23\\(\\frac{9}{100}\\) in the decimal form is: 23.09<\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 9.<br \/>\nsixty-one hundredths<br \/>\nAnswer:<br \/>\nThe representation of sixty-one hundredths in the fraction form is: \\(\\frac{61}{100}\\)<br \/>\nThe representation of sixty-one hundredths in the decimal form is: 0.61<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Sixty-one hundredths<br \/>\nSo,<br \/>\nThe representation of sixty-one hundredths in the fraction form is: \\(\\frac{61}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{61}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-100.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-100.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-100-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{61}{100}\\),<br \/>\n1 represents the hundredth&#8217;s position<br \/>\n6 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{61}{100}\\) in the decimal form is: 0.61<\/p>\n<p>Question 10.<br \/>\ntwelve and eighty-three hundredths<br \/>\nAnswer:<br \/>\nThe representation of twelve and eighty-three hundredths in the fraction form is: 12\\(\\frac{83}{100}\\)<br \/>\nThe representation of twelve and eighty-three hundredths in the decimal form is: 12.83<\/p>\n<p>Explanation:<br \/>\nThe given word form is: twelve and eighty-three hundredths<br \/>\nSo,<br \/>\nThe representation of twelve and eighty-three hundredths in the fraction form is: 12\\(\\frac{83}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 12\\(\\frac{83}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-101.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-101.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-101-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 12\\(\\frac{83}{100}\\),<br \/>\n1 represents the ten&#8217;s position<br \/>\n2 represents the one&#8217;s position<br \/>\n3 represents the hundredth&#8217;s position<br \/>\n8 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of 12\\(\\frac{83}{100}\\) in the decimal form is: 12.83<\/p>\n<p>Question 11.<br \/>\nA shelter finds homes for 100 dogs. Five of the dogs are Doberman pinschers. What portion of the dogs are Doberman pinschers? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-33.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 33\" width=\"143\" height=\"168\" \/><br \/>\nAnswer: The portion of the dogs that are Doberman pinschers in the fraction form is: 0.05<\/p>\n<p>Explanation:<br \/>\nIt is given that a shelter finds homes for 100 dogs and out of these 100 dogs, 5 dogs are Doberman pinschers<br \/>\nSo,<br \/>\nThe portion of the dogs that are Doberman pinschers = \\(\\frac{The number of dogs that are Doberman pinschers}{The total number of dogs}\\)<br \/>\n= \\(\\frac{5}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-102.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-102.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-102-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{5}{100}\\),<br \/>\n0 represents the tenth&#8217;s position<br \/>\n5 represents the hundredth&#8217;s position<br \/>\nHence,<br \/>\nThe portion of the dogs that are Doberman pinschers in the decimal form is: 0.05<\/p>\n<p>Question 12.<br \/>\nAn athlete runs 3\\(\\frac{50}{100}\\) lengths of a football field. Write this number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-33.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 33.1\" width=\"158\" height=\"162\" \/><br \/>\nAnswer: The representation of 3\\(\\frac{50}{100}\\) in the decimal form is: 3.5<\/p>\n<p>Explanation:<br \/>\nIt is given that an athlete runs 3\\(\\frac{50}{100}\\) lengths of a football field.<br \/>\nSo,<br \/>\nThe representation of 3\\(\\frac{50}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-103.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-103.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-103-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nNow,<br \/>\nIn 3\\(\\frac{50}{100}\\),<br \/>\n3 represents the one&#8217;s place<br \/>\n0 represents the hundredth&#8217;s place<br \/>\n5 represents the tenth&#8217;s position<br \/>\nNow,<br \/>\nThe given mixed fraction is: 3\\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 3\\(\\frac{50}{100}\\) is: \\(\\frac{350}{100}\\)<br \/>\nSo,<br \/>\nThe representation of 3\\(\\frac{50}{100}\\) in the decimal form is: 3.50<\/p>\n<p>Question 13.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich number of cards show three-hundredths?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-34.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 34\" width=\"243\" height=\"147\" \/><br \/>\nAnswer: From the given cards, \\(\\frac{3}{100}\\) and 0.03 shows the form of three-hundredths<\/p>\n<p>Explanation:<br \/>\nThe given number of cards is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-34.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 34\" width=\"243\" height=\"147\" \/><\/p>\n<p>The given fractions and decimal numbers in the given table are:<br \/>\nA) \\(\\frac{3}{100}\\) B) \\(\\frac{3}{10}\\) C) 300 D) 0.3 E) 0.03<br \/>\nWe can observe that<br \/>\nFrom three-hundredths, we can say that,<br \/>\nThe total number of cards are: 100<br \/>\nThe portion of cards from 100 cards is: 3<br \/>\nSo,<br \/>\nThe representation of three-hundredths in the fraction form is: \\(\\frac{3}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{3}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-104.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-104.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-104-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn \\(\\frac{3}{100}\\),<br \/>\n0 represents the tenth&#8217;s position<br \/>\n3 represents the hundredth&#8217;s position<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{100}\\) in the decimal form is: 0.03<br \/>\nhence, from the given table,<br \/>\nWe can conclude that the number of cards that represent the three-hundredths is: \\(\\frac{3}{100}\\) and 0.03<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou use 51 toothpicks to make a bridge. What portion of the container of toothpicks do you use to make the bridge? Write your answer as a decimal.<br \/>\nDraw a model to represent the container of toothpicks. Shade the same number of parts as the number of toothpicks you use to make the bridge. Write the decimal shown by the model<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-35.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 35\" width=\"377\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-35.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-35-300x235.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer:<br \/>\nIt is given that you are using 51 toothpicks to make a bridge.<br \/>\nSo,<br \/>\nThe total number of chopsticks are: 100<br \/>\nThe number of chopsticks that are using to make a bridge is: 51<br \/>\nSo,<br \/>\nThe representation of the portion of the chopsticks that are used to make chopsticks = \\(\\frac{51}{100}\\)<br \/>\nSo, from \\(\\frac{3}{100}\\),<br \/>\nWe can say that you use 51 of the container of toothpicks to make the bridge.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA book fair has 100 books. 60 of the books are chapter books. What portion of the books in the book fair are chapter books? Write your answer as a decimal.<br \/>\nAnswer: The portion of the chapter books out of the total number of books in the decimal form is: 0.60<\/p>\n<p>Explanation:<br \/>\nIt is given that a book fair has 100 books and out of these 100 books, 60 books are chapter books.<br \/>\nSo,<br \/>\nThe portion of the chapter books out of the total number of books in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-105.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-105.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-105-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nFrom \\(\\frac{60}{100}\\), we can say that<br \/>\n0 represents the hundredth&#8217;s position-<br \/>\n6 represents the tenth&#8217;s position<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the decimal form is: 0.60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the portion of the books that are the chapter books in the decimal form is: 0.60<\/p>\n<p>Question 15.<br \/>\nThe model represents the members of a marching band. What portion of the marching band plays a brass instrument? percussion instrument? Write your answers as decimals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-36.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 36\" width=\"162\" height=\"172\" \/><br \/>\nAnswer: The portion of the marching band that plays a brass instrument is: 0.47<\/p>\n<p>Explanation:<br \/>\nIt is given that the below model represents the members of a marching band.<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-36.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 36\" width=\"162\" height=\"172\" \/><br \/>\nIn the given model, there are 3 categories of marching brand<br \/>\nIn the given model, each box represents 1 unit.<br \/>\nSo,<br \/>\nFrom the model,<br \/>\nThe number of the marching band that plays a brass instrument is: 47<br \/>\nThe number of the marching band that plays a woodwind instrument is: 36<br \/>\nThe number of the marching band that plays a percussion instrument is: 17<br \/>\nThe total number of instruments are: 100<br \/>\nSo,<br \/>\nThe portion of the marching band that plays a band instrument from the total number of instruments in the fraction form is: \\(\\frac{47}{100}\\)<br \/>\nHence, from the above,<br \/>\nThe portion of the marching band that plays a band instrument from the total number of instruments i the decimal form is: 0.47<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat portion of Earth\u2019s surface is covered by water? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-37.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 37\" width=\"211\" height=\"183\" \/><br \/>\nAnswer: The portion of Earth&#8217;s surface that is covered by water in the fraction form is: 0.71<\/p>\n<p>Explanation:<br \/>\nIt is given that about \\(\\frac{71}{100}\\) of earth&#8217;s surface is covered by water.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{71}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-106.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-106.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-106-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nFrom \\(\\frac{71}{100}\\), we can say that<br \/>\n1 represents the hundredth&#8217;s position<br \/>\n7 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe portion of water on the Earth&#8217;s surface represented in decimal form is: 0.71<\/p>\n<h3><a id=\"Understand_Hundredths_Homework_&amp;_Practice_10.2\"><\/a>Understand Hundredths Homework &amp; Practice 10.2<\/h3>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\nWrite \\(\\frac{83}{100}\\) as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-38.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 38\" width=\"117\" height=\"118\" \/><br \/>\nAnswer: The representation of \\(\\frac{83}{100}\\) in the decimal form is: 0.98<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{83}{100}\\)<br \/>\nThe model given for \\(\\frac{83}{100}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-38.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 38\" width=\"117\" height=\"118\" \/><\/p>\n<p>So,<br \/>\nThe representation of \\(\\frac{83}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-67.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-67.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-67-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{83}{100}\\),<br \/>\n3 represents the hundredth&#8217;s position<br \/>\n8 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{83}{100}\\) in the decimal form is: 0.83<\/p>\n<p>Question 2.<br \/>\nShade the model to represent 1\\(\\frac{65}{100}\\). Then write the mixed number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-39.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 39\" width=\"218\" height=\"108\" \/><br \/>\nAnswer: The representation of \\(\\frac{65}{100}\\) in the form of a decimal number is: 1.65<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 1\\(\\frac{65}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 1\\(\\frac{65}{100}\\) is: \\(\\frac{165}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 1\\(\\frac{65}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-68.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-68.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-68-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 1\\(\\frac{65}{100}\\),<br \/>\n1 represents the one&#8217;s position<br \/>\n5 represents the hundredth position<br \/>\n6 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{65}{100}\\) in the decimal form is: 1.65<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{12}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{12}{100}\\) in the decimal form is: 0.12<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{12}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{12}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-69.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-69.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-69-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{12}{100}\\),<br \/>\n2 represents the hundredth&#8217;s position<br \/>\n1 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{12}{100}\\) in the decimal form is: 0.12<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{24}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{24}{100}\\) in the decimal form is: 0.24<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{24}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{24}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-70.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-70.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-70-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{24}{100}\\),<br \/>\n4 represents the hundredth&#8217;s position<br \/>\n2 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{24}{100}\\) in the decimal form is: 0.24<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{2}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{2}{100}\\) in the decimal form is: 0.02<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{2}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-71.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-71.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-71-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{2}{100}\\),<br \/>\n2 represents the hundredth&#8217;s position<br \/>\n0 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{100}\\) in the decimal form is: 0.02<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{8}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{8}{100}\\) in the decimal form is: 0.08<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{8}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-72.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-72.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-72-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{8}{100}\\),<br \/>\n8 represents the hundredth&#8217;s position<br \/>\n0 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{8}{100}\\) in the decimal form is: 0.08<\/p>\n<p>Question 7.<br \/>\n2\\(\\frac{59}{100}\\)<br \/>\nAnswer: The representation of 2\\(\\frac{59}{100}\\) in the form of a decimal number is: 2.59<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 2\\(\\frac{59}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 2\\(\\frac{59}{100}\\) is: \\(\\frac{259}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 2\\(\\frac{59}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-73.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-73.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-73-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 2\\(\\frac{59}{100}\\),<br \/>\n2 represents the one&#8217;s position<br \/>\n9 represents the hundredth position<br \/>\n5 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 2\\(\\frac{59}{100}\\) in the decimal form is: 2.59<\/p>\n<p>Question 8.<br \/>\n48\\(\\frac{31}{100}\\)<br \/>\nAnswer: The representation of 48\\(\\frac{31}{100}\\) in the form of a decimal number is: 48.31<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 48\\(\\frac{31}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 48\\(\\frac{31}{100}\\) is: \\(\\frac{4,831}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 48\\(\\frac{31}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-74.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-74.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-74-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 48\\(\\frac{31}{100}\\),<br \/>\n4 represents ten&#8217;s position<br \/>\n8 represents the one&#8217;s position<br \/>\n1 represents the hundredth position<br \/>\n3 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 48\\(\\frac{31}{100}\\) in the decimal form is: 48.31<\/p>\n<p>Question 9.<br \/>\n6\\(\\frac{7}{100}\\)<br \/>\nAnswer: The representation of 6\\(\\frac{7}{100}\\) in the form of a decimal number is: 6.07<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 6\\(\\frac{7}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 6\\(\\frac{7}{100}\\) is: \\(\\frac{607}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 6\\(\\frac{7}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-75.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-75.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-75-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 6\\(\\frac{7}{100}\\),<br \/>\n6 represents the one&#8217;s position<br \/>\n7 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 6\\(\\frac{7}{100}\\) in the decimal form is: 6.07<\/p>\n<p>Question 10.<br \/>\n31\\(\\frac{6}{100}\\)<br \/>\nAnswer: The representation of 31\\(\\frac{6}{100}\\) in the form of a decimal number is: 31.06<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 31\\(\\frac{6}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 31\\(\\frac{6}{100}\\) is: \\(\\frac{3,106}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 31\\(\\frac{6}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-76.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-76.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-76-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 31\\(\\frac{6}{100}\\),<br \/>\n3 represents the ten&#8217;s position<br \/>\n1 represents the one&#8217;s position<br \/>\n6 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 31\\(\\frac{6}{100}\\) in the decimal form is: 31.06<\/p>\n<p><strong>Write the number as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 11.<br \/>\nseventy-four hundredths<br \/>\nAnswer:<br \/>\nThe representation of seventy-four hundredths in the fraction form is: \\(\\frac{74}{100}\\)<br \/>\nThe representation of seventy-four hundredths in the decimal form is: 0.74<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Seventy-four hundredths<br \/>\nSo,<br \/>\nThe representation of seventy-four hundredths in the fraction form is: \\(\\frac{74}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{74}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-77.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-77.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-77-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn \\(\\frac{74}{100}\\),<br \/>\n4 represents the hundredth&#8217;s position<br \/>\n7 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{74}{100}\\) in the decimal form is: 0.74<\/p>\n<p>Question 12.<br \/>\nsixteen and thirty-one hundredths<br \/>\nAnswer:<br \/>\nThe representation of sixteen and thirty-one hundredths in the fraction form is: 16\\(\\frac{31}{100}\\)<br \/>\nThe representation of sixteen and thirty-one hundredths in the decimal form is: 16.31<\/p>\n<p>Explanation:<br \/>\nThe given word form is: sixteen and thirty-one hundredths<br \/>\nSo,<br \/>\nThe representation of sixteen and thirty-one hundredths in the fraction form is: 16\\(\\frac{31}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 16\\(\\frac{31}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-78.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-78.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-78-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 16\\(\\frac{31}{100}\\),<br \/>\n1 represents the ten&#8217;s position<br \/>\n6 represents the one&#8217;s position<br \/>\n1 represents the hundredth&#8217;s position<br \/>\n3 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of 16\\(\\frac{31}{100}\\) in the decimal form is: 16.31<\/p>\n<p><strong>Write the value of the underlined digit.<\/strong><\/p>\n<p>Question 13.<br \/>\n5.<u>8<\/u>4<br \/>\nAnswer: The value of 8 in 5.84 is: 0.8<\/p>\n<p>Explanation:<br \/>\nThe given number is: 5.84<br \/>\nThe representation of 5.84 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-79.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-79.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-79-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nIn 5.83, from the place-value chart,<br \/>\nWe can say that the value of 8 in 5.83 is: 0.8<\/p>\n<p>Question 14.<br \/>\n<u>2<\/u>1.03<br \/>\nAnswer: The value of 2 in 21.03 is: 20<\/p>\n<p>Explanation:<br \/>\nThe given number is: 21.03<br \/>\nThe representation of 21.03 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-80.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-80.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-80-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can say that the value of 2 in 21.03 is: 20<\/p>\n<p>Question 15.<br \/>\n67.3<u>2<br \/>\n<\/u>Answer: The value of 2 in 67.32 is: 0.02<u><br \/>\n<\/u><\/p>\n<p>Explanation:<br \/>\nThe given number is: 67.32<br \/>\nThe representation of 67.32 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-81.jpg\" alt=\"\" width=\"443\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-81.jpg 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-81-300x83.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can say that the value of 2 in 67.32 is: 0.02<\/p>\n<p>Question 16.<br \/>\n<u>5<\/u>06.19<br \/>\nAnswer: The value of 5 in 506.19 is: 500<\/p>\n<p>Explanation:<br \/>\nThe given number is: 506.19<br \/>\nThe representation of 506.19 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-82.jpg\" alt=\"\" width=\"759\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-82.jpg 759w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-82-300x49.jpg 300w\" sizes=\"(max-width: 759px) 100vw, 759px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can say that the value of 5 in 506.19 is: 500<\/p>\n<p>Question 17.<br \/>\nA clown has 100 balloons. She uses 56 of the balloons to make animals. What portion of the balloons does she use? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-39.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 39.1\" width=\"102\" height=\"103\" \/><br \/>\nAnswer: The portion of the balloons she used to make animals in the decimal form is: 0.56<\/p>\n<p>Explanation:<br \/>\nIt is given that a clown has 100 balloons and she uses 56 of the balloons to make animals.<br \/>\nSo,<br \/>\nThe total number of balloons are: 100<br \/>\nThe number of ballons that are used to make animals is: 56<br \/>\nSo,<br \/>\nThe portion of the balloons that are used to make animals is:\\(\\frac{56}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{56}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-83.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-83.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-83-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nWe can conclude that the portion of the balloons that are used to make animals in the decimal form is: 0.56<\/p>\n<p>Question 18.<br \/>\nYou fill a beaker 4\\(\\frac{35}{100}\\) times for an experiment. Write this number as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-40.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 40\" width=\"93\" height=\"104\" \/><br \/>\nAnswer: The representation of 4\\(\\frac{35}{100}\\) in the form of a decimal number is: 4.35<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 4\\(\\frac{35}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 4\\(\\frac{35}{100}\\) is: \\(\\frac{435}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 4\\(\\frac{35}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-84.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-84.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-84-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 4\\(\\frac{35}{100}\\),<br \/>\n4 represents the one&#8217;s position<br \/>\n5 represents the hundredth position<br \/>\n3 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 4\\(\\frac{35}{100}\\) in the decimal form is: 4.35<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nDescartes writes 2\\(\\frac{40}{100}\\) as 2.04. Is he correct? Explain.<br \/>\nAnswer:<br \/>\nThe representation of 2\\(\\frac{40}{100}\\) in the form of a decimal number is: 2.40<br \/>\nSo, Descartes is wrong.<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 2\\(\\frac{40}{100}\\)<br \/>\nSo,<br \/>\nThe improper fraction of 2\\(\\frac{40}{100}\\) is: \\(\\frac{240}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 2\\(\\frac{40}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-85.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-85.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-85-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nIn 2\\(\\frac{40}{100}\\),<br \/>\n2 represents the one&#8217;s position<br \/>\n0 represents the hundredth position<br \/>\n4 represents the tenth position<br \/>\nSo,<br \/>\nThe representation of 2\\(\\frac{40}{100}\\) in the decimal form is: 2.40<br \/>\nBut, according to Descartes,<br \/>\nThe representation of 2\\(\\frac{40}{100}\\) in the decimal form is: 2.04<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes is not correct.<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nShade each model to show 0.6 and 0.60. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-41.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 41\" width=\"228\" height=\"112\" \/><br \/>\nAnswer: From the values of 0.6 and 0.60, we can notice that the value of 6 in both numbers are the same.<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.6 and 0.60<br \/>\nThe given models of 0.6 and 0.60 are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-41.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 41\" width=\"228\" height=\"112\" \/><br \/>\nNow,<br \/>\nThe shaded models of 0.6 and 0.60 will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-86.jpg\" alt=\"\" width=\"218\" height=\"112\" \/><br \/>\nNow,<br \/>\nThe representation of 0.6 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-87.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-87.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-87-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nThe representation of 0.60 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-88.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-88.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-88-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nFrom the above 2 place-value charts,<br \/>\nWe can conclude that 0.6 and 0.60 are the same as the value of 6 in 0.6 and 0.60 is the same.<\/p>\n<p>Question 21.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou work on the puzzle shown. You connect 78 of the puzzle pieces. What portion of the puzzle have you completed? Write your answer as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-42.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 42\" width=\"256\" height=\"182\" \/><br \/>\nAnswer: The portion of the puzzles you have completed in the decimal form is: 0.78<\/p>\n<p>Explanation:<br \/>\nIt is given that you are working on a 100-box puzzle and you connected 78 of the puzzle pieces.<br \/>\nSo,<br \/>\nThe total number of puzzles are: 100<br \/>\nThe number of puzzles that are connected is: 78<br \/>\nSo,<br \/>\nThe portion of the puzzles that are connected in the fraction form is: \\(\\frac{78}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{78}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-89.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-89.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-89-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the portion of the puzzles that are connected in the decimal form is: 0.78<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-43.