{"id":90112,"date":"2022-03-29T12:28:21","date_gmt":"2022-03-29T06:58:21","guid":{"rendered":"https:\/\/bigideasmathanswers.com\/?p=90112"},"modified":"2022-04-07T14:37:07","modified_gmt":"2022-04-07T09:07:07","slug":"envision-math-common-core-grade-5-answer-key-topic-1","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/envision-math-common-core-grade-5-answer-key-topic-1\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Value"},"content":{"rendered":"<p>Practice with the help of <a href=\"https:\/\/bigideasmathanswers.com\/envision-math-common-core-grade-5-answer-key\/\">enVision Math Common Core Grade 5 Answer Key<\/a> <strong>Topic 1 Understand Place Value<\/strong> regularly and improve your accuracy in solving questions.<\/p>\n<h2>enVision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value<\/h2>\n<p>Envision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value has all the topics covered, which are related to the basics of Math by giving live examples of our daily life. This chapter is loaded with Decimals, Fractions, and how to do rounding to the nearest numbers, which are quite helpful for students to deal with Math basics. Experience the most satisfying and understandable answers and easy methods with Envision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value.<\/p>\n<h2>Envision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value<\/h2>\n<p>Are you facing difficulties to understand the simple Math problems or numbers , that we have to use in day to day life. Then you have come to the right place to grasp the simple tricks of small calculations. Envision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value. will help you with rounding the numbers , understand the place values , converting decimal into fractions .These are the major topics covered, get on the track with your kids to know them a better way of learning.<\/p>\n<p><strong>Envision STEM Project: Pollinating Insects<\/strong><\/p>\n<ul>\n<li><a href=\"#Envision_ STEM_ Project_ Pollinating_ Insects\">Envision STEM Project Pollinating Insects<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 1 Patterns with exponents and Powers of 10<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.1_ Patterns_ with_ exponents_ and_ Powers_ of_ 10\">Lesson 1.1 Patterns with exponents and Powers of 10<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2 Understand Whole Number Place Value<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.2_ Understand_ Whole_ Number_ Place_ Value\">Lesson 1.2 Understand Whole Number Place Value<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3 Decimals to Thousandths<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.3_ Decimals_ to_ Thousandths\">Lesson 1.3 Decimals to Thousandths<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4 Understand Decimal Place Value<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.4_ Understand_ Decimal_ Place_ Value\">Lesson 1.4 Understand Decimal Place Value<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5 Compare Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.5_ Compare_ Decimals\">Lesson 1.5 Compare Decimals<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 6 Round Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.6_ Round_ Decimals\">Lesson 1.6 Round Decimals<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 7 Look For and Use Structure<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_ 1.7_ Look_ For_ and_ Use_ Structure\">Lesson 1.7 Look For and Use Structure<\/a><\/li>\n<\/ul>\n<h3>\u00a0Performance Task<\/h3>\n<ul>\n<li><a href=\"#Topic_ 1_ Fluency_ Review\">Topic 1 Fluency Review<\/a><\/li>\n<li><a href=\"#Topic_ 1_ Assessment_ Practice\">Topic 1 Assessment Practice<\/a><\/li>\n<li><a href=\"#Topic_ 1_ Performance_ Task\">Topic 1 Performance Task<\/a><\/li>\n<\/ul>\n<p><strong>Essential Question:<\/strong> How are whole numbers and decimals written, compared, and ordered?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-9147\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 1\" width=\"512\" height=\"437\" \/><br \/>\n<strong><a id=\"Envision_ STEM_ Project_ Pollinating_ Insects\"><\/a>Envision STEM Project Pollinating Insects<\/strong><br \/>\n<strong>Do Research<\/strong> Use the Internet or other sources to find out more about pollinating insects in the United States. What types of insects are they? How many are there of each type? How many crops and flowering plants depend on pollinating insects in order to produce the foods we eat?<br \/>\n<strong>Journal: Write a Report<\/strong> Include what you found. Also in your report:<\/p>\n<ul>\n<li>Choose two of the pollinating insects. Estimate how many crop plants each type of insect pollinates.