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 43\" width=\"78\" height=\"40\" \/><br \/>\nAnswer: 1,308 \u00f7 5 = 261 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n1,308 \u00f7 5 = ( 1,000 + 300 + 5 ) \u00f7 5<br \/>\n= ( 1,000 \u00f7 5 ) + ( 300 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 200 + 60 + 1<br \/>\n= 261 R 3<br \/>\nHence, 1,308 \u00f7 5 = 261 R 3<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-44.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 44\" width=\"55\" height=\"38\" \/><br \/>\nAnswer: 67 \u00f7 4 = 16 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n67 \u00f7 4 = ( 56 + 8 ) \u00f7 4<br \/>\n= ( 56 \u00f7 4 ) + ( 8 \u00f7 4 )<br \/>\n= 14 + 2<br \/>\n= 16 R 3<br \/>\nHenec, 67 \u00f7 4 = 1 R 3<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-45.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 45\" width=\"61\" height=\"30\" \/><br \/>\nAnswer: 725 \u00f7 2 = 362 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n725 \u00f7 2 = ( 720 + 4 ) \u00f7 2<br \/>\n= ( 720 \u00f7 2 ) + ( 4 \u00f7 2 )<br \/>\n= 360 + 2<br \/>\n= 362 R 1<br \/>\nHence,<br \/>\n75 \u00f7 2 = 362 R 1<\/p>\n<h3><a id=\"Lesson_10.3_Fractions_and_Decimals\"><\/a>Lesson 10.3 Fractions and Decimals<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Plot each fraction or decimal on a number line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-107.jpg\" alt=\"\" width=\"555\" height=\"435\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-107.jpg 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-107-300x235.jpg 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWhat do you notice about the locations of the points? What can you conclude about the numbers?<\/p>\n<p>Answer: From the above plots, we can see that the number of lines between any two numbers is the same whether the given number is in fraction form or in the decimal form<br \/>\nSo, from the above plots, we can conclude that the location of the numbers and the gap between the two numbers is the same.<\/p>\n<p><strong>Think and Grow: Fractions and Decimals<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nWrite \\(\\frac{6}{10}\\) as hundredths in fraction form and decimal form.<br \/>\n<strong>Fraction form:<\/strong> Shade the model to help write \\(\\frac{6}{10}\\) as an equivalent fraction with a denominator of 100.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-108.jpg\" alt=\"\" width=\"255\" height=\"218\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-109.jpg\" alt=\"\" width=\"381\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-109.jpg 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-109-300x275.jpg 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Two or more decimals that have the same value are equivalent decimals.<br \/>\n<strong>Example<\/strong><br \/>\nWrite 0.40 as tenths in decimal form and fraction form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-110.jpg\" alt=\"\" width=\"368\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-110.jpg 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-110-300x152.jpg 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-111.jpg\" alt=\"\" width=\"383\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-111.jpg 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-111-300x221.jpg 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nWrite \\(\\frac{9}{10}\\) as hundredths in fraction form and decimal form.<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{9}{10}\\) as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal form is: 0.90<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{9}{10}\\)<br \/>\nSo, to write \\(\\frac{9}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{9}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 9 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-112.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-112.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-112-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{9}{10}\\) as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal form is: 0.90<\/p>\n<p>Question 2.<br \/>\nWrite 0.20 as tenths in decimal form and fraction form.<br \/>\nAnswer:<br \/>\nThe representation of 0.20 as tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{20}{100}\\)<br \/>\nSo, to write \\(\\frac{20}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{20}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 20 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}=\\frac{20 \\div 10}{100 \\div 10}=\\frac{2}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-113.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-113.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-113-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{20}{100}\\) as tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Write the number as tenths in fraction form and decimal form.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{80}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{80}{100}\\) as tenths in the fraction form is: \\(\\frac{8}{10}\\)<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{80}{100}\\)<br \/>\nSo, to write \\(\\frac{80}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{80}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 80 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}=\\frac{80 \\div 10}{100 \\div 10}=\\frac{8}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{80}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-114.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-114.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-114-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{80}{100}\\) as tenths in the fraction form is: \\(\\frac{8}{10}\\)<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{50}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{50}{100}\\) as tenths in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{50}{100}\\)<br \/>\nSo, to write \\(\\frac{50}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{50}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 50 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}=\\frac{50 \\div 10}{100 \\div 10}=\\frac{5}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{50}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-115.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-115.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-115-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{50}{100}\\) as tenths in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Question 5.<br \/>\n0.30<br \/>\nAnswer:<br \/>\nThe representation of 0.30 as tenths in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.30<br \/>\nSo,<br \/>\nThe representation of 0.30 in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo, to write \\(\\frac{30}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{30}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 30 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{30}{100}=\\frac{30 \\div 10}{100 \\div 10}=\\frac{3}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-116.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-116.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-116-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{30}{100}\\) as tenths in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p><strong>Write the number as hundredths in fraction form and decimal form.<\/strong><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{2}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nThe representation of \\(\\frac{20}{100}\\) in the decimal form is: 0.20<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{2}{10}\\)<br \/>\nSo, to write \\(\\frac{2}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{2}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 2 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{20}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-117.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-117.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-117-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nThe representation of \\(\\frac{20}{100}\\) in the decimal form is: 0.20<\/p>\n<p>Question 7.<br \/>\n0.7<br \/>\nAnswer:<br \/>\nThe representation of 0.7 as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.7<br \/>\nSo,<br \/>\nThe representation of 0.7 in the fraction form is: \\(\\frac{7}{10}\\)<br \/>\nSo, to write \\(\\frac{7}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 7 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-118.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-118.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-118-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<\/p>\n<p>Question 8.<br \/>\n2\\(\\frac{1}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of 2\\(\\frac{1}{10}\\) as hundredths in the fraction form is: 2\\(\\frac{10}{100}\\)<br \/>\nThe representation of 2\\(\\frac{10}{100}\\) in the decimal form is: 2.10<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 2\\(\\frac{1}{10}\\)<br \/>\nSo,<br \/>\nTo write 2\\(\\frac{1}{10}\\) as hundredths, multiply the fraction and numerator of 2\\(\\frac{1}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 1 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 2\\(\\frac{10}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-119.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-119.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-119-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of 2\\(\\frac{1}{10}\\) as hundredths in the fraction form is: 2\\(\\frac{10}{100}\\)<br \/>\nThe representation of 2\\(\\frac{10}{100}\\) in the decimal form is: 2.10<\/p>\n<p>Write the number represented by the point as hundredths in fraction form and decimal form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-120.jpg\" alt=\"\" width=\"571\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-120.jpg 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-120-300x34.jpg 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><br \/>\nAnswer:<br \/>\nFrom the above number line,<br \/>\n&#8216;A&#8217; is: 0.4<br \/>\n&#8216;B&#8217; is: 0.9<br \/>\n&#8216;C&#8217; is: 1.5<\/p>\n<p>Question 9.<br \/>\nA<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;A&#8217; is: 0.4<br \/>\nThe representation of 0.4 as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the decimal form is: 0.40<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.4<br \/>\nSo,<br \/>\nThe representation of 0.4 in the fraction form is: \\(\\frac{4}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{4}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{4}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 4 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-121.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-121.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-121-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the decimal form is: 0.40<\/p>\n<p>Question 10.<br \/>\nB<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;B&#8217; is: 0.9<br \/>\nThe representation of 0.9 as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal form is: 0.90<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.9<br \/>\nSo,<br \/>\nThe representation of 0.9 in the fraction form is: \\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{9}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{9}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 9 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-122.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-122.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-122-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{9}{10}\\) as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal form is: 0.90<\/p>\n<p>Question 11.<br \/>\nC<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;C&#8217; is: 1.5<br \/>\nThe representation of 1.5 as hundredths in the fraction form is: \\(\\frac{150}{100}\\)<br \/>\nThe representation of \\(\\frac{150}{100}\\) in the decimal form is: 1.50<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 1.5<br \/>\nSo,<br \/>\nThe representation of 1.5 in the fraction form is: \\(\\frac{15}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{15}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{15}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 15 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{150}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-123.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-123.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-123-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{15}{10}\\) as hundredths in the fraction form is: \\(\\frac{150}{100}\\)<br \/>\nThe representation of \\(\\frac{150}{100}\\) in the decimal form is: 1.50<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nComplete the table. Think: Can all of the numbers in the table be written as hundredths?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-124.jpg\" alt=\"\" width=\"695\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-124.jpg 695w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-124-300x136.jpg 300w\" sizes=\"(max-width: 695px) 100vw, 695px\" \/><br \/>\nAnswer: Yes, all the numbers in the table can be written as hundredths.<\/p>\n<p>Explanation:<br \/>\nA) The given mixed fraction is: 23\\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe representation of 23\\(\\frac{7}{10}\\) in the fraction form is: \\(\\frac{237}{10}\\)<br \/>\nSo,<br \/>\nTo write 23\\(\\frac{7}{10}\\) as hundredths, multiply the fraction and numerator of 23\\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 7 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 23\\(\\frac{70}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-125.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-125.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-125-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of 23\\(\\frac{7}{10}\\) as hundredths in the fraction form is: 23\\(\\frac{70}{100}\\)<br \/>\nThe representation of 23\\(\\frac{70}{100}\\) in the decimal form is: 23.70<\/p>\n<p>B) The given mixed fraction is: 18\\(\\frac{2}{10}\\)<br \/>\nSo,<br \/>\nThe representation of 18\\(\\frac{2}{10}\\) in the fraction form is: \\(\\frac{182}{10}\\)<br \/>\nSo,<br \/>\nTo write 18\\(\\frac{2}{10}\\) as hundredths, multiply the fraction and numerator of 18\\(\\frac{2}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 2 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 18\\(\\frac{20}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-126.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-126.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-126-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of 18\\(\\frac{2}{10}\\) as hundredths in the fraction form is: 18\\(\\frac{20}{100}\\)<br \/>\nThe representation of 18\\(\\frac{20}{100}\\) in the decimal form is: 18.20<br \/>\nHence, in the same way, C) and D) Expressions can also be written as hundredths and in the decimal form<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou use 100 tiles to make a mosaic. 80 of them are square tiles. Your friend uses 10 tiles to make a mosaic. Six of them are square tiles. Do the mosaics have the same fraction of square tiles?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-53.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 53\" width=\"165\" height=\"102\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-127.jpg\" alt=\"\" width=\"583\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-127.jpg 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-127-300x58.jpg 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\nDetermine whether the fractions are equivalent.<br \/>\nWrite your friend\u2019s fraction as hundredths in fraction form. Then compare.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-128.jpg\" alt=\"\" width=\"221\" height=\"124\" \/><br \/>\nHence,<br \/>\nThe mosaics don&#8217;t have the same fraction of square tiles.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nYou use 10 beads to make a bracelet. Seven of them are purple. Your friend uses 100 beads to make a bracelet. 70 of them are purple. Do the bracelets have the same fraction of purple beads?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-56.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 56\" width=\"183\" height=\"188\" \/><br \/>\nAnswer: Yes, the bracelets have the same fraction of purple beads.<\/p>\n<p>Explanation:<br \/>\nIt is given that you use 10 beads to make a bracelet and out of 10 beads, seven of them are purple.<br \/>\nSo,<br \/>\nThe portion of the bracelet that is purple is: \\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe given fraction is: \\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{7}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 7 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-129.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-129.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-129-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nIt is also given that your friend uses 100 beads to make a bracelet and out of 100, 70 beads are purple.<br \/>\nSo,<br \/>\nThe portion of purple beads from the total number of beads is: \\(\\frac{70}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the bracelet has the same fraction of purple beads<br \/>\nQuestion 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe model represents the types of trees on a tree farm. What portion of the tree farm is blue spruce? Fraser fir? white pine? Write your answers as decimals in tenths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-57.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 57\" width=\"130\" height=\"168\" \/><br \/>\nAnswer:<br \/>\nThe portion of the tree farm that is blue spruce is: 0.4<br \/>\nThe portion of the tree farm that is Fraser fir is: 0.4<br \/>\nThe portion of the tree farm that is White pine is: 0.2<\/p>\n<p>Explanation:<br \/>\nIt is given that the below model represents the types of trees on a tree farm.<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-57.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 57\" width=\"130\" height=\"168\" \/><br \/>\nIn the given model, there are 3 categories of trees<br \/>\nIn the given model, each box represents 1 unit.<br \/>\nSo,<br \/>\nFrom the model,<br \/>\nThe number of trees of blue spruce is: 40<br \/>\nThe number of trees of Frazer fir is: 40<br \/>\nThe number of trees of White pine is: 20<br \/>\nThe total number of trees in a tree farm is: 100<br \/>\nSo,<br \/>\nThe portion of the tree farm that is blue spruce from the total number of instruments in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe portion of the tree farm that is Frazer fir from the total number of instruments in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe portion of the tree farm that is White pine from the total number of instruments in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nNow, for the Blue spruce,<br \/>\nSo,<br \/>\nTo write \\(\\frac{40}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{40}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 40 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}=\\frac{40 \\div 10}{100 \\div 10}=\\frac{4}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as tenths in the decimal form is: 0.4<br \/>\nNow, for the Frazer fir,<br \/>\nSo,<br \/>\nTo write \\(\\frac{40}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{40}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 40 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}=\\frac{40 \\div 10}{100 \\div 10}=\\frac{4}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-130-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as tenths in the decimal form is: 0.4<br \/>\nNow, for the White pine,<br \/>\nSo,<br \/>\nTo write \\(\\frac{20}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{20}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 20 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}=\\frac{20 \\div 10}{100 \\div 10}=\\frac{4}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-131.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-131.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-131-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as tenths in the decimal form is: 0.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe portion of the tree farm that is blue spruce is: 0.4<br \/>\nThe portion of the tree farm that is Fraser fir is: 0.4<br \/>\nThe portion of the tree farm that is White pine is: 0.2<\/p>\n<h3><a id=\"Fractions_and_Decimals_Homework_&amp;_Practice_10.3\"><\/a>Fractions and Decimals Homework &amp; Practice 10.3<\/h3>\n<h6><\/h6>\n<h6>Write the number as tenths in fraction form and decimal form.<\/h6>\n<p>Question 1.<br \/>\n\\(\\frac{40}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{40}{100}\\) as tenths in the fraction form is: \\(\\frac{4}{10}\\)<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the decimal form is: 0.4<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{40}{100}\\)<br \/>\nSo, to write \\(\\frac{40}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{40}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 40 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}=\\frac{40 \\div 10}{100 \\div 10}=\\frac{5}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-132.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-132.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-132-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{40}{100}\\) as tenths in the fraction form is: \\(\\frac{4}{10}\\)<br \/>\nThe representation of \\(\\frac{4}{10}\\) in the decimal form is: 0.4<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{70}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{70}{100}\\) as tenths in the fraction form is: \\(\\frac{7}{10}\\)<br \/>\nThe representation of \\(\\frac{7}{10}\\) in the decimal form is: 0.7<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{70}{100}\\)<br \/>\nSo, to write \\(\\frac{70}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{70}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 70 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{70}{100}=\\frac{70 \\div 10}{100 \\div 10}=\\frac{7}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-133.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-133.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-133-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{70}{100}\\) as tenths in the fraction form is: \\(\\frac{7}{10}\\)<br \/>\nThe representation of \\(\\frac{7}{10}\\) in the decimal form is: 0.7<\/p>\n<p>Question 3.<br \/>\n0.20<br \/>\nAnswer:<br \/>\nThe representation of 2.20 as tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.20<br \/>\nSo,<br \/>\nthe representation of 0.20 in the fraction orm is: \\(\\frac{20}{100}\\)<br \/>\nSo, to write \\(\\frac{20}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{20}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 20 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}=\\frac{20 \\div 10}{100 \\div 10}=\\frac{2}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-134.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-134.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-134-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{20}{100}\\) as tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p><strong>Write the number as hundredths in fraction form and decimal form<\/strong><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{8}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nThe representation of \\(\\frac{80}{100}\\) in the decimal form is: 0.80<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{8}{10}\\)<br \/>\nSo, to write \\(\\frac{8}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{8}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 8 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{80}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-135.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-135.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-135-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nThe representation of \\(\\frac{80}{100}\\) in the decimal form is: 0.80<\/p>\n<p>Question 5.<br \/>\n0.5<br \/>\nAnswer:<br \/>\nThe representation of 0.5 as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nThe representation of \\(\\frac{50}{100}\\) in the decimal form is: 0.50<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.5<br \/>\nSo,<br \/>\nThe representation of 0.5 in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nSo, to write \\(\\frac{5}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{5}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 5 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{50}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-136.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-136.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-136-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nThe representation of \\(\\frac{50}{100}\\) in the decimal form is: 0.50<\/p>\n<p>Question 6.<br \/>\n9\\(\\frac{6}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of 9\\(\\frac{6}{10}\\) as hundredths in the fraction form is: 9\\(\\frac{60}{100}\\)<br \/>\nThe representation of 9\\(\\frac{60}{100}\\) in the decimal form is: 9.60<\/p>\n<p>Explanation:<br \/>\nThe given mixed fraction is: 9\\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nTo write 9\\(\\frac{6}{10}\\) as hundredths, multiply the fraction and numerator of 9\\(\\frac{6}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 6 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 9\\(\\frac{60}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-137.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-137.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-137-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of 9\\(\\frac{6}{10}\\) as hundredths in the fraction form is: 9\\(\\frac{60}{100}\\)<br \/>\nThe representation of 9\\(\\frac{60}{100}\\) in the decimal form is: 9.60<\/p>\n<p><strong>Write the number represented by the point as hundredths in fraction form and decimal form.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-138.jpg\" alt=\"\" width=\"600\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-138.jpg 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-138-300x34.jpg 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><br \/>\nAnswer:<br \/>\nFrom the above number line,<br \/>\n&#8216;A&#8217; value is: 0.3<br \/>\n&#8216;B&#8217; value is: 0.6<br \/>\n&#8216;c&#8217; value is: 1.8<\/p>\n<p>Question 7.<br \/>\nA<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;A&#8217; is: 0.3<br \/>\nThe representation of 0.3 as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nThe representation of \\(\\frac{30}{100}\\) in the decimal form is: 0.30<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.3<br \/>\nSo,<br \/>\nThe representation of 0.3 in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{3}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{3}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 3 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{30}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-139.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-139.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-139-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nThe representation of \\(\\frac{30}{100}\\) in the decimal form is: 0.30<\/p>\n<p>Question 8.<br \/>\nB<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;A&#8217; is: 0.6<br \/>\nThe representation of 0.6 as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the decimal form is: 0.60<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.6<br \/>\nSo,<br \/>\nThe representation of 0.6 in the fraction form is: \\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{6}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{6}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 6 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-140.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-140.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-140-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the decimal form is: 0.60<\/p>\n<p>Question 9.<br \/>\nC<br \/>\nAnswer:<br \/>\nFrom the above number line, &#8216;A&#8217; is: 1.8<br \/>\nThe representation of 1.8 as hundredths in the fraction form is: 1\\(\\frac{80}{100}\\)<br \/>\nThe representation of 1\\(\\frac{80}{100}\\) in the decimal form is: 1.80<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 1.8<br \/>\nSo,<br \/>\nThe representation of 1.8 in the fraction form is: 1\\(\\frac{8}{10}\\)<br \/>\nSo,<br \/>\nTo write 1\\(\\frac{8}{10}\\) as hundredths, multiply the fraction and numerator of 1\\(\\frac{8}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 8 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of 1\\(\\frac{80}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-141.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-141.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-141-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of 1\\(\\frac{8}{10}\\) as hundredths in the fraction form is: 1\\(\\frac{80}{100}\\)<br \/>\nThe representation of 1\\(\\frac{80}{100}\\) in the decimal form is: 1.80<\/p>\n<p>Question 10.<br \/>\n<strong>Precision<\/strong><br \/>\nWhich of the following show forty-one and nine-tenths?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-59.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 59\" width=\"284\" height=\"188\" \/><br \/>\nAnswer:<br \/>\nLet the given Expressions be named as:<br \/>\nA) 41.9 B) 41.09\u00a0 C) 40 + 1 + \\(\\frac{9}{10}\\)\u00a0 D) 40 + 1 + 9\u00a0 E) 41\\(\\frac{90}{10}\\) F) 40 + 1 + 0.9<br \/>\nHence,<br \/>\nThe representation of forty-one and nine-tenths is shown by: B), C) and F)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-59.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 59\" width=\"284\" height=\"188\" \/><br \/>\nLet the given Expressions be named as:<br \/>\nA) 41.9 B) 41.09\u00a0 C) 40 + 1 + \\(\\frac{9}{10}\\)\u00a0 D) 40 + 1 + 9\u00a0 E) 41\\(\\frac{90}{10}\\) F) 40 + 1 + 0.9<br \/>\nNow,<br \/>\nThe given word form is: Forty-one and nine-tenths<br \/>\nThe representation of forty-one and nine-tenths in the fraction form is: 41\\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\nThe expanded form of 41\\(\\frac{9}{10}\\) is: 40 + 1 + \\(\\frac{9}{10}\\)<br \/>\nThe expanded form of 41\\(\\frac{9}{10}\\) in the decimal form is: 40 + 1 + 0.9<br \/>\nThe standard form of 41\\(\\frac{9}{10}\\) is: 41.09<br \/>\nHence, from the above,<br \/>\nWe can conclude that Expressions B), C), and F) representing 41\\(\\frac{9}{10}\\)<\/p>\n<p>Question 11.<br \/>\nWhich One Doesn&#8217;t Belong? Which one does not belong with the other three?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-60.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 60\" width=\"223\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nLet the Expressions be named as:<br \/>\nA) 0.70\u00a0 B) \\(\\frac{7}{10}\\)\u00a0 C) 0.07\u00a0 D) \\(\\frac{70}{100}\\)<br \/>\nHence, from above,<br \/>\nExpression C) does not belong to the other three.<\/p>\n<p>Explanation:<br \/>\nLet the Expressions be named as:<br \/>\nA) 0.70\u00a0 B) \\(\\frac{7}{10}\\)\u00a0 C) 0.07\u00a0 D) \\(\\frac{70}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<br \/>\nSo,<br \/>\nTo write \\(\\frac{7}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 7 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-142.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-142.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-142-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that Expression C) does not belong to the other three.<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nIs Newton correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-61.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 61\" width=\"180\" height=\"177\" \/><br \/>\nAnswer: Yes, Newton is correct<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 80 and 0.8<br \/>\nWhen we compare 80 and 0.8,<br \/>\nWe can say that 0.8 is the number that we can obtain when we divide 80 with 100<br \/>\nSo,<br \/>\nWe can observe that 80 is the whole number and 0.8 is the decimal number<br \/>\nWe know that,<br \/>\nThe whole number is always greater than the decimal number.<br \/>\nHence, from the above,<br \/>\nWe can conclude that 80 is greater than 0.8 as 80 is greater than 8 according to Newton<\/p>\n<p>Question 13.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWrite two equivalent fractions and two equivalent decimals represented by the model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-62.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 62\" width=\"114\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe equivalent fractions of \\(\\frac{6}{10}\\) are: \\(\\frac{60}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nThe equivalent decimals represented by \\(\\frac{6}{10}\\) are: 0.6 and 0.60<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-62.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 62\" width=\"114\" height=\"114\" \/><br \/>\nFrom the above model,<br \/>\nThe total number of parts are: 10<br \/>\nThe number of colored parts is: 6<br \/>\nHence,<br \/>\nThe portion of the colored part out of the total number of parts is: \\(\\frac{6}{10}\\)<br \/>\nNow,<br \/>\nThe given fraction is: \\(\\frac{6}{10}\\)<br \/>\nSo, to write \\(\\frac{6}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{6}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 6 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-143.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-143.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-143-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nThe representation of \\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-144.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-144.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-144-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe equivalent fractions of the given model is: \\(\\frac{60}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nThe equivalent decimal numbers of \\(\\frac{6}{10}\\) are: 0.6 and 0.60<\/p>\n<p><span style=\"font-size: 16px;\">Question 14.<\/span><\/p>\n<p><strong>Modeling Real Life<\/strong><br \/>\nDoes each player get a base hit on the same fraction of pitches? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-63.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 63\" width=\"345\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-63.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-63-300x188.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer: Yes, each player gets a base hit on the same fraction of pitches.<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 2 types of players. They are: Major League player and Youth League player<br \/>\nIt is also given that the Major League player gets a base hit on 30 out of 100 pitches and youth League player gets a base hit on 3 out of 10 pitches<br \/>\nSo, for comparison, convert the youth League player&#8217;s base hit into hundredths.<br \/>\nNow,<br \/>\nThe representation of the youth League plyer&#8217;s base hit is: \\(\\frac{3}{10}\\)<br \/>\nSo,<br \/>\nTo write \\(\\frac{3}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{3}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 3 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{30}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-145.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-145.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-145-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence, from the above,<br \/>\nwe can conclude that each player gets a base hit on the same fraction of pitches.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the equivalent fraction<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-64.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 64\" width=\"79\" height=\"64\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{4}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 4 and 6<br \/>\n4 and 6 are the multiples of 2.\u00a0 ( Since the\u00a0 the numerator and the denominator are the even numbers )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{4}{6}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{6}=\\frac{4 \\div 2}{6 \\div 2}=\\frac{2}{3}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{2}{3}\\)<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-65.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 65\" width=\"89\" height=\"67\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{25}{100}\\) is: \\(\\frac{5}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{25}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 25 and 100<br \/>\n25 and 100 are the multiples of 5.\u00a0 ( Since the\u00a0 the numerator and the denominator are the multiples of 5 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{25}{100}\\) with 5<br \/>\nSo,<br \/>\n\\(\\frac{25}{100}=\\frac{25 \\div 5}{100 \\div 5}=\\frac{5}{20}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{25}{100}\\) is: \\(\\frac{5}{20}\\)<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-66.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 66\" width=\"80\" height=\"56\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{14}{8}\\) is: \\(\\frac{7}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{14}{8}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 14 and 8<br \/>\n14 and 8 are the multiples of 2.\u00a0 ( Since the\u00a0 the numerator and the denominator are the even numbers )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{14}{8}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{14}{8}=\\frac{14 \\div 2}{8 \\div 2}=\\frac{7}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{14}{8}\\) is: \\(\\frac{7}{4}\\)<\/p>\n<h3><a id=\"Lesson_10.4_Compare_Decimals\"><\/a>Lesson 10.4 Compare Decimals<\/h3>\n<p>Use models to compare the decimals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-147.jpg\" alt=\"\" width=\"113\" height=\"28\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-148.jpg\" alt=\"\" width=\"201\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-148.jpg 201w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-148-150x150.jpg 150w\" sizes=\"(max-width: 201px) 100vw, 201px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-149.jpg\" alt=\"\" width=\"103\" height=\"20\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-29239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-150.jpg\" alt=\"\" width=\"729\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-150.jpg 729w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-150-300x178.jpg 300w\" sizes=\"(max-width: 729px) 100vw, 729px\" \/><\/p>\n<p>By using the models, we can compare the number of boxes for the comparison of the decimal numbers.<br \/>\nEach box represents 1 unit out of 100 total units.<br \/>\nSo,<br \/>\nThe denominator will be the same i.e., the total number of boxes will be the same.<br \/>\nSo, we have to compare only numerators i.e., the number of colored boxes so that we can compare the decimal numbers<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow did you use your models to determine which decimal is greater?<\/p>\n<p>Answer: For the comparison of the decimals, equate either the numerator or the denominator so that we can compare the numerators.<br \/>\nIf we compare the numerators, then we have to make the denominators equal<br \/>\nIf we compare the denominators, then we have to make the numerators equal<br \/>\nHence, in this way, we can compare the decimal numbers.<\/p>\n<p><strong>Think and Grow: Compare Decimals<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nCompare 0.7 and 0.07.<br \/>\nAnswer: 0.7 is greater than 0.07<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.7 and 0.07<br \/>\nThe representation of 0.7 in the fraction form is: \\(\\frac{7}{10}\\)<br \/>\nThe representation of 0.07 in the fraction form is: \\(\\frac{7}{100}\\)<br \/>\nSo,<br \/>\nfor comparison, we have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{7}{10}\\) with 10<br \/>\nSo for \\(\\frac{7}{10}\\),<br \/>\nThe numerator is 7 and denominator is 10<br \/>\nSo,<br \/>\nThe numerator 7 is multiplied by 10 and the denominator is also multiplied by 10 to make the denominators equal.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) in the hundredth&#8217;s form is: \\(\\frac{70}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.7 is greater than 0.07 by comparing their fraction forms.<\/p>\n<p><strong>Example<\/strong><br \/>\nUse a place value chart. Start at the left. Compare the digits in each place until the digits differ.<br \/>\nThe digits in the one&#8217;s place are the same. Compare the tenths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-151.jpg\" alt=\"\" width=\"313\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-151.jpg 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-151-300x269.jpg 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nSo, 0.7 &gt; 0.07<\/p>\n<p><strong>Example<\/strong><br \/>\nCompare 0.25 and 0.3.<\/p>\n<p>Use a number line. 0.25 is 25 hundredths. 0.3 and 0.30 are equivalent decimals. So, 0.3 is equivalent to 30 hundredths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-152.jpg\" alt=\"\" width=\"666\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-152.jpg 666w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-152-300x108.jpg 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Compare.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-73.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 73\" width=\"316\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-73.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-73-300x143.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer: 0.46 is less than 0.44<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.46 and 0.44<br \/>\nThe representation of 0.46 and 0.44 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-153.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-153.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-153-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s and tenth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the hundredth&#8217;s position 6 and 4<br \/>\nSo, 6 hundredths &gt; 4 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.46 is greater than 0.44<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-74.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 74\" width=\"303\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-74.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-74-300x111.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer: 0.05 is less than 0.2<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are 0.05 and 0.2<br \/>\nThe representation of 0.05 in the fraction form is: \\(\\frac{5}{100}\\)<br \/>\nThe representation of 0.2 in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nSo, for comparison, change \\(\\frac{2}{10}\\) in to hundredths<br \/>\nSo, for the change of \\(\\frac{2}{10}\\) in to hundredths, multiply \\(\\frac{2}{10}\\) with 10<br \/>\nSo,<br \/>\nThe numerator 2 is multiplied by 10 and the denominator 10 is multiplied with 10<br \/>\nHence,<br \/>\nThe representation of 0.2 in hundredth&#8217;s form is: \\(\\frac{20}{100}\\)<br \/>\nSo, for comparison,<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-154.jpg\" alt=\"\" width=\"291\" height=\"84\" \/><br \/>\nSo, from the above number line,<br \/>\n0.05 is to the left of 0.20<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.05 is less than 0.20<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Use the number line to compare.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-76.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 76\" width=\"109\" height=\"38\" \/><br \/>\nAnswer: 0.85 is less than 0.96<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.85 and 0.96<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above number line, 0.85 is to the left of 0.90<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.85 is less than 0.90<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-77.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 77\" width=\"105\" height=\"40\" \/><br \/>\nAnswer: 0.25 is less than 0.52<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.25 and 0.52<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above number line,<br \/>\n0.25 is to the left of 0.52<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.25 is less than 0.52<\/p>\n<p>Explanation:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13540\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-78.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 78\" width=\"110\" height=\"47\" \/><br \/>\nAnswer: 0.11 is greater than 0.09<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.11 and 0.09<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above line, we can observe that,<br \/>\n0.11 is to the right of 0.09<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.11 is greater than 0.09<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-10-Relate-Fractions-and-Decimals-79.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 10 Relate Fractions and Decimals 79\" width=\"106\" height=\"40\" \/><br \/>\nAnswer: 0.72 is greater than 0.59<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.72 and 0.59<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above number line, we can observe that,<br \/>\n0.72 is to the right of 0.59<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.72 is greater than 0.59<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-80.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 80\" width=\"114\" height=\"38\" \/><br \/>\nAnswer: 0.04 is less than 0.40<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.04 and 0.40<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above number line, we can observe that<br \/>\n0.04 is to the left of 0.40<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.04 is less than 0.40<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-81.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 81\" width=\"99\" height=\"42\" \/><br \/>\nAnswer: 0.90 is equal to 0.9<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.90 and 0.9<br \/>\nChange the 0.9 into hundredths by multiplying 0.9 with 10.<br \/>\nNow,<br \/>\nThe representation of 0.9 in the fraction form is: \\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\nWhen we multiply \\(\\frac{9}{10}\\) with 10, we can get<br \/>\nThe representation of \\(\\frac{9}{10}\\) in hundredth&#8217;s in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nNow,<br \/>\nthe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nWe get the numer \\(\\frac{90}{100}\\) by convrting the \\(\\frac{9}{10}\\) and the given number is also \\(\\frac{90}{100}\\)<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.90 is equal to 0.9<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-82.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 82\" width=\"108\" height=\"48\" \/><br \/>\nAnswer: 0.3 is greater than 0.03<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.3 and 0.03<br \/>\nThe representation of 0.3 in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nThe representation of 0.03 in the fraction form is: \\(\\frac{3}{100}\\)<br \/>\nSo, for the conversion of \\(\\frac{3}{10}\\) into hundredth&#8217;s, we have to multiply \\(\\frac{3}{10}\\) with 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredth&#8217;s in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg\" alt=\"\" width=\"490\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155.jpg 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-155-300x75.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nFrom the above number line, we can observe that<br \/>\n0.03 is to the left of 0.30<br \/>\nHence, from the above,<br \/>\nWe can observe that 0.03 is less than 0.30<\/p>\n<p><strong>Compare<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-83.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 83\" width=\"120\" height=\"49\" \/><br \/>\nAnswer: 5.29 is greater than 5.24<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 5.29 and 5.24<br \/>\nThe representation of 5.29 and 5.24 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-156.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-156.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-156-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that one&#8217;s and the tenth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nWe have to compare the hundredth&#8217;s position of the two decimal numbers.<br \/>\nSo, 9 hundredths &gt; 4 hundredths<br \/>\nHence, from the above,<br \/>\nwe can conclude that 5.29 is greater than 5.24<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-84.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 84\" width=\"127\" height=\"52\" \/><br \/>\nAnswer: 25.94 is greater than 25.9<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 25.94 and 25.9<br \/>\nThe representation of 25.94 and 25.9 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-157.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-157.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-157-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that ten&#8217;s, one&#8217;s, and tenth&#8217;s positions are the same.<br \/>\nSo, we have to compare the hundredth&#8217;s position.<br \/>\nSo,<br \/>\n4 hundredths &gt; 0 hundredths<br \/>\nHence, from the above,<br \/>\nwe can conclude that 25.94 is greater than 25.9<\/p>\n<p><strong>Open-Ended<\/strong><br \/>\n<strong>Complete the statement to make it true.<\/strong><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-85.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 85\" width=\"121\" height=\"41\" \/><br \/>\nAnswer:<br \/>\nLet the missing numbers be 3 and 2<br \/>\nSo,<br \/>\n0.31 &gt; 0.21<\/p>\n<p>Explanation:<br \/>\nLet the decimal numbers be: 0.31 and 0.21<br \/>\nThe representation of 0.31 and 0.21 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-158.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-158.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-158-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can observe that one&#8217;s and hundredth&#8217;s positions are the same.<br \/>\nSo, we have to compare the tenth&#8217;s position of the two decimal numbers<br \/>\nSo,<br \/>\n3 tenths &gt; 2 tenths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.31 is greater than 0.21<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-86.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 86\" width=\"130\" height=\"42\" \/><br \/>\nAnswer:<br \/>\nLe the missing number be 10<br \/>\nSo,<br \/>\n12.10 = 12.10<\/p>\n<p>Explanation:<br \/>\nLet the missing decimal numbers be: 12.10 and 12.10<br \/>\nThe representation of 12.10 and 12.10 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-159.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-159.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-159-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that all the positions are the same.<br \/>\nHence, from the above,<br \/>\nWe can conclude that 12.10 is equal to 12.10<\/p>\n<p>Question 14.<br \/>\n9.43 &lt; ____<br \/>\nAnswer:<br \/>\nLet the missing number be: 9.53<br \/>\nSo,<br \/>\n9.43 &lt; 9.53<\/p>\n<p>Explanation:<br \/>\nLet the 2 decimal numbers be: 9.43 and 9.53<br \/>\nThe representation of 9.43 and 9.53 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-161.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-161.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-161-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that one&#8217;s position and hundredths position is the same.<br \/>\nSo, we can either compare the tenths position.<br \/>\nSo,<br \/>\nWhen we compare the tenths position, 4 tenths &lt; 5 tenths<br \/>\nHence, from the above<br \/>\nWe can conclude that 9.43 is less than 9.53<\/p>\n<p>Question 15.<br \/>\n<strong>Precision<\/strong><br \/>\nWrite the number that is halfway between 3.6 and 3.7. Explain how you found your answer.<br \/>\nAnswer: The number that is halfway between 3.6 and 3.7 is 3.65<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 3.6 and 3.7<br \/>\nWe know that,<br \/>\nThe middle number between two numbers = (The given first number + The given second number) \u00f7 2<br \/>\nSo,<br \/>\nThe number that is halfway between 3.6 and 3.7 = (3.6 + 3.7) \u00f7 2<br \/>\n= 7.3 \u00f7 2<br \/>\n= 3.65<br \/>\nHence, from the above,<br \/>\nwe can conclude that the number that is halfway between 3.6 and 3.7 is: 3.65<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\n<strong>Write whether the statement is true or false. If false, explain why<\/strong><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-87.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 87\" width=\"220\" height=\"63\" \/><br \/>\nAnswer: \\(\\frac{1}{10}\\) is greater than 0.07<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{10}\\) and 0.07<br \/>\nThe representation of 0.07 in the fraction form is: \\(\\frac{7}{100}\\)<br \/>\nSo, for comparison, we have to convert \\(\\frac{1}{10}\\) into hundredths form by multiplying \\(\\frac{1}{10}\\) with 10.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths in the fraction form is: \\(\\frac{10}{100}\\)<br \/>\nThe representation of 0.07 in the fraction form is: \\(\\frac{7}{100}\\)<br \/>\nHence, from the above,<br \/>\nwe can conclude that \\(\\frac{1}{10}\\) is greater than 0.07<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-88.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 88\" width=\"207\" height=\"58\" \/><br \/>\nAnswer: 0.6 is greater than 0.36<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.6 and \\(\\frac{36}{100}\\)<br \/>\nThe representation of 0.6 in the fraction form is: \\(\\frac{6}{10}\\)<br \/>\nSo, for comparison, we have to convert \\(\\frac{6}{10}\\) into hundredths form by multiplying \\(\\frac{6}{10}\\) with 10.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nThe representation of 0.36 in the fraction form is: \\(\\frac{36}{100}\\)<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.6 is greater than \\(\\frac{36}{100}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nNewton and Descartes make paper airplanes. Newton\u2019s paper Whose airplane flies 3.01 meters. Descartes\u2019s paper airplane flies 3.10 meters. Whose paper airplane flies farther?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-89.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 89\" width=\"203\" height=\"134\" \/><br \/>\nUse a place value chart. Compare the digits in each place until the digits differ.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-162.jpg\" alt=\"\" width=\"410\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-162.jpg 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-162-300x102.jpg 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nCompare Newton\u2019s distance to Descartes\u2019s distance.<br \/>\nSo,<br \/>\nDescartes&#8217;s paper airplane flies farther.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 18.<br \/>\nCompare the thickness of a nickel and a quarter. Which coin is thinner?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-91.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 91\" width=\"181\" height=\"178\" \/><br \/>\nAnswer: When we compare the thickness of nickel and quarter by observing the table, we can say that the Quarter is thinner.<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-91.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 91\" width=\"181\" height=\"178\" \/><br \/>\nFrom the given table,<br \/>\nThe thickness of the Nickel is: 1.95mm<br \/>\nThe thickness of the Quarter is: 1.75mm<br \/>\nNow,<br \/>\nThe representation of the thicknesses of the Nickel and the Quarter in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-163.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-163.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-163-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that<br \/>\n7 tenths &lt; 9 tenths<br \/>\nHence, from the above,<br \/>\nWe can conclude that the Quarter is thinner.<\/p>\n<p>Question 19.<br \/>\nYou, your cousin, and your friend run a 100-meter race. Who finishes first? second? third?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-92.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 92\" width=\"355\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-92.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-92-300x126.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nAnswer:<br \/>\nThe one who finishes first is: You<br \/>\nThe one who finishes second is: Friend<br \/>\nThe one who finishes third is: Cousin<\/p>\n<p>Explanation:<br \/>\nThe given timings are:<br \/>\nThe timing of yours is: 16.40 seconds<br \/>\nThe timing of your friend is: 16.48 seconds<br \/>\nThe timing of your cousin is: 16.58 seconds<br \/>\nNow, the representation of all the timings in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-164.