<\/li>\n<li>Estimate how many of your favorite foods and beverages come from pollinated plants.<\/li>\n<li>Make up and solve ways to compare and order your data.<\/li>\n<\/ul>\n<p>Answer: Pollinated insects are nothing but, the insects which are helpful to carry the pollinated grains along with them with the help of their legs or wings from the flower to promote the vast growth of new plants and are commonly known as insect pollinators.<\/p>\n<p>Report for the project :<\/p>\n<ul>\n<li>\u00a0Insect pollinators include bees, flies, butterflies, beetles, wasps, moths, midges and ants, among others. Of these, bees are the most important group, with both wild and managed species acting as pollinators.<\/li>\n<li>Pollinators are essential for continued plant growth in the wild. There are\u00a0seven insect pollinators\u00a0other than bees and butterflies that also help spread plant seeds and enable plant growth.<\/li>\n<li>Three-fourths of the world&#8217;s flowering plants and about 35 percent of the world&#8217;s food crops depend on animal pollinators to reproduce. More than 3,500 species of native bees help increase crop yields.<\/li>\n<li>More than 75 percent of the world&#8217;s food crops depend on pollination . When a seed forms in flowering plants, a fruit is able to grow to protect the seed.<\/li>\n<\/ul>\n<p>Among these two major pollinators are honey bees and butterflies,<br \/>\nHoney bees are the commonly known pollinators which are helpful for the crops like Okra, kiwifruit, Onion, cashew, strawberry, Broccoli, Cauliflower , Cabbage etc.<br \/>\nButterflies are mostly the pollinators of vegetables and herbs and are helpful for the crops like especially those in the carrot family (dill, fennel, celery, cilantro, parsnip), sunflower family (artichokes, lettuce, chicory, chamomile), legume family (peas, beans), mint family (lavender, basil).<\/p>\n<p><strong>Review What You Know<\/strong><\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>Choose the best term from the box. Write it on the blank.<\/p>\n<p>\u2022 digits<br \/>\n\u2022 place value<br \/>\n\u2022 period<br \/>\n\u2022 whole numbers<\/p>\n<p>Question 1.<br \/>\n____ are the symbols used to show numbers.<br \/>\nAnswer: Digits are the symbols used to show numbers.<\/p>\n<p>Explanation:<br \/>\nBecause, A digit is a single symbol used to make numerals or numbers ,<br \/>\nThat is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numerals.<br \/>\nFor example, the number 78 is a two digit number which is made up of two digits that is &#8216;7&#8217; and &#8216;8&#8217;.<\/p>\n<p>Question 2.<br \/>\nA group of 3 digits in a number is a ____<br \/>\nAnswer: A group of 3 digits in a number is a Period.<\/p>\n<p>Explanation:<br \/>\nEvery number consists of digits. The place value is the position of each digit in a number.<br \/>\nDigits are separated into groups of three by commas. So, a period is a group of three digits,<br \/>\nFor example, The number 13,456 is a 5 digit number and the ending 3 digits are called a period, because it is separated by the commas in the number which is referred to a period.<\/p>\n<p>Question 3.<br \/>\n____ is the position of a digit in a number that is used to determine the value of the digit.<br \/>\nAnswer: Place value is the position of a digit in a number that is used to determine the value of the digit.<\/p>\n<p>Explanation:<br \/>\nThe value of a digit depends on its place, or position, in the number.<br \/>\nPlace value is the value of a digit according to its position in the number\u00a0such as ones, tens, hundreds, and so on.<br \/>\nFor example, In the number 3,548<br \/>\n3 is in thousands place and its place value is 3,000,<br \/>\n5 is in hundreds place and its place value is 500,<br \/>\n4 is in tens place and its place value is 40,<br \/>\n8 is in ones place and its place value is 8.<\/p>\n<p><strong>Comparing<\/strong><\/p>\n<p>Compare. Use &lt;,&gt;, or = for each <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/>.<\/p>\n<p>Question 4.<br \/>\n869 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 912<br \/>\nAnswer: 869 &lt; 912.<\/p>\n<p>Explanation:<br \/>\nBecause 869 is less than 912.<br \/>\nFor the number 869<br \/>\n8 is in hundreds place and its place value is 800,<br \/>\n6 is in tens place and its place value is 60,<br \/>\n9 is in ones place and its place value is 9.<\/p>\n<p>And For the number 912<br \/>\n9 is in hundreds place and its place value is 900,<br \/>\n1 is in tens place and its place value is 10,<br \/>\n2 is in ones place and its place value is 2.