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-164.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-164-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-165.jpg\" alt=\"\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-165.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-165-300x67.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that:<br \/>\nThe one who finishes first is: You<br \/>\nThe one who finishes second is: Friend<br \/>\nThe one who finishes third is: Cousin<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour water bottle is 0.25 full. Your friend\u2019s water bottle is 0.5 full. You have more water than your friend. Explain how this is possible.<br \/>\nAnswer: This is not possible.<\/p>\n<p>Explanation:<br \/>\nIt is given that your water bottle is 0.25 full and your friend&#8217;s water bottle is 0.5 full.<br \/>\nSo, we have to compare 0.25 and 0.5<br \/>\nThe representation of 0.5 in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nThe representation of 0.25\u00a0in the fraction form is: \\(\\frac{25}{100}\\)<br \/>\nSo, for comparison, we have to convert \\(\\frac{5}{10}\\) as hundredths by multiplying \\(\\frac{5}{10} \\) with 10.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nHence, from the above,<br \/>\nwe can conclude that your friend&#8217;s water bottle has more water than you.<\/p>\n<h3><a id=\"Compare_Decimals_Homework_&amp;_Practice_10.4\"><\/a>Compare Decimals Homework &amp; Practice 10.4<\/h3>\n<p>Compare<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-93.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 93\" width=\"331\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-93.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-93-300x143.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer: 0.58 is greater than 0.52<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.58 and 0.52<br \/>\nThe representation of 0.58 and 0.52 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-166.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-166.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-166-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above table, we can observe that one&#8217;s and tenth&#8217;s positions are the same.<br \/>\nSo, we have to compare the hundredth&#8217;s position<br \/>\nSo,<br \/>\n8 hundredths &gt; 2 hundredths<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.58 is greater than 0.52<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-94.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 94\" width=\"304\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-94.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-94-300x123.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer: 0.25 is greater than 0.05<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.25 and 0.05<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-167.jpg\" alt=\"\" width=\"287\" height=\"109\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.05 is to the left of 0.25<br \/>\nhence, from the above,<br \/>\nWe can conclude that 0.25 is greater than 0.05<\/p>\n<p><strong>Use the number line to compare<\/strong>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-96.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 96\" width=\"109\" height=\"42\" \/><br \/>\nAnswer: 0.76 is greater than 0.59<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.76 and 0.59<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.76 is to the right of 0.59<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.76 is greater than 0.59<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-97.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 97\" width=\"120\" height=\"43\" \/><br \/>\nAnswer: 0.21 is less than 0.23<\/p>\n<p>Explanation:<br \/>\nthe given decimal numbers are: 0.21 and 0.23<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.21 is to the left of 0.23<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.21 is less than 0.23<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-98.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 98\" width=\"104\" height=\"45\" \/><br \/>\nAnswer: 0.7 is greater than 0.07<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.7 and 0.07<br \/>\nThe representation of 0.7 in the fracton form is: \\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nThe \\(\\frac{7}{10}\\) should be converted into hundredths by multiplying \\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nNow,<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.7 is to the left of 0.07<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.7 is greater than 0.07<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-99.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 99\" width=\"105\" height=\"47\" \/><br \/>\nAnswer: 0.05 is less than 0.08<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.05 and 0.08<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.05 is to the left of 0.08<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.05 is less than 0.08<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-100.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 100\" width=\"101\" height=\"37\" \/><br \/>\nAnswer: 0.10 is equal to 0.1<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.10 and 0.1<br \/>\nNow,<br \/>\nThe representation of 0.1 in the fraction form is: \\(\\frac{1}{10}\\)<br \/>\nThe representation of 0.10 in the fraction form is: \\(\\frac{1}{100}\\)<br \/>\nNow, to make the denominators equal, multiply \\(\\frac{1}{10}\\) by 2.<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths, in the fraction form is: \\(\\frac{1}{100}\\)<br \/>\nNow,<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.10 is equal to 0.1<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-101.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 101\" width=\"113\" height=\"42\" \/><br \/>\nAnswer: 0.05 is less than 0.50<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.05 and 0.50<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.05 is to the left of 0.50.<br \/>\nHence, from the above,<br \/>\nwe can conclude that 0.05 is less than 0.50<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-102.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 102\" width=\"117\" height=\"43\" \/><br \/>\nAnswer: 0.13 is less than 0.19<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.13 and 0.19<br \/>\nThe given number line is:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-29474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg\" alt=\"\" width=\"489\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-168-300x83.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that 0.13 is to the left of 0.10<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.13 is less than 0.19<\/p>\n<p><strong>Compare<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-103.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 103\" width=\"106\" height=\"52\" \/><br \/>\nAnswer: 2.2 is greater than 2.02<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 2.2 and 2.02<br \/>\nThe representation of 2.2 and 2.02 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-169.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-169.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-169-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can observe that only one&#8217;s position is the same<br \/>\nSo,<br \/>\n2 tenths &gt; 0 tenths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 2.2 is greater than 2.02<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-104.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 104\" width=\"104\" height=\"53\" \/><br \/>\nAnswer: 4.70 is equal to 4.7<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 4.70 and 4.7<br \/>\nThe representation of 4.70 in the fraction form is: 4\\(\\frac{70}{100}\\)<br \/>\nThe representation of 4.7 in the fraction form is: 4\\(\\frac{7}{10}\\)<br \/>\nSo, to compare, we have to make the denominators equal.<br \/>\nSo, multiply 4\\(\\frac{7}{10}\\) with 10<br \/>\nSo,<br \/>\nThe representation of 4\\(\\frac{7}{10}\\) as hundredth&#8217;s in the fraction form is: 4\\(\\frac{70}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that 4.70 is equal to 4.7<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-105.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 105\" width=\"115\" height=\"40\" \/><br \/>\nAnswer: 8.35 is less than 8.53<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 8.35 and 8.53<br \/>\nThe representation of 8.35 and 8.53 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-170.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-170.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-170-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can observe that only the tenth&#8217;s position can be compared.<br \/>\nSo,<br \/>\n3 tenths &lt; 5 tenths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8.35 is less than 8.53<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-106.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 106\" width=\"129\" height=\"47\" \/><br \/>\nAnswer: 35.01 is greater than 32.98<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 35.01 and 32.98<br \/>\nThe representation of 35.01 and 32.98 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-171.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-171.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-171-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can compare one&#8217;s position since it is the position with the highest value after the ten&#8217;s position.<br \/>\nSo,<br \/>\n5 ones &gt; 2 ones<br \/>\nHence, from the above,<br \/>\nwe can conclude that 35.01 is greater than 32.98<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-107.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 107\" width=\"113\" height=\"44\" \/><br \/>\nAnswer: 14.9 is less than 14.92<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 14.9 and 14.92<br \/>\nThe representation of 14.9 and 14.92 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-172.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-172.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-172-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can compare only the hundredth&#8217;s positions.<br \/>\nSo,<br \/>\n0 hundredths&lt; 2 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 14.9 is less than 14.92<\/p>\n<p>Question 15.<br \/>\n<strong>Precision<\/strong><br \/>\nExplain how to compare 0.46 and 0.48.<br \/>\nAnswer: 0.46 is less than 0.48<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.46 and 0.48<br \/>\nThe representation of 0.46 and 0.48 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-173.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-173.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-173-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart,<br \/>\nWe can compare the hundredth&#8217;s position<br \/>\nSo,<br \/>\n6 hundredths &lt; 8 hundredths<br \/>\nHence, from the above<br \/>\nWe can conclude that 0.46 is less than 0.48<\/p>\n<p>Question 16.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWhat might Descartes\u2019s number be?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-108.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 108\" width=\"220\" height=\"201\" \/><br \/>\nAnswer: Descartes&#8217;s number might be: 0.61, 0.62, 0.63, 0.64, 0.65<\/p>\n<p>Explanation:<br \/>\nGiven that my number is greater than 0.6 and less than 0.7.<br \/>\nSo,<br \/>\nThe numbers might be: 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69<br \/>\nIt is also given that the greatest digit in the number is in the tenths place.<br \/>\nSo,<br \/>\nThe numbers might be: 0.61, 0.62, 0.63, 0.64, 0.65<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes&#8217;s number might be: 0.61, 0.62, 0.63, 0.64, 0.65<\/p>\n<p>Question 17.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA traffic light is red for 23.4 seconds and green for 23.6 seconds. Does the traffic light stay red or green longer?<br \/>\nAnswer: The traffic light stay green for a long time<\/p>\n<p>Explanation:<br \/>\nIt is given that a traffic light is red for 23.4 seconds and green for 23.6 seconds.<br \/>\nSo, we have to compare 23.4 and 23.6 to see which light stay for a long time<br \/>\nNow,<br \/>\nThe representation of 23.4 and 23.6 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-174.jpg\" alt=\"\" width=\"322\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-174.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-174-300x99.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above place-value chart, we can observe that we can compare only the tenths position.<br \/>\nSo,<br \/>\n4 tenths &lt; 6 tenths<br \/>\nSo,<br \/>\n23.4 is less than 23.6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the green light stays for a long time<\/p>\n<p>Question 18.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nOrder the caterpillars from longest to shortest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-109.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 109\" width=\"242\" height=\"169\" \/><br \/>\nAnswer: Caterpillar B &gt; Caterpillar A &gt; Caterpillar C<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-109.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 109\" width=\"242\" height=\"169\" \/><br \/>\nFrom the table,<br \/>\nThe length of caterpillar A is: 3.5 cm<br \/>\nThe length of caterpillar B is: 3.65 cm<br \/>\nThe length of caterpillar C is: 3.45 cm<br \/>\nSo,<br \/>\nWhen we compare the tenth&#8217;s position in all the lengths of the caterpillars,<br \/>\nWe can observe that B &gt; A &gt; C<br \/>\nHence, from the above,<br \/>\nWe can conclude that caterpillar B &gt; caterpillar A &gt; caterpillar C<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Round the number to the nearest hundred thousand<\/strong><\/p>\n<p>Question 19.<br \/>\n695,023<br \/>\nAnswer: The nearest hundred thousand of 695,023 is: 700,000<\/p>\n<p>Explanation:<br \/>\nThe given number is: 695,023<br \/>\nWe know that,<br \/>\nThe value of a digit depends on the position of the digit<br \/>\nSo,<br \/>\nThe value of the nearest hundred thousand in 695,023 is: 700,000<\/p>\n<p>Question 20.<br \/>\n246,947<br \/>\nAnswer: The value of the nearest hundred thousand in 246,947 is: 200,000<\/p>\n<p>Explanation:<br \/>\nThe given number is: 246,947<br \/>\nWe know that,<br \/>\nThe value of a digit depends on the position of the digit<br \/>\nSo,<br \/>\nThe value of the nearest hundred thousand in 246,947 is: 200,000<\/p>\n<h3><a id=\"Lesson_10.5_Add_Decimal_Fractions_and_Decimals\"><\/a>Lesson 10.5 Add Decimal Fractions and Decimals<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>How can you use a number line to find the sum?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-110.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 110\" width=\"562\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-110.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-110-300x66.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\n0.25 + 0.7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-111.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 111\" width=\"498\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-111.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-111-300x39.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\nHow can you use models to check your answers?<\/p>\n<p>Answer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of the sum in the decimal form is:<br \/>\n0.25 + 0.7 = 0.95<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{25}{100}\\) and \\(\\frac{7}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{7}{10}\\) as the hundredths, we have to multiply \\(\\frac{7}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{25}{100}\\)<br \/>\n= \\(\\frac{70 + 25}{100}\\)<br \/>\n= \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal form is: 0.95<br \/>\nNow,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-175.jpg\" alt=\"\" width=\"510\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-175.jpg 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-175-300x61.jpg 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal form is: 0.95<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow can you add two decimal fractions with a denominator of 10? How can you add two decimal fractions with denominators of 10 and 100?<\/p>\n<p>Answer: We add the two fractions only if their numerator or denominators are equal<br \/>\nIf there are fractions with different denominators, then we will make the denominators equal either by multiplying or by dividing the fractions and add the different fractions.<\/p>\n<p><strong>Think and Grow: Add Decimal Fractions and Decimals<\/strong><\/p>\n<p>You have learned how to add fractions with the same denominator. You can use equivalent fractions to add fractions that do not have the same denominator.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-112.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 112\" width=\"219\" height=\"54\" \/><br \/>\n<strong>Step 1:<\/strong> Use equivalent fractions to write the fractions with the same denominator<br \/>\nThink: Rewrite \\(\\frac{3}{10}\\) with a denominator of 100.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-176.jpg\" alt=\"\" width=\"186\" height=\"49\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-177.jpg\" alt=\"\" width=\"239\" height=\"88\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-178.jpg\" alt=\"\" width=\"179\" height=\"53\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind 0.75 + 0.2.<br \/>\n<strong>Step 1:<\/strong> Write 0.75 and 0.2 as fractions.Think: 0.75 is 75 hundredths. 0.2 is 2 tenths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-179.jpg\" alt=\"\" width=\"229\" height=\"55\" \/><br \/>\n<strong>Step 2:<\/strong> Use equivalent fractions to write the fractions with the same denominator.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-180.jpg\" alt=\"\" width=\"190\" height=\"49\" \/><br \/>\n<strong>Step 3:<\/strong> Add the numerators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-181.jpg\" alt=\"\" width=\"154\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-181.jpg 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-181-150x47.jpg 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\n<strong>Step 4:<\/strong> Write the sum as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-182.jpg\" alt=\"\" width=\"131\" height=\"48\" \/><br \/>\nSo, 0.75 + 0.2 = 0.95<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Find the sum.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-119.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 119\" width=\"267\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{36}{100}\\) = \\(\\frac{46}{100}\\)<br \/>\nThe representation of \\(\\frac{46}{100}\\) in the decimal for is: 0.46<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{36}{100}\\) and \\(\\frac{1}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{1}{10}\\) as the hundredths, we have to multiply \\(\\frac{1}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths in the fraction form is: \\(\\frac{10}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{10}{100}\\) + \\(\\frac{36}{100}\\)<br \/>\n= \\(\\frac{10 + 36}{100}\\)<br \/>\n= \\(\\frac{46}{100}\\)<br \/>\nThe representation of \\(\\frac{46}{100}\\) in the decimal form is: 0.46<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{36}{100}\\) = \\(\\frac{46}{100}\\)<br \/>\nThe representation of \\(\\frac{46}{100}\\) in the decimal for is: 0.46<\/p>\n<p>Question 2.<br \/>\n0.5 + 0.25 = ____<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{75}{100}\\)<br \/>\nThe representation of 0.25 + 0.5 in the decimal form is: 0.75<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.5 and 0.25<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{25}{100}\\) and \\(\\frac{5}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{5}{10}\\) as the hundredths, we have to multiply \\(\\frac{5}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{25}{100}\\)<br \/>\n= \\(\\frac{50 + 25}{100}\\)<br \/>\n= \\(\\frac{75}{100}\\)<br \/>\nThe representation of \\(\\frac{75}{100}\\) in the decimal form is: 0.75<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{75}{100}\\)<br \/>\nThe representation of \\(\\frac{75}{100}\\) in the decimal for is: 0.75<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Find the sum.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-120.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 120\" width=\"158\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{37}{100}\\) = \\(\\frac{77}{100}\\)<br \/>\nThe representation of \\(\\frac{77}{100}\\) in the decimal for is: 0.77<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{37}{100}\\) and \\(\\frac{4}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{4}{10}\\) as the hundredths, we have to multiply \\(\\frac{4}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}\\) + \\(\\frac{37}{100}\\)<br \/>\n= \\(\\frac{40 + 37}{100}\\)<br \/>\n= \\(\\frac{77}{100}\\)<br \/>\nThe representation of \\(\\frac{77}{100}\\) in the decimal form is: 0.77<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{37}{100}\\) = \\(\\frac{77}{100}\\)<br \/>\nThe representation of \\(\\frac{77}{100}\\) in the decimal for is: 0.77<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-121.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 121\" width=\"147\" height=\"64\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{23}{100}\\) = \\(\\frac{43}{100}\\)<br \/>\nThe representation of \\(\\frac{43}{100}\\) in the decimal for is: 0.43<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{23}{100}\\) and \\(\\frac{2}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{2}{10}\\) as the hundredths, we have to multiply \\(\\frac{2}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}\\) + \\(\\frac{23}{100}\\)<br \/>\n= \\(\\frac{20 + 23}{100}\\)<br \/>\n= \\(\\frac{43}{100}\\)<br \/>\nThe representation of \\(\\frac{43}{100}\\) in the decimal form is: 0.43<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{23}{100}\\) = \\(\\frac{43}{100}\\)<br \/>\nThe representation of \\(\\frac{43}{100}\\) in the decimal for is: 0.43<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-122.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 122\" width=\"151\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{19}{100}\\) = \\(\\frac{89}{100}\\)<br \/>\nThe representation of \\(\\frac{89}{100}\\) in the decimal for is: 0.89<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{19}{100}\\) and \\(\\frac{7}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{7}{10}\\) as the hundredths, we have to multiply \\(\\frac{7}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{19}{100}\\)<br \/>\n= \\(\\frac{70 + 19}{100}\\)<br \/>\n= \\(\\frac{89}{100}\\)<br \/>\nThe representation of \\(\\frac{89}{100}\\) in the decimal form is: 0.89<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{19}{100}\\) = \\(\\frac{89}{100}\\)<br \/>\nThe representation of \\(\\frac{89}{100}\\) in the decimal for is: 0.89<\/p>\n<p>Question 6.<br \/>\n0.35 + 0.1 = ____<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{35}{100}\\) = \\(\\frac{45}{100}\\)<br \/>\nThe representation of 0.35 + 0.1 in the decimal for is: 0.45<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.1 and 0.35<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{35}{100}\\) and \\(\\frac{1}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{1}{10}\\) as the hundredths, we have to multiply \\(\\frac{1}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths in the fraction form is: \\(\\frac{10}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{10}{100}\\) + \\(\\frac{35}{100}\\)<br \/>\n= \\(\\frac{10 + 35}{100}\\)<br \/>\n= \\(\\frac{45}{100}\\)<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the decimal form is: 0.45<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{35}{100}\\) = \\(\\frac{45}{100}\\)<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the decimal for is: 0.45<\/p>\n<p>Question 7.<br \/>\n0.8 + 0.15 = ____<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{15}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of 0.15 + 0.8 in the decimal for is: 0.95<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.8 and 0.15<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{15}{100}\\) and \\(\\frac{8}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{8}{10}\\) as the hundredths, we have to multiply \\(\\frac{8}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}\\) + \\(\\frac{15}{100}\\)<br \/>\n= \\(\\frac{80 + 15}{100}\\)<br \/>\n= \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal form is: 0.95<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{15}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal for is: 0.95<\/p>\n<p>Question 8.<br \/>\n0.50 + 0.4 = __<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{50}{100}\\) = \\(\\frac{90}{100}\\)<br \/>\nThe representation of 0.50 + 0.4 in the decimal for is: 0.90<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.4 and 0.50<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{50}{100}\\) and \\(\\frac{4}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{4}{10}\\) as the hundredths, we have to multiply \\(\\frac{4}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}\\) + \\(\\frac{50}{100}\\)<br \/>\n= \\(\\frac{50 + 40}{100}\\)<br \/>\n= \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal form is: 0.90<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{50}{100}\\) = \\(\\frac{90}{100}\\)<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the decimal for is: 0.90<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-123.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 123\" width=\"186\" height=\"58\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{48}{100}\\) + \\(\\frac{16}{100}\\) + \\(\\frac{2}{10}\\) = \\(\\frac{84}{100}\\)<br \/>\nThe representation of \\(\\frac{84}{100}\\) in the decimal for is: 0.84<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{48}{100}\\), \\(\\frac{16}{100}\\) and \\(\\frac{2}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{2}{10}\\) as the hundredths, we have to multiply \\(\\frac{2}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{48}{100}\\) + \\(\\frac{16}{100}\\) + \\(\\frac{20}{100}\\)<br \/>\n= \\(\\frac{48 + 16 + 20}{100}\\)<br \/>\n= \\(\\frac{84}{100}\\)<br \/>\nThe representation of \\(\\frac{84}{100}\\) in the decimal form is: 0.84<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{48}{100}\\) + \\(\\frac{16}{100}\\) = \\(\\frac{84}{100}\\)<br \/>\nThe representation of \\(\\frac{84}{100}\\) in the decimal for is: 0.84<\/p>\n<p>Question 10.<br \/>\n0.3 + 0.25 + 0.1 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{1}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{65}{100}\\)<br \/>\nThe representation of 0.25 + 0.1 + 0.3 in the decimal for is: 0.65<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.3, 0.1 and 0.25<br \/>\nSo, convert the three decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{25}{100}\\) , \\(\\frac{3}{10}\\) and \\(\\frac{1}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{1}{10}\\) and \\(\\frac{3}{10}\\) as the hundredths, we have to multiply \\(\\frac{5}{10}\\) and \\(\\frac{3}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths in the fraction form is: \\(\\frac{10}{100}\\)<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{10}{100}\\) + \\(\\frac{25}{100}\\) + \\(\\frac{30}{100}\\)<br \/>\n= \\(\\frac{10 + 25 + 30}{100}\\)<br \/>\n= \\(\\frac{65}{100}\\)<br \/>\nThe representation of \\(\\frac{65}{100}\\) in the decimal form is: 0.65<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{25}{100}\\) + \\(\\frac{3}{10}\\) = \\(\\frac{65}{100}\\)<br \/>\nThe representation of \\(\\frac{65}{100}\\) in the decimal for is: 0.65<\/p>\n<p><strong>Number Sense<\/strong><br \/>\nFind the sum.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-124.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 124\" width=\"142\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{29}{100}\\) = \\(\\frac{79}{100}\\)<br \/>\nThe representation of 0.5 + \\(\\frac{29}{100}\\) in the decimal for is: 0.79<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.5 and \\(\\frac{29}{100}\\)<br \/>\nSo, convert the decimal number in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{5}{10}\\) and \\(\\frac{29}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{5}{10}\\) as the hundredths, we have to multiply \\(\\frac{5}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{29}{100}\\)<br \/>\n= \\(\\frac{50 + 29}{100}\\)<br \/>\n= \\(\\frac{79}{100}\\)<br \/>\nThe representation of \\(\\frac{79}{100}\\) in the decimal form is: 0.79<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{29}{100}\\) = \\(\\frac{79}{100}\\)<br \/>\nThe representation of \\(\\frac{79}{100}\\) in the decimal for is: 0.79<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-125.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 125\" width=\"143\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{75}{100}\\) = \\(\\frac{155}{100}\\)<br \/>\nThe representation of 0.75 + \\(\\frac{8}{10}\\) in the decimal for is: 1.55<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.75 and \\(\\frac{8}{10}\\)<br \/>\nSo, convert the decimal number in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{8}{10}\\) and \\(\\frac{75}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{8}{10}\\) as the hundredths, we have to multiply \\(\\frac{8}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}\\) + \\(\\frac{75}{100}\\)<br \/>\n= \\(\\frac{80 + 75}{100}\\)<br \/>\n= \\(\\frac{155}{100}\\)<br \/>\nThe representation of \\(\\frac{155}{100}\\) in the decimal form is: 1.55<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{75}{100}\\) = \\(\\frac{155}{100}\\)<br \/>\nThe representation of \\(\\frac{155}{100}\\) in the decimal for is: 1.55<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says Newton and Descartes are both correct. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-126.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 126\" width=\"344\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-126.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-126-300x172.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nAnswer: Yes, your friend is correct.<\/p>\n<p>Explanation:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{5}{100}\\) + \\(\\frac{55}{100}\\) = \\(\\frac{110}{100}\\)<br \/>\nThe representation of 0.55 + 0.5 + 0.05 in the decimal for is: 1.10<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.05, 0.5 and 0.55<br \/>\nSo, convert the three decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{55}{100}\\) , \\(\\frac{5}{10}\\) and \\(\\frac{5}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{5}{10}\\)\u00a0 as the hundredths, we have to multiply \\(\\frac{5}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{55}{100}\\) + \\(\\frac{5}{100}\\)<br \/>\n= \\(\\frac{50 + 55 + 5}{100}\\)<br \/>\n= \\(\\frac{110}{100}\\)<br \/>\nThe representation of \\(\\frac{110}{100}\\) in the decimal form is: 1.10<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{55}{100}\\) + \\(\\frac{5}{100}\\) = \\(\\frac{110}{100}\\)<br \/>\nThe representation of \\(\\frac{110}{100}\\) in the decimal for is: 1.10 or 1.1<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite and solve a decimal addition problem represented by the model. Write your answer as a decimal and as a mixed number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-127.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 127\" width=\"249\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nFrom the above model,<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{47}{100}\\) = \\(\\frac{107}{100}\\) = 1\\(\\frac{7}{100}\\)<br \/>\nThe representation of \\(\\frac{107}{100}\\) in the decimal for is: 1.07<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-127.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 127\" width=\"249\" height=\"114\" \/><br \/>\nFrom the model,<br \/>\nThe given fractions are: \\(\\frac{47}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{6}{10}\\) as the hundredths, we have to multiply \\(\\frac{6}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{60}{100}\\) + \\(\\frac{47}{100}\\)<br \/>\n= \\(\\frac{60 + 47}{100}\\)<br \/>\n= \\(\\frac{107}{100}\\)<br \/>\nThe representation of \\(\\frac{107}{100}\\) in the decimal form is: 1.07<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{47}{100}\\) = \\(\\frac{107}{100}\\) = 1\\(\\frac{7}{100}\\)<br \/>\nThe representation of \\(\\frac{107}{100}\\) in the decimal for is: 1.07<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou use \\(\\frac{8}{10}\\) pound of clay to make a cup. You make a handle for the cup with \\(\\frac{15}{100}\\) pound of clay and attach the handle to the cup. What fraction of a pound does your cup weigh in all?<br \/>\nAdd the fractions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-136.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 136\" width=\"137\" height=\"98\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-183.jpg\" alt=\"\" width=\"115\" height=\"62\" \/><br \/>\nUse equivalent fractions to write the fractions with the same denominator.<br \/>\nRewrite \\(\\frac{8}{10}\\) with a denominator of 100.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-184.jpg\" alt=\"\" width=\"605\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-184.jpg 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-184-300x78.jpg 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nEach morning, you walk \\(\\frac{25}{100}\\) mile to your friend\u2019s house and then \\(\\frac{5}{10}\\) mile to school. What fraction of a mile do you walk each morning?<br \/>\nAnswer:<br \/>\nThe fraction of a mile you walk each morning is:<br \/>\n\\(\\frac{25}{100}\\) + \\(\\frac{5}{10}\\) = \\(\\frac{75}{100}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that each morning, you walk \\(\\frac{25}{100}\\) mile to your friend&#8217;s house and then \\(\\frac{5}{10}\\) mile to school.<br \/>\nSo,<br \/>\nTo find the portion of a mile you walk in the morning, you have to add the fractions.<br \/>\nSo,<br \/>\nNow, first, we have to convert \\(\\frac{5}{10}\\) as hundredths so that we can add both the fractions because denominators have to be equal for the addition.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{5}{10}\\) with 10 to convert it as hundredths<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{25}{100}\\) + \\(\\frac{50}{100}\\)<br \/>\n= \\(\\frac{75}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the portion of a mile you walk in the morning is: \\(\\frac{75}{100}\\)<\/p>\n<p>Question 16.<br \/>\nYou ride a zip line that is mile-long \\(\\frac{15}{100}\\) mile long. You ride another zip line that is \\(\\frac{3}{10}\\) mile long. Your friend rides a total of \\(\\frac{40}{100}\\) mile on zip lines. Who rides farther on zip lines?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-138.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 138\" width=\"134\" height=\"113\" \/><br \/>\nAnswer: Your friend rides farther on zip lines.<\/p>\n<p>Explanation:<br \/>\nIt is given that you ride a zip line that is mile-long \\(\\frac{15}{100}\\) mile long. You ride another zip line that is \\(\\frac{3}{10}\\) mile long and your friend rides a total of \\(\\frac{40}{100}\\) mile on zip<br \/>\nlines.<br \/>\nSo, the given three fractions are:<br \/>\n\\(\\frac{15}{100}\\), \\(\\frac{3}{10}\\) and \\(\\frac{40}{100}\\)<br \/>\nSo, for the comparison of the three fractions, we have to make the denominators equal.<br \/>\nSo, we have to convert \\(\\frac{3}{10}\\) as hundredths.<br \/>\nSo,<br \/>\nWe have to multiply \\(\\frac{3}{10}\\) with 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nNow,<br \/>\nAs the denominators are equal, compare the numerators.<br \/>\nSo, we have to compare 15, 30, and 40<br \/>\nBy comparing, we can observe that 40 &gt; 30 &gt; 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend rides farther on zip lines than you.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou ship a package that weighs 0.8 pounds. Your package is 0.75 pounds lighter than your friend\u2019s package. How much does your friend\u2019s package weigh? Write your answer in decimal form.<br \/>\nAnswer: The weight of your friend&#8217;s package is: 1.55 pounds<\/p>\n<p>Explanation:<br \/>\nThe two given decimal numbers are: 0.8 and 0.75<br \/>\nIt is given that your package is 0.75 pounds lighter than your friend&#8217;s package.<br \/>\nSo,<br \/>\nThe weight of your friend&#8217;s package = 0.8 + 0.75<br \/>\nNow, first, convert the given decimal numbers into fractions.<br \/>\nSo, The representation of 0.8 and 0.75 in the fraction forms is: \\(\\frac{8}{10}\\) and \\(\\frac{75}{100}\\)<br \/>\nNow, for addition, we have to make the denominators of the two fractions equal.<br \/>\nSo,<br \/>\nWe have to multiply \\(\\frac{3}{10}\\) with 10, to make the denominator equal to 100<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{30}{100}\\) + \\(\\frac{75}{100}\\)<br \/>\n= \\(\\frac{105}{100}\\)<br \/>\nThe representation of \\(\\frac{105}{100}\\) in the decimal form is: 1.05<br \/>\nHence, from the above,<br \/>\nWe can conclude that the weight of your friend&#8217;s package in the decimal form is: 1.05 pounds<\/p>\n<h3><a id=\"Add_Decimal_Fractions_and_Decimals_Homework_&amp;_Practice_10.5\"><\/a>Add Decimal Fractions and Decimals Homework &amp; Practice 10.5<\/h3>\n<p>Find the sum.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-139.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 139\" width=\"144\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{32}{100}\\) = \\(\\frac{72}{100}\\)<br \/>\nThe representation of \\(\\frac{72}{100}\\) in the decimal for is: 0.72<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{32}{100}\\) and \\(\\frac{4}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{4}{10}\\) as the hundredths, we have to multiply \\(\\frac{4}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}\\) + \\(\\frac{32}{100}\\)<br \/>\n= \\(\\frac{40 + 32}{100}\\)<br \/>\n= \\(\\frac{72}{100}\\)<br \/>\nThe representation of \\(\\frac{72}{100}\\) in the decimal form is: 0.72<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{32}{100}\\) = \\(\\frac{72}{100}\\)<br \/>\nThe representation of \\(\\frac{72}{100}\\) in the decimal for is: 0.72<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-140.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 140\" width=\"157\" height=\"63\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{3}{100}\\) = \\(\\frac{83}{100}\\)<br \/>\nThe representation of \\(\\frac{83}{100}\\) in the decimal for is: 0.83<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{100}\\) and \\(\\frac{8}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{8}{10}\\) as the hundredths, we have to multiply \\(\\frac{8}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}\\) + \\(\\frac{3}{100}\\)<br \/>\n= \\(\\frac{80 + 3}{100}\\)<br \/>\n= \\(\\frac{83}{100}\\)<br \/>\nThe representation of \\(\\frac{83}{100}\\) in the decimal form is: 0.83<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{3}{100}\\) = \\(\\frac{83}{100}\\)<br \/>\nThe representation of \\(\\frac{83}{100}\\) in the decimal for is: 0.83<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-141.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 141\" width=\"143\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{15}{100}\\) = \\(\\frac{35}{100}\\)<br \/>\nThe representation of \\(\\frac{35}{100}\\) in the decimal for is: 0.35<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{15}{100}\\) and \\(\\frac{2}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{2}{10}\\) as the hundredths, we have to multiply \\(\\frac{2}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}\\) + \\(\\frac{15}{100}\\)<br \/>\n= \\(\\frac{20 + 15}{100}\\)<br \/>\n= \\(\\frac{35}{100}\\)<br \/>\nThe representation of \\(\\frac{35}{100}\\) in the decimal form is: 0.35<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{15}{100}\\) = \\(\\frac{35}{100}\\)<br \/>\nThe representation of \\(\\frac{35}{100}\\) in the decimal for is: 0.35<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-142.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 142\" width=\"151\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{45}{100}\\) = \\(\\frac{55}{100}\\)<br \/>\nThe representation of \\(\\frac{55}{100}\\) in the decimal for is: 0.55<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{45}{100}\\) and \\(\\frac{1}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{1}{10}\\) as the hundredths, we have to multiply \\(\\frac{1}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{10}\\) as hundredths in the fraction form is: \\(\\frac{10}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{10}{100}\\) + \\(\\frac{45}{100}\\)<br \/>\n= \\(\\frac{10 + 45}{100}\\)<br \/>\n= \\(\\frac{55}{100}\\)<br \/>\nThe representation of \\(\\frac{55}{100}\\) in the decimal form is: 0.55<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{45}{100}\\) = \\(\\frac{55}{100}\\)<br \/>\nThe representation of \\(\\frac{55}{100}\\) in the decimal for is: 0.55<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-143.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 143\" width=\"148\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{22}{100}\\) = \\(\\frac{92}{100}\\)<br \/>\nThe representation of \\(\\frac{92}{100}\\) in the decimal for is: 0.92<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{22}{100}\\) and \\(\\frac{7}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{7}{10}\\) as the hundredths, we have to multiply \\(\\frac{7}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{22}{100}\\)<br \/>\n= \\(\\frac{70 + 22}{100}\\)<br \/>\n= \\(\\frac{92}{100}\\)<br \/>\nThe representation of \\(\\frac{92}{100}\\) in the decimal form is: 0.92<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{22}{100}\\) = \\(\\frac{92}{100}\\)<br \/>\nThe representation of \\(\\frac{92}{100}\\) in the decimal for is: 0.92<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-144.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 144\" width=\"149\" height=\"70\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{17}{100}\\) = \\(\\frac{67}{100}\\)<br \/>\nThe representation of \\(\\frac{67}{100}\\) in the decimal for is: 0.67<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{17}{100}\\) and \\(\\frac{5}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{5}{10}\\) as the hundredths, we have to multiply \\(\\frac{5}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{17}{100}\\)<br \/>\n= \\(\\frac{50 + 17}{100}\\)<br \/>\n= \\(\\frac{67}{100}\\)<br \/>\nThe representation of \\(\\frac{67}{100}\\) in the decimal form is: 0.67<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{17}{100}\\) = \\(\\frac{67}{100}\\)<br \/>\nThe representation of \\(\\frac{67}{100}\\) in the decimal for is: 0.67<\/p>\n<p>Question 7.<br \/>\n0.6 + 0.25 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{85}{100}\\)<br \/>\nThe representation of 0.25 + 0.6 in the decimal form is: 0.85<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.6 and 0.25<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{25}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{6}{10}\\) as the hundredths, we have to multiply \\(\\frac{6}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{60}{100}\\) + \\(\\frac{25}{100}\\)<br \/>\n= \\(\\frac{60 + 25}{100}\\)<br \/>\n= \\(\\frac{85}{100}\\)<br \/>\nThe representation of \\(\\frac{85}{100}\\) in the decimal form is: 0.85<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{85}{100}\\)<br \/>\nThe representation of \\(\\frac{85}{100}\\) in the decimal for is: 0.85<\/p>\n<p>Question 8.<br \/>\n0.3 + 0.40 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{40}{100}\\) = \\(\\frac{70}{100}\\)<br \/>\nThe representation of 0.40 + 0.3 in the decimal form is: 0.70<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.3 and 0.40<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{40}{100}\\) and \\(\\frac{3}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{3}{10}\\) as the hundredths, we have to multiply \\(\\frac{3}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{30}{100}\\) + \\(\\frac{40}{100}\\)<br \/>\n= \\(\\frac{30 + 40}{100}\\)<br \/>\n= \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{40}{100}\\) = \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal for is: 0.70<\/p>\n<p>Question 9.<br \/>\n0.05 + 0.9 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{9}{10}\\) + \\(\\frac{5}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of 0.05 + 0.9 in the decimal form is: 0.95<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.05 and 0.9<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{5}{100}\\) and \\(\\frac{9}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{9}{10}\\) as the hundredths, we have to multiply \\(\\frac{9}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{9}{10}\\) as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{100}\\) + \\(\\frac{90}{100}\\)<br \/>\n= \\(\\frac{5 + 90}{100}\\)<br \/>\n= \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal form is: 0.95<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{9}{10}\\) + \\(\\frac{5}{100}\\) = \\(\\frac{95}{100}\\)<br \/>\nThe representation of \\(\\frac{95}{100}\\) in the decimal for is: 0.95<\/p>\n<p><strong>Find the sum.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-145.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals 145\" width=\"189\" height=\"59\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{41}{100}\\) + \\(\\frac{22}{100}\\) + \\(\\frac{3}{10}\\) = \\(\\frac{93}{100}\\)<br \/>\nThe representation of \\(\\frac{93}{100}\\) in the decimal for is: 0.93<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{41}{100}\\), \\(\\frac{22}{100}\\) and \\(\\frac{3}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{3}{10}\\) as the hundredths, we have to multiply \\(\\frac{3}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{41}{100}\\) + \\(\\frac{22}{100}\\) + \\(\\frac{30}{100}\\)<br \/>\n= \\(\\frac{41 + 22 + 30}{100}\\)<br \/>\n= \\(\\frac{93}{100}\\)<br \/>\nThe representation of \\(\\frac{93}{100}\\) in the decimal form is: 0.93<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{41}{100}\\) + \\(\\frac{22}{100}\\) = \\(\\frac{93}{100}\\)<br \/>\nThe representation of \\(\\frac{93}{100}\\) in the decimal for is: 0.93<\/p>\n<p>Question 11.<br \/>\n0.8 + 0.25 + 0.75 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{75}{100}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{180}{100}\\)<br \/>\nThe representation of 0.25 + 0.75 + 0.8 in the decimal for is: 1.80<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.8, 0.75 and 0.25<br \/>\nSo, convert the three decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{25}{100}\\) , \\(\\frac{8}{10}\\) and \\(\\frac{75}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{8}{10}\\)\u00a0 as the hundredths, we have to multiply \\(\\frac{}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{8}{10}\\) as hundredths in the fraction form is: \\(\\frac{80}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}\\) + \\(\\frac{25}{100}\\) + \\(\\frac{75}{100}\\)<br \/>\n= \\(\\frac{80 + 25 + 75}{100}\\)<br \/>\n= \\(\\frac{180}{100}\\)<br \/>\nThe representation of \\(\\frac{180}{100}\\) in the decimal form is: 1.80<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{25}{100}\\) + \\(\\frac{75}{100}\\) = \\(\\frac{180}{100}\\)<br \/>\nThe representation of \\(\\frac{180}{100}\\) in the decimal for is: 1.80<\/p>\n<p>Question 12.<br \/>\n<strong>Patterns<\/strong><br \/>\nDescribe and complete the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-185.jpg\" alt=\"\" width=\"200\" height=\"265\" \/><\/p>\n<p>Answer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{9}{100}\\) = \\(\\frac{19}{100}\\)<br \/>\nThe representation of \\(\\frac{19}{100}\\) in the decimal for is: 0.19<\/p>\n<p>The representation of the sum in the fraction form is:<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{18}{100}\\) = \\(\\frac{38}{100}\\)<br \/>\nThe representation of \\(\\frac{38}{100}\\) in the decimal for is: 0.38<\/p>\n<p>The representation of the sum in the fraction form is:<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{27}{100}\\) = \\(\\frac{57}{100}\\)<br \/>\nThe representation of \\(\\frac{114}{100}\\) in the decimal for is: 0.57<br \/>\nNow,<br \/>\nWhwn we add all the three results, we will get<br \/>\nThe last result&#8217;s representation in the fraction form is:<br \/>\n\\(\\frac{19}{100}\\) + \\(\\frac{38}{100}\\) + \\(\\frac{57}{100}\\) = \\(\\frac{114}{100}\\)<br \/>\nThe last result&#8217;s representation in the decimal form is:<br \/>\n0.19 + 0.38 + 0.57 = 1.14<\/p>\n<p>Question 13.<br \/>\nWhich One Doesn\u2019t Belong? Which expression does not belong with the other three?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-147.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 147\" width=\"261\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nLet the Expressions be named as A, B, C, and D<br \/>\nThe given expressions are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-147.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 147\" width=\"261\" height=\"131\" \/><br \/>\nFrom the above expressions, Expression D does not belong with the other three<\/p>\n<p>Explanation:<br \/>\nLet the expressions be named\u00a0 A, B, C, and D<br \/>\nSo,<br \/>\nThe expressions are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-147.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 147\" width=\"261\" height=\"131\" \/><br \/>\nSo, from the above expressions,<br \/>\nWe can observe that the Expression D does not belong with the other three<\/p>\n<p>Question 14.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nIn an aquarium, \\(\\frac{5}{10}\\) of the fish are red and \\(\\frac{3}{100}\\) of the fish are yellow. What fraction of the fish is more?<br \/>\nAnswer: The fraction of the fish that is red is more in the aquarium<\/p>\n<p>Explanation:<br \/>\nIt is given that in the aquarium,<br \/>\nThere are \\(\\frac{5}{10}\\) of the fish are red and \\(\\frac{3}{100}\\) of the fish are yellow.<br \/>\nSo, for comparison, we have to equal the denominators<br \/>\nSo,<br \/>\n\\(\\frac{5}{10}\\) has to be multiplied by 10 to make the denominator of \\(\\frac{5}{10}\\) as hundredths<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo, when we compare the fishes that are red and yellow,<br \/>\nWe will get that<br \/>\nRed fishes &gt; Yellow fishes<br \/>\nhence, from the above,<br \/>\nWe can conclude that the red fishes are more than yellow fishes in the aquarium<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhich gecko is longer? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-148.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 148\" width=\"275\" height=\"237\" \/><br \/>\nAnswer: Leopard Gecko is longer<\/p>\n<p>Explanation:<br \/>\nIt is given that<br \/>\nThe total length of Leopard Gecko is: 0.05 + 0.06 = 0.11 m = \\(\\frac{11}{100}\\)<br \/>\nThe length of Adult Electric Blue Gecko is: \\(\\frac{7}{100}\\)<br \/>\nSo, from the above,<br \/>\nWe can say that the numerators of both the fractions are equal.<br \/>\nSo, when we compare,<br \/>\nWe can see that leopard gecko is longer than adult Electric Blue Gecko<br \/>\nHence, from the above,<br \/>\nWe can conclude that the Leopard Gecko is longer than the Adult Electric Blue Gecko<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 16.<br \/>\n38 \u00f7 4<br \/>\nAnswer: 38 \u00f7 4 = 9 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n38 \u00f7 4 = ( 32 + 4 ) \u00f7 4<br \/>\n= ( 32 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 8 + 1<br \/>\n= 9 R 2<br \/>\nHence, 38 \u00f7 4 = 9 R 2<\/p>\n<p>Question 17.<br \/>\n641 \u00f7 9<br \/>\nAnswer: 641 \u00f7 9 = 71 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n641 \u00f7 9 = ( 630 + 9 ) \u00f7 9<br \/>\n= ( 630 \u00f7 9 ) + ( 9 \u00f7 9 (<br \/>\n= 70 + 1<br \/>\n= 71 R 2<br \/>\nHence, 641 \u00f7 9 = 71 R 2<\/p>\n<p>Question 18.<br \/>\n52 \u00f7 7<br \/>\nAnswer: 52 \u00f7 7 = 7 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n52 \u00f7 7 = (42 + 7 ) \u00f7 7<br \/>\n= ( 42 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 6 + 1<br \/>\n= 7 R 3<br \/>\nHence, 52 \u00f7 7 = 7 R 3<\/p>\n<h3><a id=\"Lesson_10.6_Fractions,_Decimals_and_Money\"><\/a>Lesson 10.6 Fractions, Decimals and Money<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Shade the model to show each money moment.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-186.jpg\" alt=\"\" width=\"548\" height=\"320\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-186.jpg 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-186-300x175.jpg 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Answer: Here, we have taken the reference of 1 dollar and find out the amount by them that is equal to 1 dollar<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = 0.25 dollar<br \/>\n1 dime = 0.1 dollar<br \/>\n1 nickel = 0.05 dollar<br \/>\n1 penny = 0.01 dollar<br \/>\nHence, the above values are marked in the above-given model.<\/p>\n<p><strong>Reasoning<\/strong><\/p>\n<p>How can you write each money amount as a fraction and a decimal in terms of dollars?<\/p>\n<p>Answer:<br \/>\nThe representation of the Quarter, in the dollar in the fraction form is: \\(\\frac{25}{100}\\) dollar<br \/>\nThe representation of the Quarter, in the dollar in the decimal form is: 0.25<\/p>\n<p>The representation of the dime, in the dollar in the fraction form is: \\(\\frac{10}{100}\\) dollar<br \/>\nThe representation of the dime, in the dollar in the decimal form is: 0.10<\/p>\n<p>The representation of the nickel, in the dollar in the fraction form is: \\(\\frac{5}{100}\\) dollar<br \/>\nThe representation of the nickel, in the dollar in the decimal form is: 0.05<\/p>\n<p>The representation of the penny, in the dollar in the fraction form is: \\(\\frac{1}{100}\\) dollar<br \/>\nThe representation of the penny, in the dollar in the decimal form is: 0.01<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = 0.25 dollar<br \/>\n1 dime = 0.1 dollar<br \/>\n1 nickel = 0.05 dollar<br \/>\n1 penny = 0.01 dollar<br \/>\nSo, all the money moments are represented in the terms of dollars.<br \/>\nSo, the representation of all the money moments in terms of dollars in the fraction and the decimal forms is:<br \/>\nThe representation of the Quarter, in the dollar in the fraction form is: \\(\\frac{25}{100}\\) dollar<br \/>\nThe representation of the Quarter, in the dollar in the decimal form is: 0.25<\/p>\n<p>The representation of the dime, in the dollar in the fraction form is: \\(\\frac{10}{100}\\) dollar<br \/>\nThe representation of the dime, in the dollar in the decimal form is: 0.10<\/p>\n<p>The representation of the nickel, in the dollar in the fraction form is: \\(\\frac{5}{100}\\) dollar<br \/>\nThe representation of the nickel, in the dollar in the decimal form is: 0.05<\/p>\n<p>The representation of the penny, in the dollar in the fraction form is: \\(\\frac{1}{100}\\) dollar<br \/>\nThe representation of the penny, in the dollar in the decimal form is: 0.01<\/p>\n<p><strong>Think and Grow: Fractions, Decimals, and Money<\/strong><\/p>\n<p>You can use a dollar sign and a decimal point to write a money amount. Just as a decimal point separates ones from tenths and hundredths, it also separates whole dollars from cents.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-150.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 150\" width=\"664\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-150.png 664w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-150-300x118.png 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>Use the total money amount to complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-187.jpg\" alt=\"\" width=\"638\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-187.jpg 638w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-187-300x144.jpg 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Find the total money amount. Then write the amount as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-152.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 152\" width=\"153\" height=\"90\" \/><br \/>\nAnswer: The total amount of money is: $0.66<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 2 Quarters, 3 nickels, and 1 penny<br \/>\nSo,<br \/>\nThe total amount of money = ( 2 \u00d7 0.25 ) + ( 3 \u00d7 0.05 ) + ( 1 \u00d7 0.01 )<br \/>\n= 0.50 + 0.15 + 0.01<br \/>\n= 0.06<br \/>\nHence,<br \/>\nThe total amount of money is: $0.06<br \/>\nThe representation of $0.06 in the fraction form is: \\(\\frac{6}{100}\\) dollar<br \/>\nThe representation of $0.06 in the decimal form is: $0.06<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-153.