<\/p>\n<p>So, 869 is less than 912.<\/p>\n<p>Question 5.<br \/>\n9,033 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 9,133<br \/>\nAnswer: 9,033 &lt; 9,133<\/p>\n<p>Explanation:<br \/>\nBecause 9,033 is less than 9,133<br \/>\nFor the number 9,033<br \/>\n9 is in thousands place and its place value is 9,000,<br \/>\n0 is in hundreds place and its place value is 000,<br \/>\n3 is in tens place and its place value is 30,<br \/>\n3 is in ones place and its place value is 3.<\/p>\n<p>And For the number 9,133<br \/>\n9 is in thousands place and its place value is 9,000,<br \/>\n1 is in hundreds place and its place value is 100,<br \/>\n3 is in tens place and its place value is 30,<br \/>\n3 is in ones place and its place value is 3.<\/p>\n<p>So, 9,033 is less than 9,133<\/p>\n<p>Question 6.<br \/>\n1,338 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 1,388<br \/>\nAnswer:\u00a0 1,338 &lt; 1,388<\/p>\n<p>Explanation:<br \/>\nBecause 1,338 is less than 1,388<br \/>\nFor the number 1,338<br \/>\n1 is in thousands place and its place value is 1,000,<br \/>\n3 is in hundreds place and its place value is 300,<br \/>\n3 is in tens place and its place value is 30,<br \/>\n8 is in ones place and its place value is 8.<\/p>\n<p>And For the number 1,388<br \/>\n1 is in thousands place and its place value is 1,000,<br \/>\n3 is in hundreds place and its place value is 300,<br \/>\n8 is in tens place and its place value is 80,<br \/>\n8 is in ones place and its place value is 8.<\/p>\n<p>So, 1,338 is less than 1,388<\/p>\n<p>Question 7.<br \/>\n417,986 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 417,986<br \/>\nAnswer: 417,986 = 417,986<\/p>\n<p>Explanation:<br \/>\nBecause, Numbers given are the same digits having the same place value .<\/p>\n<p>So, 417,986 Equal to 417,986<\/p>\n<p>Question 8.<br \/>\n0.25 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 0.3<br \/>\nAnswer:\u00a0 0.25 &lt; 0.3<\/p>\n<p>Explanation:<br \/>\nBecause, regarding with its place value the number\u00a0 0.25 is less than 0.3<\/p>\n<p>Question 9.<br \/>\n0.5 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9148\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 2\" width=\"26\" height=\"32\" \/> 0.50<br \/>\nAnswer:\u00a0 0.5 = 0.50<\/p>\n<p>Explanation:<br \/>\nBecause the 0 after the number next to decimal is exactly the same number with or without 0<br \/>\nBoth the given numbers are in their same places with respect to each other<br \/>\nSo, 0.5 is equal to 0.50.<\/p>\n<p>Question 10.<br \/>\nKamal has 7,325 songs on his computer. Benito has 7,321 songs on his computer. Who has more songs?<br \/>\nAnswer:\u00a0 Kamal has more songs than Benito.<\/p>\n<p>Explanation:<br \/>\nGiven , Kamal has 7,325 songs on his computer.<br \/>\nBenito has 7,321 songs on his computer.<br \/>\nThen 7,325 &gt; 7,321 or 7,325 is greater than 7,321<\/p>\n<p>So, Kamal has more songs than Benito.<\/p>\n<p><strong>Adding Whole Numbers<\/strong><\/p>\n<p>Find each sum.<\/p>\n<p>Question 11.<br \/>\n10,000 + 2,000 + 60 + 1<br \/>\nAnswer: 12,061<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20171\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.1.png\" alt=\"\" width=\"157\" height=\"237\" \/><br \/>\nAdding all the given numbers by placing them in order of their place value of the digit<br \/>\nSo, the total sum is 12,061.<\/p>\n<p>Question 12.<br \/>\n20,000 + 5,000 + 400 + 3<br \/>\nAnswer: 25,403<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20672\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.2.png\" alt=\"\" width=\"157\" height=\"240\" \/><br \/>\nAdding all the given numbers by placing them in order of their place value of the digit<br \/>\nSo, the total sum is 25,403.<\/p>\n<p>Question 13.<br \/>\n900,000 + 8,000 + 200 + 70 + 6<br \/>\nAnswer: 9,08,276<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20673\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.3.png\" alt=\"\" width=\"181\" height=\"281\" \/><br \/>\nAdding all the given numbers by placing them in order of their place value of the digit<br \/>\nSo, the total sum is 9,08,276.<\/p>\n<p>Question 14.<br \/>\n7,000,000 + 50,000 + 900 + 4<br \/>\nAnswer: 70,50,904<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20674\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.4.png\" alt=\"\" width=\"173\" height=\"257\" \/><br \/>\nAdding all the given numbers by placing them in order of their place value of the digit<br \/>\nSo, the total sum is 70,50,904.<\/p>\n<p><strong>Place Value<\/strong><\/p>\n<p>Question 15.<br \/>\nThe largest playing card structure was made of 218,792 cards. What is the value of the digit 8 in 218,792?<br \/>\nA. 80<br \/>\nB. 800<br \/>\nC. 8,000<br \/>\nD. 80,000<br \/>\nAnswer: C<\/p>\n<p>Explanation:<br \/>\nGiven, The largest playing card structure was made of 218,792 cards.<br \/>\nAccording to the place value method, the value of the digit 8 in 218,792 is 8,000<\/p>\n<p>Question 16.<br \/>\n<strong>Construct Arguments<\/strong> In the number 767, does the first 7 have the same value as the final 7? Why or why not?<br \/>\nAnswer: In the number\u00a0 767, The first 7 does not have the same value as the final 7.<\/p>\n<p>Explanation:<br \/>\nGiven , number is 767 , The first 7 does not have the same value as the final 7.<br \/>\nBecause, the place value is counted from right to left by ones, tens, hundreds, thousand and so on.<br \/>\nSo, in this number 767, the first\u00a0 number 7 holds the hundreds place and the final number 7 holds the ones place, giving it a different value for both the numbers in their place respectively.<\/p>\n<p><strong>Pick a Project<\/strong><\/p>\n<p><strong>PROJECT 1A<\/strong><br \/>\nManatees or sea cows?<br \/>\nProject: Create a Manatee Poster<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9149\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.1\" width=\"433\" height=\"229\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-20694\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.5.png\" alt=\"\" width=\"167\" height=\"164\" \/><\/p>\n<p><strong>PROJECT 1B<\/strong><br \/>\nWhat makes a game fun?<br \/>\nProject: Design a Game with Place-Value Blocks<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9150\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.2\" width=\"432\" height=\"286\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-20695\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.6.png\" alt=\"\" width=\"659\" height=\"348\" \/><\/p>\n<p><strong>PROJECT 1\u0421<\/strong><br \/>\nHow far are we from the sun?<br \/>\nProject: Research Measurements in Our Solar System<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9151\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.3.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.3\" width=\"460\" height=\"263\" \/><\/p>\n<p>Answer: The Sun is at an average distance of about 93,000,000 miles (150 million kilometers) away from Earth. It is so far away that light from the Sun, traveling at a speed of 186,000 miles (300,000 kilometers) per second, takes about 8 minutes to reach us.<\/p>\n<h3><a id=\"Lesson_ 1.1_ Patterns_ with_ exponents_ and_ Powers_ of_ 10\"><\/a>Lesson 1.1 Patterns with exponents and Powers of 10<\/h3>\n<p><strong>Solve &amp; share<\/strong><br \/>\nA store sells AA batteries in packages of 10 batteries. They also sell boxes of 10 packages, cases of 10 boxes, and cartons of 10 cases. How many AA batteries are in one case? One carton? 10 cartons? Solve these problems any way you choose.<\/p>\n<p>You can use appropriate tools, such as place-value blocks, to help solve the problems. However you choose to solve it, show your work!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9152\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.4.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.4\" width=\"448\" height=\"401\" \/><\/p>\n<p><strong>Look Back!<\/strong> How many 10s are in 100? How many 10s are in 1,000? Write equations to show your work.<\/p>\n<p>Answer: There are 1000 AA batteries in one case , 10,000 batteries in one carton and 1,00,000 batteries in 10 cartons.<\/p>\n<p>Explanation:<br \/>\nGiven, A store sells AA batteries in packages of 10 batteries, boxes of 10 packages, cases of 10 boxes, and cartons of 10 cases.<br \/>\nThen we have 10 batteries for one package and given that 1 box contains 10 packages ,<br \/>\n10 \u00d7 10 = 100 , that is 100 batteries for each box.<br \/>\nNext for 10 boxes we have a case which means 100 \u00d7 10 = 1000 batteries ,<br \/>\nThat is each case contains 1000 batteries.<br \/>\nNow for 10 cases we have a carton which means 1000 \u00d7 10 = 10,000 batteries ,<br \/>\nThat is each carton contains 10,000 batteries.<br \/>\nAnd now they asked for 10 cartons ,<br \/>\nSo, for 10 cartons we have 10,000 \u00d7 10 = 1,00,000 batteries .<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong><br \/>\nHow Can You Explain Patterns in the Number of Zeros in a Product?<br \/>\nAnswer: An exponent identifies\u00a0a quantity representing the power to which a given number or expression is to be raised.<\/p>\n<p>Explanation:<br \/>\nFor example , 4 \u00d7 60<br \/>\n= 4 x (6 x 10)<br \/>\n= (4 x 6) x 10<br \/>\n= 24 x 10<br \/>\n=240<br \/>\nor<br \/>\n50 x 700<br \/>\n= (5 x 10) + (7 x 100)<br \/>\n= (5 x 7) x (10 x 100)<br \/>\n= 35 x 1,000<br \/>\n= 35,000.