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 153\" width=\"249\" height=\"113\" \/><br \/>\nAnswer: The total amount of money is: $2.30<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\nThe given money is: 2 dollars, 1 Quarter, and 1 nickel<br \/>\nSo,<br \/>\nThe total amount of money = ( 2 \u00d7 1 ) + ( 1 \u00d7 0.25 ) + ( 1 \u00d7 0.05 )<br \/>\n= 2 + 0.25 + 0.05<br \/>\n= 2.30<br \/>\nHence,<br \/>\nThe total amount of money is: $2.30<br \/>\nThe representation of $2.30 in the fraction form is: 2\\(\\frac{30}{100}\\) dollar<br \/>\nThe representation of $2.30 in the decimal form is: $2.30<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Find the total money amount. Then write the amount as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-154.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 154\" width=\"289\" height=\"99\" \/><br \/>\nAnswer: The total amount of money is: $0.46<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 dime = $0.10<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 6 pennies, 1 Quarter, 1 dime, and 1 nickel<br \/>\nSo,<br \/>\nThe total amount of money = ( 6 \u00d7 0.01 ) + ( 1 \u00d7 0.25 ) + ( 1 \u00d7 0.05 ) + ( 1 \u00d7 0.10 )<br \/>\n= 0.06 + 0.25 + 0.05 + 0.10<br \/>\n= 0.46<br \/>\nHence,<br \/>\nThe total amount of money is: $0.46<br \/>\nThe representation of $0.46 in the fraction form is: \\(\\frac{46}{100}\\) dollar<br \/>\nThe representation of $0.46 in the decimal form is: $0.46<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-155.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 155\" width=\"298\" height=\"113\" \/><br \/>\nAnswer: The total amount of money is: $0.46<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n4 Quarters = 1 dollar<br \/>\nThe given money is: 4 Quarters, 1 dollar, and 1 nickel<br \/>\nSo,<br \/>\nThe total amount of money = ( 1 \u00d7 1 ) + ( 4 \u00d7 0.25 ) + ( 1 \u00d7 0.05 )<br \/>\n= 1 + 1 + 0.05<br \/>\n= 2.05<br \/>\nHence,<br \/>\nThe total amount of money is: $2.05<br \/>\nThe representation of $2.05 in the fraction form is: 2\\(\\frac{5}{100}\\) dollar<br \/>\nThe representation of $2.05 in the decimal form is: $2.05<\/p>\n<p><strong>Write the fraction or mixed number as a money amount and as a decimal.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{53}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{53}{100}\\) as the total amount of money is: $0.53<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{53}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.53<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{4}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{4}{100}\\) as the total amount of money is: $0.04<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{4}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.04<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{100}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{100}{100}\\) as the total amount of money is: $1<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{100}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $1<\/p>\n<p>Question 8.<br \/>\n1\\(\\frac{22}{100}\\)<br \/>\nAnswer: The representation of 1\\(\\frac{22}{100}\\) as the total amount of money is: $1.22<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 1\\(\\frac{22}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $1.22<\/p>\n<p>Question 9.<br \/>\n1\\(\\frac{18}{100}\\)<br \/>\nAnswer: The representation of 1\\(\\frac{18}{100}\\) as the total amount of money is: $1.18<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 1\\(\\frac{18}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $1.18<\/p>\n<p>Question 10.<br \/>\n1\\(\\frac{70}{100}\\)<br \/>\nAnswer: The representation of 1\\(\\frac{70}{100}\\) as the total amount of money is: $1.70<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 1\\(\\frac{70}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $1.70<\/p>\n<p>Question 11.<br \/>\nYou \ufb01nd 1 dime, 3 nickels, and 2 pennies on the ground. How much money do you \ufb01nd? Write your answer in three different ways.<br \/>\nAnswer: The total amount of money you find on the ground is: $0.27<\/p>\n<p>Explanation:<br \/>\nThe given amount that you find on the ground is: 1 dime, 3 nickels, and 2 pennies<br \/>\nWe know that,<br \/>\n1 dime = 0.10 dollars<br \/>\n1 nickel = $0.05 dollars<br \/>\n1 penny = $0.01 dollars<br \/>\nSo,<br \/>\nThe total amount of money you find on the ground = ( 1 \u00d7 0.10 ) + ( 3 \u00d7 0.05 ) + (2 \u00d7 0.01 )<br \/>\n= 0.10 + 0.15 + 0.02<br \/>\n= 0.27<br \/>\nHence from the above,<br \/>\nWe can conclude that the three ways of representing the total amount of money is:<br \/>\nThe total amount of money you find on the ground is: $0.27<br \/>\nThe representation of the total amount of money in the fraction form is: \\(\\frac{27}{100}\\) dollar<br \/>\nThe representation of the total amount of money in the decimal form is: $0.27<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend has three $1 bills and 2 pennies. Your friend writes, &#8220;I have $ 3.2.&#8221; Is your friend correct? Explain.<br \/>\nAnswer: No, your friend is wrong<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend has three $1 bills and 2 pennies.<br \/>\nSo,<br \/>\nThe given amount your friend has: 3 $1 bills and 2 pennies<br \/>\nWe know that,<br \/>\n1 penny = 0.01 dollars<br \/>\nSo,<br \/>\nThe total amount of money your friend has = ( 3 \u00d7 1 ) + ( 2 \u00d7 0.01 )<br \/>\n= 3 + 0.02<br \/>\n= 3.02<br \/>\nHence,<br \/>\nThe total amount of money your friend has: $3.02 dollars or 3 dollars and 2 pennies<br \/>\nBut, your friend has written $3.02 as $3.20 which means 3 dollars and 2 dimes<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is wrong<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have \\(\\frac{1}{4}\\) dollar in coins. Draw two possible groups of coins that you could have.<br \/>\nAnswer: The possible group of coins that you could have for \\(\\frac{1}{4}\\) is: Quarter<\/p>\n<p>Explanation:<br \/>\nIt is given that you have \\(\\frac{1}{4}\\) dollar in coins.<br \/>\nBut, we have al, the money moments in terms of 100.<br \/>\nSo, to make the denominator of \\(\\frac{1}{4}\\) 100, multiply \\(\\frac{1}{4}\\) by 25<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{1}{4}\\) as hundredths in the fraction form is: \\(\\frac{25}{100}\\)<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\nHence, from the above,<br \/>\nWe can conclude that the possible group of coins that you could have for \\(\\frac{1}{4}\\) is: Quarter<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nNewton has \\(\\frac{85}{100}\\) dollar. Can he buy the spinning toy? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-156.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 156\" width=\"203\" height=\"148\" \/><br \/>\nWrite the fraction as a money amount.<br \/>\n\\(\\frac{85}{100}\\) as a money amount is $0.85.<br \/>\nCompare the amount of money Newton has to the price of the toy.<br \/>\nNewton can&#8217;t buy the spinning toy.<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton has \\(\\frac{85}{100}\\) dollar<br \/>\nSo,<br \/>\nThe amount of money that Newton has in the decimal form is: $0.85<br \/>\nBut, it is also given that<br \/>\nThe cost of spinning toy is: \\(\\frac{99}{100}\\) dollar<br \/>\nSo, for comparison, we have to make either the numerators or the denominators equal.<br \/>\nHere, both the denominators are equal.<br \/>\nSo, we can compare both the fractions directly.<br \/>\nSo, by comparing, we get,<br \/>\n0.85 &lt; 0.99<br \/>\nHence,<br \/>\nWe can conclude that Newton can&#8217;t buy the spinning toy.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nDescartes has \\(\\frac{76}{100}\\) dollar. Can he buy the bouncy ball? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-156.1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 156.1\" width=\"186\" height=\"109\" \/><br \/>\nAnswer: Yes, he can buy the bouncy ball<\/p>\n<p>Explanation:<br \/>\nIt is given that Descartes has \\(\\frac{76}{100}\\) dollar<br \/>\nSo,<br \/>\nThe amount of money that Descartes has in the decimal form is: $0.76<br \/>\nBut, it is also given that<br \/>\nThe cost of bouncy ball is: \\(\\frac{50}{100}\\) dollar<br \/>\nSo, for comparison, we have to make either the numerators or the denominators equal.<br \/>\nHere, both the denominators are equal.<br \/>\nSo, we can compare both the fractions directly.<br \/>\nSo, by comparing, we get,<br \/>\n0.76 &gt; 0.50<br \/>\nHence,<br \/>\nWe can conclude that Descartes can buy the bouncy ball.<\/p>\n<p>Question 15.<br \/>\nYou throw 3 dimes, 3 nickels, and 8 pennies into a fountain. Your friend throws 1 quarter, 4 nickels, and 5 pennies. Who throws a greater amount of money into the fountain?<br \/>\nAnswer: You throw a greater amount of money into the fountain when compared to your friend.<\/p>\n<p>Explanation:<br \/>\nIt is given that you throw 3 dimes, 3 nickels, and 8 pennies and your friend throws 1 quarter, 4 nickels, and 5 pennies<br \/>\nSo,<br \/>\nThe amount that you have is: 3 dimes, 3 nickels, and 8 pennies<br \/>\nThe amount that your friend has is: 1 quarter, 4 nickels, and 5 pennies<br \/>\nWe know that,<br \/>\n1 quarter = $0.25<br \/>\n1 dime = $0.10<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nSo,<br \/>\nThe total amount of money you have = ( 3 \u00d7 0.10 ) + ( 3 \u00d7 0.05 ) + ( 8 \u00d7 0.01 )<br \/>\n= 0.30 + 0.15 + 0.08<br \/>\n= $0.53<br \/>\nThe total amount of money your friend has = ( 1 \u00d7 0.25 ) + ( 4 \u00d7 0.05 ) + ( 5 \u00d7 0.01 )<br \/>\n= 0.25 + 0.20 + 0.05<br \/>\n= $0.50<br \/>\nNow,<br \/>\nThe representation of the amount of money you have in the fraction form is: \\(\\frac{53}{100}\\) dollars<br \/>\nThe representation of the amount of money your friend has in the fraction form is: \\(\\frac{50}{100}\\) dollars<br \/>\nSo, by comparing these two amounts,<br \/>\nWe can conclude that you have a greater amount of money than your friend<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nComplete the table. Which piggy bank has the greatest amount of money? the least amount of money?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188.jpg\" alt=\"\" width=\"481\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188.jpg 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188-300x87.jpg 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nAnswer:<br \/>\nThe piggy bank which has the greatest amount of money is: B<br \/>\nthe piggy bank which has the least amount of money is: C<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188.jpg\" alt=\"\" width=\"481\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188.jpg 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-188-300x87.jpg 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nFrom the given table,<br \/>\nThe amount of money present in all the three piggy banks is: Quarters, Dimes, Nickels,\u00a0 and pennies<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 dime = $0.10<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nSo,<br \/>\nThe total amount of money that all the three piggy banks have:<br \/>\nA: ( 3 \u00d7 0.25 ) + ( 1 \u00d7 0.10 ) + ( 4 \u00d7 0.05 ) + ( 2 \u00d7 0.01 ) = $1.07<br \/>\nB: ( 1 \u00d7 0.25 ) + ( 7 \u00d7 0.10 ) + ( 3 \u00d7 0.05 ) + ( 0 \u00d7 0.01 ) = $1.10<br \/>\nC: ( 2 \u00d7 0.25 ) + ( 0 \u00d7 0.10 ) + ( 8 \u00d7 0.05 ) + ( 11 \u00d7 0.01 ) = $1.01<br \/>\nHence, from the above,<br \/>\nwe can conclude that<br \/>\nThe piggy bank that has the greatest amount of money is: B<br \/>\nThe piggy bank that has the least amount of money is: C<\/p>\n<h3><a id=\"Fractions,_Decimals_and_Money_Homework_&amp;_Practice_10.6\"><\/a>Fractions, Decimals and Money Homework &amp; Practice 10.6<\/h3>\n<p><strong>Write the money amount as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n$ 0.53<br \/>\nAnswer: The representation of $0.53 as the total amount of money in the fraction form is: \\(\\frac{53}{100}\\) dollar<\/p>\n<p>Explanation:<br \/>\nThe given amount of money in the decimal form is: $0.53<br \/>\nThe given decimal form will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the fraction form is: \\(\\frac{53}{100}\\) dollars<br \/>\nThe total amount of money in the decimal form is: $0.53<\/p>\n<p>Question 2.<br \/>\n$ 0.40<br \/>\nAnswer: The representation of $0.40 as the total amount of money in the fraction form is: \\(\\frac{40}{100}\\) dollar<\/p>\n<p>Explanation:<br \/>\nThe given amount of money in the decimal form is: $0.40<br \/>\nThe given decimal form will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the fraction form is: \\(\\frac{40}{100}\\) dollars<br \/>\nThe total amount of money in the decimal form is: $0.40<\/p>\n<p>Question 3.<br \/>\n$1.01<br \/>\nAnswer: The representation of $1.01 as the total amount of money in the fraction form is: 1\\(\\frac{1}{100}\\) dollar<\/p>\n<p>Explanation:<br \/>\nThe given amount of money in the decimal form is: $1.01<br \/>\nThe given decimal form will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the fraction form is: 1\\(\\frac{1}{100}\\) dollars<br \/>\nThe total amount of money in the decimal form is: $1.01<\/p>\n<p><strong>Find the total money amount. Then write the amount as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-158.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 158\" width=\"214\" height=\"95\" \/><br \/>\nAnswer: The total amount of money is: $0.65<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 dime = $0.10<br \/>\nThe given money is: 1 Quarter, 2 dimes, and 4 nickel<br \/>\nSo,<br \/>\nThe total amount of money = ( 1 \u00d7 0.25 ) + ( 4 \u00d7 0.05 ) + ( 2 \u00d7 0.10 )<br \/>\n=\u00a0 0.25 + 0.20 + 0.20<br \/>\n= 0.65<br \/>\nHence,<br \/>\nThe total amount of money is: $0.65<br \/>\nThe representation of $0.65 in the fraction form is: \\(\\frac{65}{100}\\) dollar<br \/>\nThe representation of $0.65 in the decimal form is: $0.65<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-159.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 159\" width=\"305\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-159.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-159-300x106.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer: The total amount of money is: $2.13<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 dime = $0.10<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 3 pennies, 1 dime, and 2 dollars<br \/>\nSo,<br \/>\nThe total amount of money = ( 3 \u00d7 0.01 ) + ( 2 \u00d7 1 ) + ( 1 \u00d7 0.10 )<br \/>\n= 0.03 + 2 + 0.10<br \/>\n= 2.13<br \/>\nHence,<br \/>\nThe total amount of money is: $2.13<br \/>\nThe representation of $2.13 in the fraction form is: 2\\(\\frac{13}{100}\\) dollar<br \/>\nThe representation of $2.13 in the decimal form is: $2.13<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-160.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 160\" width=\"204\" height=\"113\" \/><br \/>\nAnswer: The total amount of money is: $0.92<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 dime = $0.10<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 2 pennies, 2 Quarters, 4 dimes<br \/>\nSo,<br \/>\nThe total amount of money = ( 2 \u00d7 0.01 ) + ( 2 \u00d7 0.25 ) + ( 4 \u00d7 0.10 )<br \/>\n= 0.02 +0.50 + 0.40<br \/>\n= 0.92<br \/>\nHence,<br \/>\nThe total amount of money is: $0.92<br \/>\nThe representation of $0.92 in the fraction form is: \\(\\frac{92}{100}\\) dollar<br \/>\nThe representation of $0.92 in the decimal form is: $0.92<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-161.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 161\" width=\"304\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-161.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-161-300x106.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer: The total amount of money is: $3.15<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 dime = $0.10<br \/>\nThe given money is: 4 Quarters, 2 dollars, 1 dime, and 1 nickel<br \/>\nSo,<br \/>\nThe total amount of money = ( 2 \u00d7 1 ) + ( 4 \u00d7 0.25 ) + ( 1 \u00d7 0.05 ) + ( 1 \u00d7 0.10 )<br \/>\n= 2 + 1 + 0.05 + 0.10<br \/>\n= 3.15<br \/>\nHence,<br \/>\nThe total amount of money is: $3.15<br \/>\nThe representation of $3.15 in the fraction form is: 3\\(\\frac{15}{100}\\) dollar<br \/>\nThe representation of $3.15 in the decimal form is: $3.15<\/p>\n<p><strong>Write the fraction or mixed number as a money amount and as a decimal.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{87}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{87}{100}\\) as the total amount of money is: $0.87<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{87}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.87<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{12}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{12}{100}\\) as the total amount of money is: $0.12<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{12}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.12<\/p>\n<p>Question 10.<br \/>\n1\\(\\frac{9}{100}\\)<br \/>\nAnswer: The representation of 1\\(\\frac{9}{100}\\) as the total amount of money is: $1.09<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 1\\(\\frac{9}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $1.09<\/p>\n<p>Question 11.<br \/>\nYou find 3 quarters, 2 nickels, and 1 penny in your backpack. How much money do you find? Write your answer in three different ways.<br \/>\nAnswer: The amount of money you find is: $0.86<\/p>\n<p>Explanation:<br \/>\nIt is given that you find 3 quarters, 2 nickels, and 1 penny in your backpack<br \/>\nSo,<br \/>\nThe amount of money you have is: 3 quarters, 2 nickels, and 1 penny<br \/>\nWe know that,<br \/>\n1 quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nSo,<br \/>\nThe total amount of money you have = ( 3 \u00d7 0.25 ) + ( 2 \u00d7 0.05 ) + ( 1 \u00d7 0.01 )<br \/>\n= 0.75 + 0.10 + 0.01<br \/>\n= 0.86<br \/>\nHence,<br \/>\nThe total amount of money you have is: $0.86<br \/>\nThe total amount of money you have in the fraction form is: \\(\\frac{86}{100}\\)<br \/>\nThe total amount of money you have in the decimal form is: $0.86<\/p>\n<p>Question 12.<br \/>\nWhich One Doesn&#8217;t Belong? Which one does not belong with the other three?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-162.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 162\" width=\"599\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-162.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-162-300x44.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\nAnswer:<br \/>\nLet the amounts be named A, B, C, and D<br \/>\nSo, from the amounts,<br \/>\nwe can say that A) does not belong to the other three.<\/p>\n<p>Explanation:<br \/>\nLe the amounts named as A, B, C, and D<br \/>\nNow,<br \/>\nA) 3 pennies\u00a0 B) \\(\\frac{3}{10}\\)\u00a0 C) 0.30 dollars\u00a0 D) \\(\\frac{30}{100}\\)<br \/>\nWe know that,<br \/>\n1 penny = $0.01<br \/>\nSo,<br \/>\n3 pennies = $0.03<br \/>\nHence, from the above,<br \/>\nwe can conclude that A) does not belong to the other three.<\/p>\n<p>Question 13.<br \/>\nReasoning<br \/>\nWould you rather have \\(\\frac{2}{10}\\) of a dollar or 6 nickels? Explain.<br \/>\nAnswer: You would rather have 6 nickels<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{2}{10}\\) of a dollar<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nThe representation of \\(\\frac{20}{100}\\) in the decimal form is: 0.20<br \/>\nWe know that,<br \/>\n1 nickel = $0.05<br \/>\nSo,<br \/>\n6 nickels = 6 \u00d7 0.05 = $0.30<br \/>\nNow,<br \/>\nWhen we compare the given fraction and 6 nickels, w can observe that<br \/>\n6 nickels &gt; \\(\\frac{2}{10}\\) of a dollar<br \/>\nHence, from the above,<br \/>\nwe can conclude that you would have to rather have 6 nickels than \\(\\frac{2}{10}\\) of a dollar<\/p>\n<p>Question 14.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nNewton has \\(\\frac{46}{100}\\) dollar. Can he buys the key chain ? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-163.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 10 Relate Fractions and Decimals 163\" width=\"164\" height=\"176\" \/><br \/>\nAnswer: No, Newton can&#8217;t buy the key chain<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton has \\(\\frac{46}{10}\\) dollar<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{46}{10}\\) in the decimal form is: $0.46<br \/>\nIt is also given that,<br \/>\nThe cost of the key chain is: $0.49<br \/>\nNow,<br \/>\nWhen we compare the fractions, we have to equate either the numerators or the denominators.<br \/>\nHere, both the denominators are equal.<br \/>\nSo,<br \/>\nWhen we compare, we will observe<br \/>\n0.46 &lt; 0.49<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton can&#8217;t buy the key chain<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nDescartes has $1. Can he buy 2 key chains? Explain how you know without calculating.<br \/>\nAnswer: Yes, Descartes can buy 2 key chains<\/p>\n<p>Explanation:<br \/>\nFrom the above problem,<br \/>\nThe cost of 1 key chain is: $0.49<br \/>\nIt is given that Descartes has $1 and he wants to buy the 2 key chains<br \/>\nSo,<br \/>\nThe cost of 2 key chains = 0.49 + 0.49 = $0.98<br \/>\nBut, Descartes has $1<br \/>\nSo,<br \/>\nThe money that Descartes left = 1 &#8211; 0.98 = 0.02<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes can buy the 2 key chains<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-164.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 164\" width=\"148\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{24}{100}\\) + \\(\\frac{35}{100}\\) = \\(\\frac{59}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{24}{100}\\) and \\(\\frac{35}{100}\\)<br \/>\nSo, for the addition of the fractions, we have to equate either both the numerators or both the denominators.<br \/>\nHere, both the denominators are equal.<br \/>\nHence,<br \/>\n\\(\\frac{24}{100}\\) + \\(\\frac{35}{100}\\) = \\(\\frac{59}{100}\\)<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-165.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 165\" width=\"134\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{10}{8}\\) + \\(\\frac{3}{8}\\) = \\(\\frac{13}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{10}{8}\\) and \\(\\frac{3}{8}\\)<br \/>\nSo, for the addition of the fractions, we have to see whether the denominators are equal or the numerators are equal.<br \/>\nHere, both the denominators are equal.<br \/>\nHence,<br \/>\n\\(\\frac{10}{8}\\) + \\(\\frac{3}{8}\\) = \\(\\frac{13}{8}\\)<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-166.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 166\" width=\"169\" height=\"70\" \/><br \/>\nAnswer: \\(\\frac{1}{10}\\) + \\(\\frac{3}{10}\\) + \\(\\frac{6}{10}\\) = \\(\\frac{10}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{10}\\), \\(\\frac{3}{10}\\) and \\(\\frac{6}{10}\\)<br \/>\nSo, in addition,<br \/>\nWe have to equate either both the numerators or both the denominators.<br \/>\nHere,<br \/>\nThe denominators of all the fractions are equal.<br \/>\nHence,<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{3}{10}\\) + \\(\\frac{6}{10}\\) = \\(\\frac{10}{10}\\)<\/p>\n<h3><a id=\"Lesson_10.7_Operations_with_Money\"><\/a>Lesson 10.7 Operations with Money<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Draw bills and coins to solve each problem. How much do all of the toys cost?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-167.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 167\" width=\"197\" height=\"152\" \/><\/p>\n<ol>\n<li>You pay for one of the toys with a $10 bill. What is your change?<\/li>\n<\/ol>\n<p>Answer:<br \/>\nLet the toy be an Action figure.<br \/>\nNow,<br \/>\nIt is given that the cost of an Action figure is: $5.50<br \/>\nIt is also given that you pay for one of the toys with a $10 bill<br \/>\nSo,<br \/>\nYour change = 10 &#8211; 5.50 = $4.50<br \/>\nHence, from the above,<br \/>\nWe can conclude that the change is: $4.50<\/p>\n<p>2. You buy three of the same toys. How much do the toys cost in all?<\/p>\n<p>Answer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-167.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 167\" width=\"197\" height=\"152\" \/><br \/>\nFrom the given table,<br \/>\nThe cost of an Action figure is: $5.50<br \/>\nThe cost of a whistle is: $1.25<br \/>\nThe cost of a Board game is: $3.75<br \/>\nSo,<br \/>\nThe cost of 3 Action figures = 3 \u00d7 5.50 = $16.50<br \/>\nThe cost of 3 whistles = 3 \u00d7 1.25 = $3.75<br \/>\nThe cost of 3 board games = 3 \u00d7 3.75 = $11.15<\/p>\n<p>3. You and your friend put your money together to buy some of the toys. The cashier gives you a $4.50 change. You want to share the change equally. How much money does each of you get?<\/p>\n<p>Answer: It is given that you and your friend put your money together to buy some of the toys. It is also given that the cashier gives you a $4.50 change.<br \/>\nSo,<br \/>\nThe amount that should be shared equally between you and your friend = 4.50 \u00f7 2<br \/>\n= (4 \u00f7 2 ) + ( 0.50 \u00f7 2 )<br \/>\n= 2 + 0.25<br \/>\n= 2.25<br \/>\nHence, from the above,<br \/>\nwe can conclude that the amount that should be shared equally between you and your friend is: $2.25<\/p>\n<p><strong>Precision<\/strong><br \/>\nCompare your work to your partner\u2019s.<\/p>\n<p><strong>Think and Grow:<\/strong><br \/>\nNewton has $1.35. Descartes has $1.25. How much money do they have altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-168.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 168\" width=\"246\" height=\"205\" \/><br \/>\nAnswer:<br \/>\nIt is given that Newton has $1.35 and Descartes has $1.25.<br \/>\nSo,<br \/>\nThe total amount of money they have altogether = $1.35 + $1.25<br \/>\n= $2.60<br \/>\nHence, from the above,<br \/>\nWe can conclude that they have $2.60 altogether.<\/p>\n<p><strong>Example<\/strong><br \/>\nNewton has $2.45. He spends $1.10. How much money does he have left?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-189.jpg\" alt=\"\" width=\"385\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-189.jpg 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-189-300x187.jpg 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><br \/>\nHe has $1.35 left.<br \/>\n<strong>Example<\/strong><br \/>\nThree friends each have$0.60. How much money do they have in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-170.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 170\" width=\"228\" height=\"197\" \/><br \/>\nAnswer: It is given that the three friends each have $0.60<br \/>\nSo,<br \/>\nthe total amount of money that the three friends have = 0.60 \u00d7 3 = $1.80<br \/>\nHence, from the above,<br \/>\nWe can conclude that they have $1.80 in all.<br \/>\n<strong>Example<\/strong><br \/>\nYou and a friend have a total of $ 1.48. You want to share the money equally. How much money should each of you get?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-171.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 171\" width=\"284\" height=\"146\" \/><br \/>\nAnswer: It is given that you and a friend have a total of $1.48<br \/>\nIt is also given that you want to share the money equally<br \/>\nSo,<br \/>\nThe amount of money that you and your friend share the money equally = 1.48 \u00f7 2<br \/>\n= ( 1 \u00f7 2 ) + ( 0.48 \u00f7 2 )<br \/>\n= 0.5 + 0.24<br \/>\n= 0.74<br \/>\nHence, from the above,<br \/>\nWe can conclude that you each should get $0.74.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nYou pay a total of $2.25 for 3 granola bars. How much money does each bar cost? Draw bills and coins to solve.<br \/>\nAnswer: The amount of money does each bar cost is: $0.75<\/p>\n<p>Explanation:<br \/>\nIt is given that you pay a total of $2.25 for 3 granola bars<br \/>\nSo,<br \/>\nThe amount of money that each bar cost = The total cost of 3 granola bars \u00f7 3<br \/>\n= 2.25 \u00f7 3<br \/>\n= 0.75<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money does each ba cost is: $0.75<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Question 2.<br \/>\nYou buy 2 stamps. Each stamp costs $0.49. How much money do you spend in all?<br \/>\nAnswer: The total amount of money you spend is: $0.98<\/p>\n<p>Explanation:<br \/>\nIt is given that you buy 2 stamps and each stamp costs $0.49<br \/>\nSo,<br \/>\nThe total amount of money you spent on buying stamps = The cost of each stamp \u00d7 2<br \/>\n= 0.49 \u00d7 2<br \/>\n= $0.98<br \/>\nHence, from the above,<br \/>\nwe can conclude that the amount of money you spent on buying the 2 stamps is: $0.98<\/p>\n<p>Question 3.<br \/>\nNewton has $2.50. He spends $1.07 on a flying disk. How much money does Newton have left?