<\/p>\n<p><strong>A.<\/strong><br \/>\nTamara&#8217;s new horse weighs about 1,000 pounds. How can you show 1,000 as a power of 10 using an exponent?<\/p>\n<p>The exponent is the number that tells how many times a base number is used as a factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9153\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.5.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.5\" width=\"297\" height=\"220\" \/><\/p>\n<p>Answer: 10\u00b3<\/p>\n<p>Explanation:<br \/>\nGiven, horse weighs about 1,000 pounds. then show 1,000 as a power of 10 using an exponent<br \/>\nSo we can write 1000 as 10 \u00d7 10 \u00d7 10 = 10\u00b3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9154\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.6.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.6\" width=\"255\" height=\"219\" \/><\/p>\n<p><strong>B.<\/strong><br \/>\nWrite 1,000 as a product using 10 as a factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9155\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-4.7.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 4.7\" width=\"230\" height=\"111\" \/><br \/>\nThe exponent, 3, shows that the base number, 10, is multiplied 3 times.<br \/>\nSo, 1,000 is written as 10<sup>3<\/sup> using exponents.<\/p>\n<p><strong>C.<\/strong><br \/>\nTamara estimates that her horse will eat about 5,000 pounds of hay each year. How can you write 5,000 using exponents? 5 \u00d7 10<sup>1<\/sup> = 5 \u00d7 10 = 50<br \/>\n5 \u00d7 10<sup>2<\/sup> = 5 \u00d7 10 \u00d7 10 = 500<br \/>\n5 \u00d7 10<sup>3<\/sup> = 5 \u00d7 10 \u00d7 10 \u00d7 10 = 5,000<br \/>\nThe number of zeros in the product is the same as the exponent.<br \/>\nSo, 5,000 is written as 5 \u00d7 10<sup>3<\/sup> using exponents.<\/p>\n<p><strong>Convince Me! Look for Relationships<\/strong> What pattern do you notice in the number of zeros in the products in box C above?<\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nWhy are there three zeros in the product of 6 \u00d7 10<sup>3<\/sup>?<br \/>\nAnswer: The product of 6 \u00d7 10\u00b3 is 6,000 so it contains three zeros.<\/p>\n<p>Explanation:<br \/>\nThe product of 6 \u00d7 10\u00b3 is 6,000,<br \/>\nBecause, 6 \u00d7 10 \u00d7 10 \u00d7 10 = 6,000.<br \/>\nSo it contains three zeros.<\/p>\n<p>Question 2.<br \/>\nSusan said that 10<sup>5<\/sup> is 50. What mistake did Susan make? What is the correct answer?<br \/>\nAnswer: The correct answer is 1,00,000.<\/p>\n<p>Explanation:<br \/>\n10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 = 1,00,000.<br \/>\nThe mistake Susan made is he multiplied the exponent with the base.<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>In 3 and 4, complete the pattern.<\/p>\n<p>Question 3.<br \/>\n10<sup>1<\/sup> =<br \/>\n10<sup>2<\/sup> =<br \/>\n10<sup>3<\/sup> =<br \/>\n10<sup>4<\/sup> =<br \/>\nAnswer:<br \/>\n10<sup>1<\/sup> = 10<br \/>\n10<sup>2<\/sup> = 100<br \/>\n10<sup>3<\/sup> = 1000<br \/>\n10<sup>4<\/sup> =\u00a0 10,000<\/p>\n<p>Explanation:<br \/>\n10\u00a0 = 10<br \/>\n10 \u00d7 10\u00a0 =\u00a0 100<br \/>\n10 \u00d7 10 \u00d7 10\u00a0 =\u00a0 1000<br \/>\n10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 10,000.<\/p>\n<p>Question 4.<br \/>\n= 7 \u00d7 10<sup>1<\/sup><br \/>\n= 7 \u00d7 10<sup>2<\/sup><br \/>\n= 7 \u00d7 10<sup>3<\/sup><br \/>\n= 7 \u00d7 10<sup>4<\/sup><br \/>\nAnswer:<br \/>\n70 = 7 \u00d7 10<sup>1<\/sup><br \/>\n700 = 7 \u00d7 10<sup>2<\/sup><br \/>\n7,000 = 7 \u00d7 10<sup>3<\/sup><br \/>\n70,000\u00a0 = 7 \u00d7 10<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven, 7 \u00d710\u00a0 = 70<br \/>\n7 \u00d7 10 \u00d7 10\u00a0 =\u00a0 700<br \/>\n7 \u00d710 \u00d7 10 \u00d7 10\u00a0 =\u00a0 7,000<br \/>\n7 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 70,000.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 5-15, find each product. Use patterns to help.<\/p>\n<p>Question 5.<br \/>\n3 \u00d7 10<sup>1<\/sup> =<br \/>\n3 \u00d7 10<sup>2<\/sup> =<br \/>\n3 \u00d7 10<sup>3<\/sup> =<br \/>\n3 \u00d7 10<sup>4<\/sup> =<br \/>\nAnswer:<br \/>\n3 \u00d7 10<sup>1<\/sup> = 30<br \/>\n3 \u00d7 10<sup>2<\/sup> = 300<br \/>\n3 \u00d7 10<sup>3<\/sup> = 3,000<br \/>\n3 \u00d7 10<sup>4<\/sup> = 30,000<\/p>\n<p>Explanation:<br \/>\n3 \u00d710\u00a0 = 30<br \/>\n3 \u00d7 10 \u00d7 10\u00a0 =\u00a0 300<br \/>\n3 \u00d710 \u00d7 10 \u00d7 10\u00a0 =\u00a0 3,000<br \/>\n3 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 30,000.<\/p>\n<p>Question 6.<br \/>\n2 \u00d7 10 =<br \/>\n2 \u00d7 100 =<br \/>\n2 \u00d7 1,000 =<br \/>\n2 \u00d7 10,000 =<br \/>\nAnswer:<br \/>\n2 \u00d7 10 =\u00a0 20<br \/>\n2 \u00d7 100 = 200<br \/>\n2 \u00d7 1,000 = 2,000<br \/>\n2 \u00d7 10,000 = 20,000<\/p>\n<p>Explanation:<br \/>\n2 \u00d7 10 =\u00a0 2 \u00d7 10<sup>1<\/sup> = 20<br \/>\n2 \u00d7 100 = 2 \u00d7\u00a0 10<sup>2<\/sup> =\u00a0 2 \u00d7 10 \u00d7 10 = 200<br \/>\n2 \u00d7 1,000 = 2 \u00d7 10<sup>3<\/sup> \u00a0=\u00a0 2 \u00d7 10 \u00d7 10 \u00d7 10 = 2,000<br \/>\n2 \u00d7 10,000 = 2 \u00d7 10<sup>4<\/sup> \u00a0= 2 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 \u00d7 10 = 20,000<\/p>\n<p>Question 7.<br \/>\n= 9 \u00d7 10<sup>1<\/sup><br \/>\n= 9 \u00d7 10<sup>2<\/sup><br \/>\n= 9 \u00d7 10<sup>3<\/sup><br \/>\n= 9 \u00d7 10<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>90 = 9 \u00d7 10<sup>1<\/sup><br \/>\n900 = 9 \u00d7 10<sup>2<\/sup><br \/>\n9,000 = 9 \u00d7 10<sup>3<\/sup><br \/>\n90,000\u00a0 = 9 \u00d7 10<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven, 7 \u00d710\u00a0 = 70<br \/>\n7 \u00d7 10 \u00d7 10\u00a0 =\u00a0 700<br \/>\n7 \u00d710 \u00d7 10 \u00d7 10\u00a0 =\u00a0 7,000<br \/>\n7 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 70,000.<\/p>\n<p>Question 8.<br \/>\n8 \u00d7 10<sup>4<\/sup><br \/>\nAnswer:\u00a0 8 \u00d7 10<sup>4<\/sup> = 80,000<\/p>\n<p>Explanation:<br \/>\n8 \u00d7 10<sup>4<\/sup> = 8\u00a0\u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 80,000<\/p>\n<p>Question 9.<br \/>\n4 \u00d7 1,000<br \/>\nAnswer:\u00a0 4 \u00d7 1,000 = 4,000<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>3<\/sup> \u00a0= 4 \u00d710 \u00d7 10 \u00d7 10\u00a0 =\u00a0 4,000<\/p>\n<p>Question 10.<br \/>\n5 \u00d7 10<sup>2<\/sup><br \/>\nAnswer:\u00a0 5 \u00d7 10<sup>2<\/sup> = 500<\/p>\n<p>Explanation:<br \/>\n5 \u00d7 10<sup>2<\/sup> =\u00a0 5\u00a0\u00d7 10 \u00d7 10\u00a0 = 500<\/p>\n<p>Question 11.<br \/>\n6 \u00d7 10,000<br \/>\nAnswer:\u00a0 6 \u00d7 10,000 = 60,000<\/p>\n<p>Explanation:<br \/>\n6 \u00d7 10,000 =\u00a0 6 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 6 \u00d7 10<sup>4<\/sup> = 60,000<\/p>\n<p>Question 12.<br \/>\n4 \u00d7 10<sup>1<\/sup><br \/>\nAnswer:\u00a0 4 \u00d7 10<sup>1<\/sup>\u00a0 =\u00a0 40<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>1<\/sup>\u00a0 =\u00a0 40<\/p>\n<p>Question 13.<br \/>\n100 \u00d7 9<br \/>\nAnswer: 100 \u00d7 9 = 900<\/p>\n<p>Explanation:<br \/>\n100 \u00d7 9\u00a0 = 10 \u00d7 10\u00a0 \u00d7 9 = 900<\/p>\n<p>Question 14.<br \/>\n10<sup>3<\/sup> \u00d7 6<br \/>\nAnswer:\u00a0 10<sup>3<\/sup> \u00d7 6 = 6,000<\/p>\n<p>Explanation:<br \/>\n10<sup>3<\/sup> \u00d7 6 = 10 \u00d7 10 \u00d7 10 \u00d7 6 \u00a0= 6,000<\/p>\n<p>Question 15.<br \/>\n8 \u00d7 10<sup>5<\/sup><br \/>\nAnswer: 8 \u00d7 10<sup>5<\/sup> \u00a0= 8,00,000<\/p>\n<p>Explanation:<br \/>\n8 \u00d7 10<sup>5<\/sup> \u00a0= 8 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 = 8,00,000<\/p>\n<p>Question 16.<br \/>\nWrite 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 with an exponent. Explain how you decided what exponent to write.<br \/>\nAnswer: 10<sup>6<\/sup><\/p>\n<p>Explanation:<br \/>\nAs Given there are 6 tens together<br \/>\nSo, 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 10<sup>6<\/sup><\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 17.<br \/>\nOne box of printer paper has 3 \u00d7 10<sup>2<\/sup> sheets of paper. Another box has 103 sheets of paper. What is the total number of sheets in both boxes?<br \/>\nAnswer: The total number of sheets in both boxes is 403<\/p>\n<p>Explanation:<br \/>\nGiven, One box of printer paper has 3 \u00d7 10<sup>2<\/sup> sheets of paper. then , 3 \u00d7 10<sup>2<\/sup>\u00a0= 300<br \/>\nAnother box has 103 sheets of paper.<br \/>\nSo, 300 + 103\u00a0 = 403<br \/>\nThe total number of sheets in both boxes is 403<\/p>\n<p>Question 18.<br \/>\nA post is put every 6 feet along a fence around a rectangular field that is 42 ft long and 36 ft wide. How many posts are needed?<br \/>\nAnswer: 26 posts are needed.<\/p>\n<p>Explanation:<br \/>\n42 feet for one side, 42 feet for the parallel side<br \/>\n36 feet for one side, 36 feet for the parallel side<br \/>\n42 \u00f7 6 = 7 ,One of these posts is a corner, so make it 6 because we do not want to count a corner post more than once.<br \/>\n36 \u00f7 6 = 6 ,One of these posts is a corner, so make it 5 because we do not want to count a corner post more than once<br \/>\nWe now add these: 2 x 6 + 2 x 5 = 12 + 10 = 22<br \/>\nAdd in the four corner posts: 22 + 4 = 26 posts.<br \/>\nSo , 26 posts are needed.<\/p>\n<p>Question 19.<br \/>\n<strong>Number Sense<\/strong> A company had 9 \u00d7 10<sup>6<\/sup> dollars in sales last year. Explain how to find the product 9 \u00d7 10<sup>6<\/sup>.