<br \/>\nAnswer: The amount of money does Newton have left is: $1.43<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton has $2.50 and he spends $1.07 on a flying disk<br \/>\nSo,<br \/>\nThe amount of money does Newton have left = The amount of money that Newton has &#8211; The amount of money that Newton spent<br \/>\n= 2.50 &#8211; 107<br \/>\n= $1.43<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money does Newton have left is: $1.43<\/p>\n<p>Question 4.<br \/>\nA tube of toothpaste costs $2.71 and a toothbrush costs $1.62. How much more money does the toothpaste cost more than the toothbrush?<br \/>\nAnswer: The amount of money that the toothpaste cost more than the toothbrush is: $1.09<\/p>\n<p>Explanation:<br \/>\nIt is given that a tube of toothpaste costs $2.71 and a toothbrush costs $1.62.<br \/>\nSo,<br \/>\nThe amount of money that the toothpaste cost more than the toothbrush = The cost of toothpaste -The cost of the toothbrush<br \/>\n= 2.71 &#8211; 1.62<br \/>\n= $1.07<br \/>\nHence, from the above,<br \/>\nWe can conclude that the more money does the toothpaste cost more than the toothbrush is: $1.07<\/p>\n<p>Question 5.<br \/>\nTwo fingerboards cost a total of $7.20. Each fingerboard costs the same amount. How much does each fingerboard cost?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-172.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 172\" width=\"146\" height=\"70\" \/><br \/>\nAnswer: Each fingerboard costs: 0.36<\/p>\n<p>Explanation:<br \/>\nIt is given that the two fingerboards cost a total of $7.20<br \/>\nIt is also given that each fingerboard costs the same amount.<br \/>\nSo,<br \/>\nThe cost of each fingerboard = The cost of 2 fingerboards \u00f7 2<br \/>\n= 7.20 \u00f7 2<br \/>\n= ( 7 \u00f7 2 ) + ( 0.2 \u00f7 2 )<br \/>\n= 3.5 + 0.1<br \/>\n= 3.6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the cost of each fingerboard is: $0.36<\/p>\n<p>Question 6.<br \/>\nIn Exercise 2, you pay for the stamps using a $1 bill. What is your change?<br \/>\nAnswer:<br \/>\nFrom Exercise 2,<br \/>\nThe total cost of buying 2 stamps is: $0.98<br \/>\nIn this exercise, it is given that you pay for the stamps using a $1 bill.<br \/>\nSo,<br \/>\nThe change = 1 &#8211; 0.98<br \/>\n= 0.02<br \/>\nHence, from the above,<br \/>\nWe can conclude that The change after paying the $1 bill for paying the stamps is: $0.02<\/p>\n<p>Question 7.<br \/>\nYou have four $1 bills and 3 dimes. Do you have enough money to buy the tube of toothpaste and the toothbrush in Exercise 4? Explain.<br \/>\nAnswer: No, you don&#8217;t have enough money to buy the tube of toothbrush and toothpaste which is explained in Exercise 4<\/p>\n<p>Explanation:<br \/>\nFrom Exercise 4,<br \/>\nThe total cost of money to buy the tube of toothpaste and the toothbrush = 2.71 + 1.62 = $4.33<br \/>\nIt is given that you have 4 $1 bills and 3 dimes<br \/>\nWe know that,<br \/>\n1 dime = $0.10<br \/>\nSo,<br \/>\nThe total amount of money you have = (4 \u00d7 1 ) + ( 3 \u00d7 0.10 )<br \/>\n= 4 + 0.30<br \/>\n= 4.30<br \/>\nNow,<br \/>\nWe have to compare 4.33 and 4.30<br \/>\nSo, by comparing the 2 values, we will observe<br \/>\n4.33 &gt; 4.30<br \/>\nHence, from the above,<br \/>\nWe can conclude that you don&#8217;t have enough money to buy the toothpaste and the toothbrush<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have $1.10 less than Descartes. How much money do you, Newton, and Descartes have altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-173.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 173\" width=\"374\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-173.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-173-300x160.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nAnswer:<br \/>\nIt is given that you have $1.10 less than Descartes<br \/>\nFrom the above figure,<br \/>\nNewton has $1.50 and Descartes has $1.25 more than Newton<br \/>\nSo,<br \/>\nThe amount of money that Descartes has = The amount of money Newton has + 1.25<br \/>\n= 1.50 + 1.25<br \/>\n= $2.75<br \/>\nThe amount of money you have = The amount of money Descartes has &#8211; 1.10<br \/>\n= 2.75 &#8211; 1.10<br \/>\n= $1.65<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe amount of money you have is: $1.65<br \/>\nThe amount of money Newton has is: $1.50<br \/>\nThe amount of money Descartes has is: $2.75<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou buy a joke book that costs $3.50 and a book about science experiments that costs $4.25. You give the cashier $8. What is your change?<br \/>\nThink: What do you know? What do you need to find? How will you solve?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-174.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 174\" width=\"273\" height=\"189\" \/><br \/>\n<strong>Step 1:<\/strong> Draw bills and coins to show the money you give the cashier, $8.<br \/>\n<strong>Step 2:<\/strong> Subtract the cost of the joke book. Subtract $3.50 by taking away<br \/>\n3 $1 bills and 2 quarters.<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-175.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 175\" width=\"245\" height=\"261\" \/><br \/>\n<strong>Step 3:<\/strong> Subtract the cost of the science experiment book.<br \/>\nSubtract $4.25 by taking away<br \/>\n4 $1 bills and 1 quarter.<br \/>\n<strong>Step 4:<\/strong> The remaining coin represents your change.<br \/>\nYour change is $1.75<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 9.<br \/>\nYou buy a gel pen that costs $1.10 and a school shirt that costs $5.85. You give the cashier $7. What is your change?<br \/>\nAnswer: The change is: $0.05<\/p>\n<p>Explanation:<br \/>\nIt is given that you buy a gel pen that costs $1.10 and a school shirt that costs $5.85.<br \/>\nSo,<br \/>\nThe total cost of the gel pen and the school skirt = 5.85 + 1.10 = $ 6.95<br \/>\nIt is also given that you give the cashier $7<br \/>\nSo,<br \/>\nthe change = The money given to the cashier &#8211; The total cost of the gel pen and the school skirt<br \/>\n= 7 &#8211; 6.95<br \/>\n= 0.05<br \/>\nHence, from the above,<br \/>\nWe can conclude that the change is: $0.05<\/p>\n<p>Question 10.<br \/>\nYou have $2.50. Your friend has 2 times as much money as you. How much money do you and your friend have altogether?<br \/>\nAnswer: The amount of money you and your friend have altogether is: $7.50<\/p>\n<p>Explanation:<br \/>\nIt is given that you have $2.50 and your friend has 2 times as much money as you.<br \/>\nSo,<br \/>\nThe amount of money your friend has = 2.50 \u00d7 2 = $5<br \/>\nSo,<br \/>\nThe amount of money you and your friend have altogether = The amount of money you have + The amount of money your friend has<br \/>\n= 5 + 2.5<br \/>\n= $7.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money you and your friend have altogether is: $7.50<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have $8.38. Your friend has $3.16. How much money can you give to your friend so that you each have the same amount?<br \/>\nAnswer: The amount of money you can give to your friend so that you each have the same amount = $5.22<\/p>\n<p>Explanation:<br \/>\nIt is given that you have $8.38 and your friend has $3.16<br \/>\nSo,<br \/>\nThe amount of money you can give to your friend so that you each have the same amount = The amount of money you have &#8211; The amount of money your friend has<br \/>\n= 8.38 &#8211; 3.16<br \/>\n= $5.22<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money you can give to your friend so that you each have the same amount is: $5.22<\/p>\n<h3><a id=\"Operations_with_Money_Homework_&amp;_Practice_10.7\"><\/a>Operations with Money Homework &amp; Practice 10.7<\/h3>\n<p><strong>Draw bills and coins to solve.<\/strong><\/p>\n<p>Question 1.<br \/>\nA sketch pad is $2.85 and a sketching pencil is $1.25. How much more money is the sketch pad than the sketching pencil?<br \/>\nAnswer: The amount of money the sketch pad needs more than the sketching pencil is: $1.60<\/p>\n<p>Explanation:<br \/>\nIt is given that a sketch pad is $2.85 and a sketching pencil is $1.25.<br \/>\nSo,<br \/>\nThe cost of a sketch pad is: $2.85<br \/>\nThe cost of a sketching pencil is: $1.25<br \/>\nSo,<br \/>\nthe amount of money more than the sketching pencil = The cost of sketch pad &#8211; The cost of the sketching pencil<br \/>\n= 2.85 &#8211; 1.25<br \/>\n= $1.60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money needed more than the sketching pencil is: $.1.60<\/p>\n<p>Question 2.<br \/>\nDescartes buys two toys for a total of $2.54. Each toy costs the same amount. How much does each toy cost?<br \/>\nAnswer: The cost of each boy is: $1.27<\/p>\n<p>Explanation:<br \/>\nIt is given that Descartes buys 2 toys for a total of $2.54 and it is also given that each toy costs the same amount<br \/>\nSo,<br \/>\nThe cost of each toy = The total cost of the two toys \u00f7 2<br \/>\n= 2.54 \u00f7 2<br \/>\n= $1.27<br \/>\nHence, from the above,<br \/>\nWe can conclude that the cost of each toy is: $1.27<\/p>\n<p>Question 3.<br \/>\nYou buy 4 bags of the water balloons shown. How much money do you spend in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-177.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 177\" width=\"183\" height=\"159\" \/><br \/>\nAnswer: The total cost of the 4 bags of balloons are: $4.80<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 4 bags of balloons and it is also given that the cost of each bag of balloon is $1.20<br \/>\nSo,<br \/>\nThe total cost of the four bags of balloons = 4 \u00d7 1.20<br \/>\n= $4.80<br \/>\nhence, from the above,<br \/>\nWe can conclude that the cost of the four bags of balloons is: $4.80<\/p>\n<p>Question 4.<br \/>\nYou have four $1 bills and 2 nickels. Do you have enough money to buy the sketch pad and the sketching pencil in Exercise 1? Explain.<br \/>\nAnswer: No, we have enough money to buy the sketch pad and the sketching pencil<\/p>\n<p>Explanation:<br \/>\nFrom Exercise 1,<br \/>\nThe total cost of the sketch pen and the sketching pencil = 2.85 + 1.25<br \/>\n= $4.10<br \/>\nIn this exercise, it is given that you have 4 $1 bills and 2 nickels.<br \/>\nWe know that,<br \/>\n1 nickel = $0.05<br \/>\nSo,<br \/>\nThe total amount of money = ( 4 \u00d7 1 ) + ( 2 \u00d7 0.05 )<br \/>\n=\u00a0 + 0.1<br \/>\n= $4.1<br \/>\nSo,<br \/>\nThe total amount from exercise 1 and the money you have are equal<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have enough money to buy the sketch pen and the sketching pencil<\/p>\n<p>Question 5.<br \/>\n<strong>Reasoning<\/strong><br \/>\nYou have 3 jars, with $2.32 in each jar. Do you have enough money to buy the model car? If not, how much more money do you need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-178.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 178\" width=\"204\" height=\"119\" \/><br \/>\nAnswer: You don&#8217;t have enough money to buy the model car<br \/>\nThe amount of money that you needed more to buy the model car is: $0.53<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 3 jars, with $2.32 in each jar<br \/>\nSo,<br \/>\nThe total amount of money n the three jars = 3 \u00d7 2.32 = $6.96<br \/>\nIt is also given that<br \/>\nThe cost of the model car is: $7.49<br \/>\nSo,<br \/>\nThe amount of money needed more to buy the model car = The cost of the model car &#8211; The total amount of money in the three jars<br \/>\n= 7.49 &#8211; 6.96<br \/>\n= $0.53<br \/>\nHence, from the above,<br \/>\nWe can conclude that we don&#8217;t have enough money to buy the model car<br \/>\nThe amount of money needed more to buy the car is: $0.53<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nDescartes has 3 quarters, 1 dime, and 3 nickels. He wants to put the same amount of money into each of the two piggy banks. How can he do this with these coins?<br \/>\nAnswer: The amount of money in each of the two piggy banks is: $0.5<\/p>\n<p>Explanation:<br \/>\nIt is given that Descartes has 3 quarters, 1 dime, and 3 nickels.<br \/>\nSo,<br \/>\nThe amount of money Descartes possess is: 3 quarters, 1 dime, and 3 nickels<br \/>\nWe know that,<br \/>\n1 quarter = $0.25<br \/>\n1 dime = $0.10<br \/>\n1 nickel = $0.05<br \/>\nSo,<br \/>\nThe total amount of money Descartes possesses = ( 3 \u00d7 0.25 ) + ( 1 \u00d7 0.10 ) + ( 3 \u00d7 0.05 )<br \/>\n= 0.75 + 0.10 + 0.15<br \/>\n= $1.00<br \/>\nSo,<br \/>\nThe amount of money in each of the two piggy banks = 1 \u00f7 2 = $0.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money in each of the two piggy banks is: $0.5<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou buy the key chains shown. You pay with a $5 bill. What is your change?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 179\" width=\"312\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179-300x150.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer: The change is: $1.10<\/p>\n<p>Explanation:<br \/>\nIt is given that you have bought some key chains as shown in the below figure.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 179\" width=\"312\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-179-300x150.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nFrom the above figure,<br \/>\nThe cost of a basketball key chain is: $2.53<br \/>\nThe cost of a football chain is: $2.37<br \/>\nSo,<br \/>\nThe total cost of the two key chains = 2.53 + 2.37<br \/>\n= $4.90<br \/>\nIt is also given that you pay with a $5 bill<br \/>\nSo,<br \/>\nThe change = 5 &#8211; The total cost of the key chains<br \/>\n= 5 &#8211; 4.90<br \/>\n= $1.10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the change obtained after buying the key chains is: $1.10<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour class collects pennies and nickels in separate jars. Your class collects $5.87 in pennies and $2.65 in nickels. You divide the total amount of money collected between two charities. How many pennies do you put in the nickel jar so that both jars have the same amount of money?<br \/>\nAnswer:<br \/>\nThe total amount of money divided between the 2 charities is: $4.26<br \/>\nThe number of pennies you need to put in the nickel jar is: $3.22<\/p>\n<p>Explanation:<br \/>\nIt is given that your class collects pennies and nickels in separate jars. It is also given that your class collects $5.87 in pennies and $2.65 in nickels.<br \/>\nIt is given that you divide the total amount of money collected between two charities.<br \/>\nSo,<br \/>\nThe total amount of money collected by the class = 5.87 + 2.65 = $8.52<br \/>\nNow,<br \/>\nThe total amount of money divided between the 2 charities = 8.52 \u00f7 2<br \/>\n= ( 8 \u00f7 2 ) + ( 0.52 \u00f7 2 )<br \/>\n= 4 + 0.26<br \/>\n= $ 4.26<br \/>\nNow,<br \/>\nThe amount of money needed more to add pennies into the nickel jars = 5.87 &#8211; 2.65 = $3.22<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe total amount of money divided between the 2 charities is: $4.26<br \/>\nThe number of pennies you need to put in the nickel jar is: $3.22<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-180.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 180\" width=\"85\" height=\"48\" \/><br \/>\nAnswer: The product of 6 and \\(\\frac{7}{12}\\) is: \\(\\frac{14}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{6}{1}\\) and \\(\\frac{7}{12}\\)<br \/>\nFor multiplication,<br \/>\nMultiply numerators and denominators separately.<br \/>\nSo,<br \/>\n\\(\\frac{6}{1}\\) \u00d7 \\(\\frac{7}{12}\\) = \\(\\frac{6 \u00d7 7 }{1 \u00d7 12}\\)<br \/>\n= \\(\\frac{42}{12}\\)<br \/>\nFor the simplified form of \\(\\frac{42}{12}\\), divide \\(\\frac{42}{12}\\) by 3 as 42 and 12 are the multiples of 3<br \/>\nHence,<br \/>\n\\(\\frac{7}{12}\\) \u00d7 \\(\\frac{6}{1}\\) = \\(\\frac{42}{12}\\) = \\(\\frac{14}{4}\\)<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-181.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 181\" width=\"62\" height=\"53\" \/><br \/>\nAnswer: The product of 2 and \\(\\frac{5}{6}\\) is: \\(\\frac{5}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{1}\\) and \\(\\frac{5}{6}\\)<br \/>\nFor multiplication,<br \/>\nMultiply numerators and denominators separately.<br \/>\nSo,<br \/>\n\\(\\frac{2}{1}\\) \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{2 \u00d7 5 }{1 \u00d7 6}\\)<br \/>\n= \\(\\frac{10}{6}\\)<br \/>\nFor the simplified form of \\(\\frac{10}{6}\\), divide \\(\\frac{10}{6}\\) by 2 as 10 and 6 are the multiples of 2<br \/>\nHence,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{2}{1}\\) = \\(\\frac{10}{6}\\) = \\(\\frac{5}{3}\\)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-182.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 182\" width=\"66\" height=\"51\" \/><br \/>\nAnswer: The product of 10 and \\(\\frac{3}{8}\\) is: \\(\\frac{15}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{10}{1}\\) and \\(\\frac{3}{8}\\)<br \/>\nFor multiplication,<br \/>\nMultiply numerators and denominators separately.<br \/>\nSo,<br \/>\n\\(\\frac{10}{1}\\) \u00d7 \\(\\frac{3}{8}\\) = \\(\\frac{10 \u00d7 3 }{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{30}{8}\\)<br \/>\nFor the simplified form of \\(\\frac{30}{8}\\), divide \\(\\frac{30}{8}\\) by 2 as 30 and 8 are the multiples of 2<br \/>\nHence,<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{10}{1}\\) = \\(\\frac{30}{8}\\) = \\(\\frac{15}{4}\\)<\/p>\n<h3><a id=\"Relate_Fractions_and_Decimals_Performance_Task_10\"><\/a>Relate Fractions and Decimals Performance Task 10<\/h3>\n<p>You have a recipe to make one loaf of home made whole wheat bread. You want to make 8 loaves of bread.<\/p>\n<p>1. You need between 6.5 cups and 7 cups of whole wheat flour for one loaf of bread.<br \/>\na. So far, you measure 3\\(\\frac{1}{4}\\) cups of flour for one loaf. What is the least amount of cups you need to add?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-183.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 183\" width=\"240\" height=\"153\" \/><\/p>\n<p>Answer: The least amount of cups you need to add is: 3.25<\/p>\n<p>Explanation:<br \/>\nIt is given that you need between 6.5 and 7 cups of whole wheat flour for one loaf of bread.<br \/>\nIt is given that you measured so far 3\\(\\frac{1}{4}\\) cups of flour for one loaf<br \/>\nSo,<br \/>\nThe least number of cups you need to add to make one loaf of bread = 6.5 &#8211; 3\\(\\frac{1}{4}\\)<br \/>\nThe representation of 3\\(\\frac{1}{4}\\) in the decimal form is: 3.25<br \/>\nSo,<br \/>\nThe least number of cups you need = 6.5 &#8211; 3.25 = 3.25 cups<br \/>\nHence, from the above,<br \/>\nWe can conclude that you need a minimum of 3.25 cups of wheat flour to make a loaf of bread<\/p>\n<p>b. There are about 4 cups of flour in 1 pound. How many 5-pound bags of whole wheat flour should you buy to make all of the bread?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13517\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-184.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 184\" width=\"176\" height=\"138\" \/><\/p>\n<p>Answer: You should buy about 20 cups of flour to make all the bread<\/p>\n<p>Explanation:<br \/>\nIt is given that we need about 4 cups of flour in 1 pound.<br \/>\nSo,<br \/>\nThe number of cups you need for five-pound bags = 4 \u00d7 5 = 20 cups<br \/>\nHence, from the above,<br \/>\nWe can conclude that we will need about 20 cups of flour to make all the bread<\/p>\n<p>c. You use a $10 bill to buy enough bags of whole wheat flour for 8 loaves. What is your change?<br \/>\nAnswer: Your change is: $4.8<\/p>\n<p>Explanation:<br \/>\nIt is given that you use a $10 bill to buy enough bags of whole wheat flour for 8 loaves.<br \/>\nSo,<br \/>\nThe total cost of wheat flour = 2.69 \u00d7 2 = $5.38<br \/>\nSo,<br \/>\nYour change = 10 &#8211; 5.38 = $4.62<br \/>\nHence, from the above,<br \/>\nWe can conclude that the change is: $4.62<\/p>\n<p>Question 2.<br \/>\nYou need to add 2\\(\\frac{1}{4}\\) cups of warm water for one loaf of bread. The temperature of the water should be about 110\u00b0F.<br \/>\na. How many cups of water do you need for all of the bread?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-185.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 185\" width=\"241\" height=\"201\" \/><\/p>\n<p>Answer: The number of cups of warm water you need for all the bread is: 18 cups<\/p>\n<p>Explanation:<br \/>\nIt is given that you need to add 2\\(\\frac{1}{4}\\) cups of warm water for one loaf of bread.<br \/>\nBut, it is given for the whole read, there are 8 loaves of bread.<br \/>\nSo,<br \/>\nThe total number of cups you need to make all the bread = 2\\(\\frac{1}{4}\\) \u00d7 8<br \/>\n= 2.25 \u00d7 8<br \/>\n= 18 cups<br \/>\nHence, from the above,<br \/>\nWe can conclude that we will need 18 cups of warm water to make all the whole bread<\/p>\n<p>b. You find the temperatures of 3 different samples of water. Which sample of water should you use? Explain.<br \/>\nAnswer: We will use a C sample of water<\/p>\n<p>Explanation:<br \/>\nThe given temperatures are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-185.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 185\" width=\"241\" height=\"201\" \/><br \/>\nFrom the above table,<br \/>\nThe temperature of A is: 105.5<br \/>\nThe temperature of B is: 114.4<br \/>\nThe temperature of C is: 109.6<br \/>\nIt is given that the temperature to make the bread is: 110<br \/>\nSo,<br \/>\nWe will choose sample C to make the bread.<br \/>\nHence, from the above,<br \/>\nwe can conclude that we will use C&#8217;s sample of water to make the bread<\/p>\n<h3><a id=\"Relate_Fractions_and_Decimals_Activity\"><\/a>Relate Fractions and Decimals Activity<\/h3>\n<p><strong>Decimal Boss<\/strong><\/p>\n<p><strong>Directions:<\/strong><\/p>\n<ol>\n<li>Divide the Decimal Boss Cards equally between both players.<\/li>\n<li>Each player \ufb02ips a Decimal Boss Card.<\/li>\n<li>Players compare their numbers. The player with the greater number takes both cards.<\/li>\n<li>The player with the most cards at the end of the round wins!<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13519\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-186.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 186\" width=\"550\" height=\"569\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-186.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-186-290x300.png 290w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<h3><a id=\"Relate_Fractions_and_Decimals_Chapter_Practice_10\"><\/a>Relate Fractions and Decimals Chapter Practice 10<\/h3>\n<p><strong>10.1 Understand Tenths<\/strong><\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{8}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{8}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-190.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-190.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-190-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn \\(\\frac{8}{10}\\),<br \/>\n8 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{8}{10}\\) in the decimal form is: 0.8<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{10}\\)<br \/>\nAnswer: The representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{3}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-191.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-191.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-191-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn \\(\\frac{3}{10}\\),<br \/>\n3 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Question 3.<br \/>\n6\\(\\frac{7}{10}\\)<br \/>\nAnswer: The representation of 6\\(\\frac{7}{10}\\) in the decimal form is: 6.7<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 6\\(\\frac{7}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 6\\(\\frac{7}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-192.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-192.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-192-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn 6\\(\\frac{7}{10}\\),<br \/>\n6 represents the one&#8217;s position<br \/>\n7 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 6\\(\\frac{7}{10}\\) in the decimal form is: 6.7<\/p>\n<p>Question 4.<br \/>\n15\\(\\frac{4}{10}\\)<br \/>\nAnswer: The representation of 15\\(\\frac{4}{10}\\) in the decimal form is: 15.4<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 15\\(\\frac{4}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 15\\(\\frac{4}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-193.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-193.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-193-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn 15\\(\\frac{4}{10}\\),<br \/>\n1 represents the ten&#8217;s position<br \/>\n5 represents the one&#8217;s position<br \/>\n4 represents the tenth&#8217;s position<br \/>\nThe formula for converting fraction to a decimal is Decimal = Numerator \u00f7 Denominator<br \/>\nHence,<br \/>\nThe representation of 15\\(\\frac{4}{10}\\) in the decimal form is: 15.4<\/p>\n<p><strong>Write the number as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 5.<br \/>\ntwo tenths<br \/>\nAnswer:<br \/>\nThe representation of two-tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nThe representation of two-tenths in the decimal form is: 0.2<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Two-tenths<br \/>\nSo,<br \/>\nThe representation of two-tenths in the fraction form is: \\(\\frac{2}{10}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-194.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-194.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-194-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn \\(\\frac{2}{10}\\),<br \/>\n2 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{2}{10}\\) in the decimal form is: 0.2<\/p>\n<p>Question 6.<br \/>\nthirteen and six tenths<br \/>\nAnswer:<br \/>\nThe representation of thirteen and six-tenths in the fraction form is: 13\\(\\frac{6}{10}\\)<br \/>\nThe representation of thirteen and six-tenths in the decimal form is: 13.6<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Thirteen and six-tenths<br \/>\nSo,<br \/>\nThe representation of thirteen and six-tenths in the fraction form is: 13\\(\\frac{6}{10}\\)<br \/>\nNow,<br \/>\nThe representation of 13\\(\\frac{6}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-195.jpg\" alt=\"\" width=\"306\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-195.jpg 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-195-300x84.jpg 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIn 13\\(\\frac{6}{10}\\),<br \/>\n1 represents the ten&#8217;s position<br \/>\n3 represents the one&#8217;s position<br \/>\n6 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of 13\\(\\frac{6}{10}\\) in the decimal form is: 13.6<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou bake 2 loaves of banana bread for a party. You cut each loaf into10 equal pieces. The guests eat 18 pieces. Write the fraction and decimal that represent how many loaves the guests eat in all.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-187.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 187\" width=\"208\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe representation of the loaves that the guests eat in the fraction form is: \\(\\frac{18}{20}\\)<br \/>\nThe representation of the loaves that the guests eat in the decimal form is: 0.9<\/p>\n<p>Explanation:<br \/>\nIt is given that you bake 2 loaves of banana bread and you cut each banana bread into 10 pieces<br \/>\nSo,<br \/>\nThe total number of pieces is: 20 pieces<br \/>\nIt is also given that the guests eat 18 pieces.<br \/>\nSo,<br \/>\nThe number of pieces eaten by guests is: 18<br \/>\nSo,<br \/>\nThe representation of the loaves that the guests eat in the fraction form is: \\(\\frac{18}{20}\\)<br \/>\nThe representation of the loaves that the guests eat in the decimal form is: 0.9<\/p>\n<p><strong>10.2 Understand Hundredths<\/strong><\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{10}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{10}{100}\\) in the form of decimal number is: 0.10<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{10}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{10}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-196.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-196.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-196-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn \\(\\frac{10}{100}\\),<br \/>\n0 represents the hundredth position<br \/>\n1 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{10}{100}\\) in the decimal form is: 0.10<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{6}{100}\\)<br \/>\nAnswer: The representation of \\(\\frac{6}{100}\\) in the form of decimal number is: 0.06<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{6}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{6}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-197.