<br \/>\nAnswer:\u00a0 9 \u00d7 10<sup>6<\/sup> \u00a0 = 9,000,000.<\/p>\n<p>Explanation:<br \/>\n9 \u00d7 10<sup>6<\/sup>\u00a0 =\u00a0 9 \u00d710 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 = 9,000,000.<\/p>\n<p>Question 20.<br \/>\nAn aquarium has the same shape as the solid figure shown below. What is the name of this solid figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9156\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-15.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 15\" width=\"178\" height=\"102\" \/><br \/>\nAnswer: A Rectangular prism.<\/p>\n<p>Explanation:<br \/>\na solid figure that has six sides, called faces, that are rectangles.<br \/>\nSo, they are known as Rectangular prism.<\/p>\n<p>Question 21.<br \/>\n<strong>Model with Math<\/strong> Isaac takes 5 minutes to ride his bike down the hill to school and 10 minutes to ride up the hill from school. He attends school Monday through Friday. How many minutes does he spend biking to and from school in two weeks? Write an equation to model your work.<br \/>\nAnswer:\u00a0 It takes 150 minutes<\/p>\n<p>Explanation:<br \/>\nGiven, Issac take 5 minutes to ride his bike down the hill to school<br \/>\nAnd 10 minutes to ride up the hill from school .<br \/>\nSo, it takes 15 min each day to and from school He attends school Monday through Friday,<br \/>\nSo, 5 days in a week for 5 days it takes\u00a0 15 \u00d7 5 = 75 minutes<br \/>\nFor 2 weeks , 75 \u00d7 2 = 150 minutes.<\/p>\n<p>Question 22.<br \/>\n<strong>Higher Order Thinking<\/strong> Santiago hopes to buy a 4-horse trailer for about $12,000. Describe all the numbers that when rounded to the nearest hundred are 12,000.<br \/>\nAnswer: Any number from 11,950 to 12,049, will result to 12,000 when rounded to the nearest hundred.\u00a0<span class=\"copyright-span\"><br \/>\n<\/span><\/p>\n<p>Explanation:<br \/>\nSince we have given that,<br \/>\nNumber of horse trailer = 4 Cost of 4 horse trailer = $12000 ,<br \/>\nAs we know about the &#8220;Estimation&#8221;, if there is a number greater or equal to 5 in tens place then it will be rounded off to the nearest next greatest integer.<br \/>\nSo, if this number is $11950 to 12049.<br \/>\nSo, the possible numbers that when rounded to the nearest hundred are 12000 are from 11500 to 12049.<\/p>\n<p>Assessment Practice<\/p>\n<p>Question 23.<br \/>\nChoose all the equations that are true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 10 \u00d7 10 \u00d7 10 \u00d7 10 = 40<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10<sup>4<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 10 \u00d7 10 \u00d7 10 \u00d7 10 = 1,000,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10,000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 10 \u00d7 10 \u00d7 10 \u00d7 10 = 4 \u00d7 10<sup>4<\/sup><br \/>\nAnswer:\u00a0 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10<sup>4<\/sup>\u00a0 and\u00a0 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10,000<\/p>\n<p>Explanation:<br \/>\nThere are 4 tens in 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10<sup>4<\/sup><br \/>\nSo, 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10,000.<\/p>\n<p>Question 24.<br \/>\nChoose all the equations that are true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 6 \u00d7 10<sup>5<\/sup> = 6 \u00d7 100,000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 6 \u00d7 10<sup>5<\/sup> = 6 \u00d7 10,000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 6 \u00d7 10<sup>5<\/sup> = 600,000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 6 \u00d7 10<sup>5<\/sup> = 60,000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9157\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-16.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 16\" width=\"34\" height=\"31\" \/> 6 \u00d7 10<sup>5<\/sup> = 650,000<br \/>\nAnswer: 6 \u00d7 10<sup>5<\/sup> = 6 \u00d7 100,000 and\u00a0 6 \u00d7 10<sup>5<\/sup> = 600,000<\/p>\n<p>Explanation:<br \/>\n6 \u00d7 10<sup>5 <\/sup>= 6 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 \u00d7 10 = 6,00,000. or<br \/>\n6 \u00d7 10<sup>5 <\/sup>= 6 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 \u00d7 10 = 6 \u00d7 100,000.<\/p>\n<h3><a id=\"Lesson_ 1.2_ Understand_ Whole_ Number_ Place_ Value\"><\/a>Lesson 1.2 Understand Whole Number Place Value<\/h3>\n<p><strong>Activity<\/strong><\/p>\n<p><strong>Solve &amp; Share<\/strong><\/p>\n<p>The population of a city is 1,880,000. What is the value of each of the two 8s in this number? How are the two values related? Use tools like this place-value chart to help solve the problem.