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-197.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-197-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn \\(\\frac{6}{100}\\),<br \/>\n6 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{6}{100}\\) in the decimal form is: 0.06<\/p>\n<p>Question 10.<br \/>\n8\\(\\frac{75}{100}\\)<br \/>\nAnswer: The representation of 8\\(\\frac{75}{100}\\) in the form of a decimal number is: 8.75<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 8\\(\\frac{75}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 8\\(\\frac{75}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn 8\\(\\frac{75}{100}\\),<br \/>\n8 represents the one&#8217;s position<br \/>\n5 represents the hundredth position<br \/>\n7 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 8\\(\\frac{75}{100}\\) in the decimal form is: 8.75<\/p>\n<p>Question 11.<br \/>\n34\\(\\frac{2}{100}\\)<br \/>\nAnswer: The representation of 34\\(\\frac{2}{100}\\) in the form of a decimal number is: 34.02<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: 34\\(\\frac{2}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 34\\(\\frac{2}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-198-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn 8\\(\\frac{75}{100}\\),<br \/>\n3 represents the ten&#8217;s position<br \/>\n4 represents the one&#8217;s position<br \/>\n2 represents the hundredth position<br \/>\n0 represents the tenth position<br \/>\nHence,<br \/>\nThe representation of 34\\(\\frac{2}{100}\\) in the decimal form is: 34.02<\/p>\n<p><strong>Write the number as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 12.<br \/>\nthirty-seven hundredths<br \/>\nAnswer:<br \/>\nThe representation of thirty-seven hundredths in the fraction form is: \\(\\frac{37}{100}\\)<br \/>\nThe representation of thirty-seven hundredths in the decimal form is: 0.37<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Thirty-seven hundredths<br \/>\nSo,<br \/>\nThe representation of thirty-seven hundredths in the fraction form is: \\(\\frac{37}{100}\\)<br \/>\nNow,<br \/>\nThe representation of \\(\\frac{37}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-199.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-199.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-199-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn \\(\\frac{37}{100}\\),<br \/>\n7 represents the hundredth&#8217;s position<br \/>\n3 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of \\(\\frac{37}{100}\\) in the decimal form is: 0.37<\/p>\n<p>Question 13.<br \/>\nnineteen and forty-one hundredths<br \/>\nAnswer:<br \/>\nThe representation of nineteen and forty-seven hundredths in the fraction form is: 19\\(\\frac{47}{100}\\)<br \/>\nThe representation of nineteen and forty-seven hundredths in the decimal form is: 19.47<\/p>\n<p>Explanation:<br \/>\nThe given word form is: Nineteen and forty-seven hundredths<br \/>\nSo,<br \/>\nThe representation of nineteen and forty-seven hundredths in the fraction form is: 19\\(\\frac{47}{100}\\)<br \/>\nNow,<br \/>\nThe representation of 19\\(\\frac{47}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-200.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-200.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-200-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nIn 19\\(\\frac{47}{100}\\),<br \/>\n1 represents the ten&#8217;s position<br \/>\n9 represents the one&#8217;s position<br \/>\n7 represents the hundredth&#8217;s position<br \/>\n4 represents the tenth&#8217;s position<br \/>\nHence,<br \/>\nThe representation of 19\\(\\frac{47}{100}\\) in the decimal form is: 19.47<\/p>\n<p><strong>10.3 Fractions and Decimals<\/strong><\/p>\n<p><strong>Write the number as tenths in fraction form and decimal form.<\/strong><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{30}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{30}{100}\\) as tenths in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{30}{100}\\)<br \/>\nSo, to write \\(\\frac{30}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{30}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 30 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{30}{100}=\\frac{30 \\div 10}{100 \\div 10}=\\frac{8}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{30}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{30}{100}\\) as tenths in the fraction form is: \\(\\frac{3}{10}\\)<br \/>\nThe representation of \\(\\frac{3}{10}\\) in the decimal form is: 0.3<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{90}{100}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{90}{100}\\) as tenths in the fraction form is: \\(\\frac{39{10}\\)<br \/>\nThe representation of \\(\\frac{39}{10}\\) in the decimal form is: 0.9<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{90}{100}\\)<br \/>\nSo, to write \\(\\frac{390}{100}\\) as tenths, divide the fraction and numerator of \\(\\frac{90}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 90 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nSo,<br \/>\n\\(\\frac{90}{100}=\\frac{90 \\div 10}{100 \\div 10}=\\frac{8}{10}\\)<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{90}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-201-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{90}{100}\\) as tenths in the fraction form is: \\(\\frac{9}{10}\\)<br \/>\nThe representation of \\(\\frac{9}{10}\\) in the decimal form is: 0.9<\/p>\n<p>Question 16.<br \/>\n0.50<br \/>\nAnswer:<br \/>\nThe representation of 0.50 as tenths in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.50<br \/>\nSo,<br \/>\nThe representation of 0.50 in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo, to write \\(\\frac{50}{100}\\) as tenths,divide the fraction and numerator of \\(\\frac{50}{100}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 50 and 10 are divided and then the denominators 100 and 10 are divided<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-202.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-202.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-202-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{50}{100}\\) as tenths in the fraction form is: \\(\\frac{5}{10}\\)<br \/>\nThe representation of \\(\\frac{5}{10}\\) in the decimal form is: 0.5<\/p>\n<p><strong>Write the number as hundredths in fraction form and decimal form.<\/strong><\/p>\n<p>Question 17.<br \/>\n\\(\\frac{7}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{7}{10}\\)<br \/>\nSo, to write \\(\\frac{7}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{7}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 7 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-203.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-203.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-203-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{7}{10}\\) as hundredths in the fraction form is: \\(\\frac{70}{100}\\)<br \/>\nThe representation of \\(\\frac{70}{100}\\) in the decimal form is: 0.70<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{4}{10}\\)<br \/>\nAnswer:<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the decimal form is: 0.40<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{4}{10}\\)<br \/>\nSo, to write \\(\\frac{4}{10}\\) as hundredths, multiply the fraction and numerator of \\(\\frac{4}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 4 and 10 are multiplied and then the denominators 10 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-204.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-204.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-204-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nThe representation of \\(\\frac{40}{100}\\) in the decimal form is: 0.40<\/p>\n<p>Question 19.<br \/>\n0.6<br \/>\nAnswer:<br \/>\nThe representation of 0.6 as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the decimal form is: 0.60<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.6<br \/>\nSo,<br \/>\nThe representation of 0.6 in the fraction form is: \\(\\frac{6}{10}\\)<br \/>\nSo, to write \\(\\frac{6}{10}\\) as hundredths,multiply the fraction and numerator of \\(\\frac{6}{10}\\) with 10.<br \/>\nSo,<br \/>\nFirstly the numerators 6 and 10 are multiplied and then the denominators 100 and 10 are multiplied<br \/>\nWe know that,<br \/>\nDecimal = Numerator \u00f7 Denominator<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-205.jpg\" alt=\"\" width=\"404\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-205.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-205-300x60.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nThe representation of \\(\\frac{60}{100}\\) in the decimal form is: 0.60<\/p>\n<p><strong>10.4 Compare Decimals<\/strong><\/p>\n<p>Compare<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-188.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 188\" width=\"105\" height=\"40\" \/><br \/>\nAnswer: 0.79 is greater than 0.72<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.79 and 0.72<br \/>\nThe representation of 0.79 and 0.72 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-206.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-206.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-206-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s and tenth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the hundredth&#8217;s position 9 and 2<br \/>\nSo, 9 hundredths &gt; 2 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.79 is greater than 0.72<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-189.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 189\" width=\"109\" height=\"51\" \/><br \/>\nAnswer: 9.16 is less than 9.56<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 9.16 and 9.56<br \/>\nThe representation of 9.16 and 9.56 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-207.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-207.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-207-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s and hundredth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the tenth&#8217;s position 1 and 5<br \/>\nSo, 1 hundredths &lt; 5 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 9.16 is less than 9.56<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-190.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 190\" width=\"121\" height=\"47\" \/><br \/>\nAnswer: 11.40 is equal to 11.4<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 11.40 and 11.4<br \/>\nThe representation of 11.40 and 11.4 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-208.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-208.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-208-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s, tenth&#8217;s, and hundredth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the tenth&#8217;s position 4 and 4<br \/>\nSo, 4 hundredths = 4 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 11.40 is equal to 11.4<\/p>\n<p><strong>Open-Ended<\/strong><br \/>\nComplete the statement to make it true.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-191.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 191\" width=\"124\" height=\"44\" \/><br \/>\nAnswer: 0.19 is greater than 0.15<\/p>\n<p>Explanation:<br \/>\nLet the missing number be 1<br \/>\nSo,<br \/>\nThe given decimal numbers are: 0.19 and 0.15<br \/>\nThe representation of 0.19 and 0.15 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-209.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-209.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-209-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s and tenth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the hundredth&#8217;s position 9 and 5<br \/>\nSo, 9 hundredths &gt; 5 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 0.19 is less than 0.15<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-192.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 192\" width=\"105\" height=\"46\" \/><br \/>\nAnswer: 6.30 is equal to 6.3<\/p>\n<p>Explanation:<br \/>\nLet the missing number be 0<br \/>\nSo,<br \/>\nThe given decimal numbers are: 6.30 and 6.3<br \/>\nThe representation of 6.30 and 6.3 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-210.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-210.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-210-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s, hundredth&#8217;s, and tenth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the hundredth&#8217;s position 0 and 0<br \/>\nSo, 0 hundredths = 0 hundredths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 6.30 is equal to 6.3<\/p>\n<p>Question 25.<br \/>\n___ &gt; 40.48<br \/>\nAnswer: 40.58 is greater than 40.48<\/p>\n<p>Explanation:<br \/>\nLet the missing number be 40.58<br \/>\nSo,<br \/>\nThe given decimal numbers are: 40.58 and 40.48<br \/>\nThe representation of 40.58 and 40.48 in the place-value chart is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-211.jpg\" alt=\"\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-211.jpg 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-10-211-300x98.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nSo,<br \/>\nFrom the above place-value chart,<br \/>\nwe can observe that one&#8217;s and hundredth&#8217;s positions are the same.<br \/>\nSo,<br \/>\nCompare the tenth&#8217;s position 9 and 5<br \/>\nSo, 5 tenths &gt; 4 tenths<br \/>\nHence, from the above,<br \/>\nWe can conclude that 40.58 is greater than 40.48<\/p>\n<p>Question 26.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWhat might Newton\u2019s number be?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-193.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 193\" width=\"218\" height=\"214\" \/><br \/>\nAnswer: Newton&#8217;s number might be: 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton&#8217;s number will be between 0.2 and 0.3<br \/>\nSo,<br \/>\nNewton&#8217;s number might be: 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29<br \/>\nIt is also given that the highest digit will be in the hundredth&#8217;s place<br \/>\nHence,<br \/>\nNewton&#8217;s number might be: 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29<\/p>\n<p><strong>10.5 Add Decimal Fractions and Decimals<\/strong><\/p>\n<p>Find the sum.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-194.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 194\" width=\"145\" height=\"52\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{14}{100}\\) = \\(\\frac{74}{100}\\)<br \/>\nThe representation of \\(\\frac{74}{100}\\) in the decimal for is: 0.74<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{14}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{6}{10}\\) as the hundredths, we have to multiply \\(\\frac{6}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{60}{100}\\) + \\(\\frac{14}{100}\\)<br \/>\n= \\(\\frac{60 + 14}{100}\\)<br \/>\n= \\(\\frac{74}{100}\\)<br \/>\nThe representation of \\(\\frac{74}{100}\\) in the decimal form is: 0.74<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{14}{100}\\) = \\(\\frac{74}{100}\\)<br \/>\nThe representation of \\(\\frac{74}{100}\\) in the decimal for is: 0.74<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-195.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 195\" width=\"139\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{52}{100}\\) = \\(\\frac{82}{100}\\)<br \/>\nThe representation of \\(\\frac{82}{100}\\) in the decimal for is: 0.82<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{52}{100}\\) and \\(\\frac{3}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{3}{10}\\) as the hundredths, we have to multiply \\(\\frac{3}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3}{10}\\) as hundredths in the fraction form is: \\(\\frac{30}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{30}{100}\\) + \\(\\frac{52}{100}\\)<br \/>\n= \\(\\frac{30 + 52}{100}\\)<br \/>\n= \\(\\frac{82}{100}\\)<br \/>\nThe representation of \\(\\frac{82}{100}\\) in the decimal form is: 0.82<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{3}{10}\\) + \\(\\frac{52}{100}\\) = \\(\\frac{82}{100}\\)<br \/>\nThe representation of \\(\\frac{82}{100}\\) in the decimal for is: 0.82<\/p>\n<p>Question 29.<br \/>\n0.12 + 0.6 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{12}{100}\\) = \\(\\frac{72}{100}\\)<br \/>\nThe representation of 012 + 0.6 in the decimal form is: 0.72<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.6 and 0.12<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{12}{100}\\) and \\(\\frac{6}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{6}{10}\\) as the hundredths, we have to multiply \\(\\frac{6}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{6}{10}\\) as hundredths in the fraction form is: \\(\\frac{60}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{60}{100}\\) + \\(\\frac{12}{100}\\)<br \/>\n= \\(\\frac{60 + 12}{100}\\)<br \/>\n= \\(\\frac{72}{100}\\)<br \/>\nThe representation of \\(\\frac{72}{100}\\) in the decimal form is: 0.72<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{6}{10}\\) + \\(\\frac{12}{100}\\) = \\(\\frac{72}{100}\\)<br \/>\nThe representation of \\(\\frac{72}{100}\\) in the decimal for is: 0.72<\/p>\n<p>Question 30.<br \/>\n0.4 + 0.72 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{72}{100}\\) = \\(\\frac{112}{100}\\)<br \/>\nThe representation of 0.4 + 0.72 in the decimal form is: 1.12<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.4 and 0.72<br \/>\nSo, convert the two decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{72}{100}\\) and \\(\\frac{4}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{4}{10}\\) as the hundredths, we have to multiply \\(\\frac{4}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4}{10}\\) as hundredths in the fraction form is: \\(\\frac{40}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{40}{100}\\) + \\(\\frac{72}{100}\\)<br \/>\n= \\(\\frac{72 + 40}{100}\\)<br \/>\n= \\(\\frac{112}{100}\\)<br \/>\nThe representation of \\(\\frac{112}{100}\\) in the decimal form is: 1.12<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{4}{10}\\) + \\(\\frac{72}{100}\\) = \\(\\frac{112}{100}\\)<br \/>\nThe representation of \\(\\frac{112}{100}\\) in the decimal for is: 1.12<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-196.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 196\" width=\"197\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{23}{100}\\) + \\(\\frac{36}{100}\\) + \\(\\frac{2}{10}\\) = \\(\\frac{79}{100}\\)<br \/>\nThe representation of \\(\\frac{79}{100}\\) in the decimal for is: 0.79<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{23}{100}\\), \\(\\frac{36}{100}\\) and \\(\\frac{2}{10}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{2}{10}\\) as the hundredths, we have to multiply \\(\\frac{2}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{23}{100}\\) + \\(\\frac{36}{100}\\) + \\(\\frac{20}{100}\\)<br \/>\n= \\(\\frac{23 + 36 + 20}{100}\\)<br \/>\n= \\(\\frac{79}{100}\\)<br \/>\nThe representation of \\(\\frac{79}{100}\\) in the decimal form is: 0.79<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{23}{100}\\) + \\(\\frac{36}{100}\\) = \\(\\frac{79}{100}\\)<br \/>\nThe representation of \\(\\frac{79}{100}\\) in the decimal for is: 0.79<\/p>\n<p>Question 32.<br \/>\n0.18 + 0.2 + 0.07 = ___<br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{18}{100}\\) + \\(\\frac{7}{100}\\) = \\(\\frac{45}{100}\\)<br \/>\nThe representation of 0.18 + 0.2 + 0.07 in the decimal for is: 0.45<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.18, 0.2 and 0.07<br \/>\nSo, convert the three decimal numbers in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{18}{100}\\) , \\(\\frac{2}{10}\\) and \\(\\frac{7}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{2}{10}\\)\u00a0 as the hundredths, we have to multiply \\(\\frac{2}{10}\\)\u00a0 by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{2}{10}\\) as hundredths in the fraction form is: \\(\\frac{20}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{20}{100}\\) + \\(\\frac{18}{100}\\) + \\(\\frac{7}{100}\\)<br \/>\n= \\(\\frac{20 + 18 + 7}{100}\\)<br \/>\n= \\(\\frac{45}{100}\\)<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the decimal form is: 0.45<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{2}{10}\\) + \\(\\frac{18}{100}\\) + \\(\\frac{7}{100}\\) = \\(\\frac{45}{100}\\)<br \/>\nThe representation of \\(\\frac{45}{100}\\) in the decimal for is: 0.45<\/p>\n<p><strong>Number Sense<\/strong><br \/>\nFind the sum.<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-197.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 197\" width=\"148\" height=\"55\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{48}{100}\\) = \\(\\frac{98}{100}\\)<br \/>\nThe representation of 0.5 + \\(\\frac{48}{100}\\) in the decimal for is: 0.98<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.5 and \\(\\frac{48}{100}\\)<br \/>\nSo, convert the decimal number in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{5}{10}\\) and \\(\\frac{48}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{5}{10}\\) as the hundredths, we have to multiply \\(\\frac{5}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{5}{10}\\) as hundredths in the fraction form is: \\(\\frac{50}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{48}{100}\\)<br \/>\n= \\(\\frac{50 + 48}{100}\\)<br \/>\n= \\(\\frac{98}{100}\\)<br \/>\nThe representation of \\(\\frac{98}{100}\\) in the decimal form is: 0.98<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{5}{10}\\) + \\(\\frac{48}{100}\\) = \\(\\frac{98}{100}\\)<br \/>\nThe representation of \\(\\frac{98}{100}\\) in the decimal for is: 0.98<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-198.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 198\" width=\"147\" height=\"57\" \/><br \/>\nAnswer:<br \/>\nThe representation of the sum in the fraction form is:<br \/>\n\\(\\frac{9}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{115}{100}\\)<br \/>\nThe representation of 0.25 + \\(\\frac{9}{10}\\) in the decimal for is: 1.15<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.25 and \\(\\frac{9}{10}\\)<br \/>\nSo, convert the decimal number in to respective fractions.<br \/>\nSo,<br \/>\nThe given fractions are: \\(\\frac{9}{10}\\) and \\(\\frac{25}{100}\\)<br \/>\nFor addition, we have to make either denominators or the numerators equal.<br \/>\nso,<br \/>\nFor making \\(\\frac{9}{10}\\) as the hundredths, we have to multiply \\(\\frac{9}{10}\\) by 10<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{9}{10}\\) as hundredths in the fraction form is: \\(\\frac{90}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{90}{100}\\) + \\(\\frac{25}{100}\\)<br \/>\n= \\(\\frac{90 + 25}{100}\\)<br \/>\n= \\(\\frac{115}{100}\\)<br \/>\nThe representation of \\(\\frac{115}{100}\\) in the decimal form is: 1.15<br \/>\nHence from the above,<br \/>\nWe can conclude that<br \/>\n\\(\\frac{9}{10}\\) + \\(\\frac{25}{100}\\) = \\(\\frac{115}{100}\\)<br \/>\nThe representation of \\(\\frac{115}{100}\\) in the decimal for is: 1.15<\/p>\n<p><strong>10.6 Fractions, Decimals, and Money<\/strong><\/p>\n<p><strong>Find the total money amount. Then write the amount as a fraction or mixed number and as a decimal.<\/strong><\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-199.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 199\" width=\"273\" height=\"103\" \/><br \/>\nAnswer: The total amount of money is: $1.13<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 3 pennies, 4 Quarters, and 2 nickels<br \/>\nSo,<br \/>\nThe total amount of money =\u00a0 ( 4 \u00d7 0.25 ) + ( 2 \u00d7 0.05 ) + ( 3 \u00d7 0.01 )<br \/>\n= 1 + 0.10 + 0.03<br \/>\n= 1.13<br \/>\nHence,<br \/>\nThe total amount of money is: $1.13<br \/>\nThe representation of $1.13 in the fraction form is: 1\\(\\frac{13}{100}\\) dollar<br \/>\nThe representation of $1.13 in the decimal form is: 1.13<\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13533\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-200.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 200\" width=\"295\" height=\"129\" \/><br \/>\nAnswer: The total amount of money is: $2.11<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 Quarter = $0.25<br \/>\n1 nickel = $0.05<br \/>\n1 penny = $0.01<br \/>\nThe given money is: 1 penny, 4 Quarters, 1 dollar, and 2 nickels<br \/>\nSo,<br \/>\nThe total amount of money = ( 1 \u00d7 1 ) + ( 4 \u00d7 0.25 ) + ( 2 \u00d7 0.05 ) + ( 1 \u00d7 0.01 )<br \/>\n= 1 + 1 + 0.1 + 0.01<br \/>\n= 2.11<br \/>\nHence,<br \/>\nThe total amount of money is: $2.11<br \/>\nThe representation of $2.11 in the fraction form is: 2\\(\\frac{11}{100}\\) dollar<br \/>\nThe representation if $2.11 in the decimal form is: 2.11<\/p>\n<p>Question 37.<br \/>\nWrite \\(\\frac{18}{100}\\) as a money amount and as a decimal.<br \/>\nAnswer: The representation of \\(\\frac{18}{100}\\) as the total amount of money is: $0.18<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{18}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.18<\/p>\n<p>Question 38.<br \/>\nWrite $0.94 as a fraction and as a decimal.<br \/>\nAnswer: The representation of 0.94 as the total amount of money is: $0.94<\/p>\n<p>Explanation:<br \/>\nThe given decimal number is: 0.94<br \/>\nSo,<br \/>\nThe representation of 0.94 in the fraction form is: \\(\\frac{94}{100}\\)<br \/>\nThe given fraction will be given as an amount in dollars.<br \/>\nSo,<br \/>\nThe total amount of money in the decimal form is: $0.94<\/p>\n<p><strong>10.7 Operations with Money<\/strong><\/p>\n<p><strong>Draw bills and coins to solve.<\/strong><\/p>\n<p>Question 39.<br \/>\nBananas cost $0.29 per pound. You buy 3 pounds of bananas. How much money do you spend in all?<br \/>\nAnswer: The total amount of money you spent is: $0.87<\/p>\n<p>Explanation:<br \/>\nIt is given that bananas cost $0.29 per pound and you bought 3 pounds of bananas<br \/>\nSo,<br \/>\nThe cost of bananas per pound is: $0.29<br \/>\nSo,<br \/>\nThe cost of 3 pounds of bananas = 3 \u00d7 0.29 = $0.87<br \/>\nhence, from the above,<br \/>\nWe can conclude that the total amount of money you spent is: $0.89<\/p>\n<p>Question 40.<br \/>\nDescartes has $3.50. He spends $1.75 on a journal. How much money does Descartes have left?<br \/>\nAnswer: The amount of money Descartes left is: $1.75<\/p>\n<p>Explanation:<br \/>\nIt is given that Descartes has $3.50 and he spent $1.75 on a journal<br \/>\nSo,<br \/>\nThe total amount of money Descartes has: $3.50<br \/>\nThe amount of money Descartes spent is: $1.75<br \/>\nSo,<br \/>\nThe amount of money Descartes left = The total amount of money Descartes has &#8211; The amount of money Descartes spent<br \/>\n= 3.50 &#8211; 1.75<br \/>\n= $1.75<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money Descartes left is: $1.75<\/p>\n<p>Question 41.<br \/>\nYou buy the items shown at a book fair. How much money do you spend in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-201.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 201\" width=\"233\" height=\"137\" \/><br \/>\nAnswer: The total amount of money you spent is: $7.49<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-10-Relate-Fractions-and-Decimals-201.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 10 Relate Fractions and Decimals 201\" width=\"233\" height=\"137\" \/><br \/>\nFrom the given figure,<br \/>\nThe cost of a book is: $6.99<br \/>\nThe cost of the pen is: $0.50<br \/>\nHence,<br \/>\nThe total amount of money you spent = The cost of a book + The cost of a pen<br \/>\n= 6.99 + 0.50<br \/>\n= $7.49<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money you spent is: $7.49<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>All detailed and step by step explanations are covered in the Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals. The solutions are prepared by the highly experienced subject experts after the ample research. This will help you to score the highest marks in the exams. Keep in touch with us to get the solution key of all Big Ideas Math Grade 4 Chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do you want to become proficient in Math? Then, must follow our Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals. Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals is the one-stop destination for all your practice. 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