<\/p>\n<p>Answer: These are the values of each number<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20724\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.7.png\" alt=\"\" width=\"725\" height=\"82\" \/><\/p>\n<p>Explanation:<br \/>\nAdd up all these values and we will have 1,880,000.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20725\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.8.png\" alt=\"\" width=\"297\" height=\"318\" \/><\/p>\n<p><strong>Use Structure<\/strong> You can use place value to analyze the relationship between the digits of a number. Show your work!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9158\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-17.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 17\" width=\"561\" height=\"379\" \/><\/p>\n<p><strong>Look Back!<\/strong> Is the relationship between the value of the two 85 in 1,088,000 the same as the relationship between the value of the two 8s in the problem above? Explain.<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong><br \/>\nHow Are Place-Value Positions Related?<\/p>\n<p><strong>A.<\/strong><br \/>\nAccording to the 2010 U.S. Census, the population of Phoeni\u00d7, Arizona is about 1,440,000. What is the relationship between the value of the two 4s in this number?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9159\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-18.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 18\" width=\"361\" height=\"242\" \/><br \/>\nWriting the number in expanded form can help.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9160\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-19.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 19\" width=\"182\" height=\"160\" \/><\/p>\n<p><strong>C.<\/strong><br \/>\nLook at the expanded form of 1,440,000. The value of the 4 in the hundred thousands place is 400,000. The value of the 4 in the ten thousands place is 40,000.<br \/>\n400,000 is 10 times as great as 40,000.<br \/>\n40,000 is \\(\\frac{1}{10}\\) of 400,000.<\/p>\n<p>Sometimes word form is used instead of number name.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9169\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20\" width=\"86\" height=\"103\" \/><br \/>\n<strong>Standard form<\/strong><br \/>\n1,440,000<br \/>\n<strong>Expanded form:<\/strong><br \/>\n1 \u00d7 1,000,000 + 4 \u00d7 100,000 + 4 \u00d7 10,000<br \/>\nUsing exponents, this can be written as:<br \/>\n(1 \u00d7 10<sup>6<\/sup>) + (4 \u00d7 10<sup>5<\/sup>) + (4 \u00d7 10<sup>4<\/sup>)<br \/>\n<strong>Number name:<\/strong><br \/>\none million, four hundred forty thousand<\/p>\n<p><strong>Convince Me! Construct Arguments<\/strong> is the value of the 1 in 1,440,000 10 times as great as the value of the 4 in the hundred thousands place? Explain.<\/p>\n<p><strong>Another example<\/strong><br \/>\nWhen two digits next to each other in a number are the same, the digit on the left has 10 times the value of the digit to its right.<br \/>\nWhen two digits next to each other are the same, the digit on the right has to the value of the digit to its left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9161\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.1\" width=\"156\" height=\"83\" \/><\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nIn 9,290, is the value of the first 9 ten times as great as the value of the second 9? Explain.<br \/>\nAnswer:\u00a0 No<span class=\"copyright-span\"><br \/>\n<\/span><\/p>\n<p>Explanation:<br \/>\nThe first 9 is on the place of the thousands, while the second 9 is on the place of the tens. so the first 9 is a hundred times as great as the second 9<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>Question 2.<br \/>\nWrite 4,050 in expanded form.<br \/>\nAnswer:\u00a0 4,000 + 50<\/p>\n<p>Explanation:<br \/>\n4,000 + 50\u00a0 = 4,050.<\/p>\n<p>In 3 and 4, write the values of the given digits.<\/p>\n<p>Question 3.<br \/>\nthe 7s in 7,700<br \/>\nAnswer:\u00a0 7,000 + 700<\/p>\n<p>Explanation:<br \/>\nThe first 7 is on the place of the thousands, while the second 7 is on the place of the hundreds.<\/p>\n<p>Question 4.<br \/>\nthe 2s in 522<br \/>\nAnswer:\u00a0 500 + 22<\/p>\n<p>Explanation:<br \/>\nThe first 2 is on the place of the tens, while the second 2 is on the place of the ones.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 5-7, write each number in standard form.<\/p>\n<p>Question 5.<br \/>\n8,000,000 + 300 + 9<br \/>\nAnswer: 8,000,309.<\/p>\n<p>Explanation:<br \/>\n8,000,000 + 300 + 9 = 8,000,309.<\/p>\n<p>Question 6.<br \/>\n(4 \u00d7 10<sup>4<\/sup>) + (6 \u00d7 10<sup>2<\/sup>)<br \/>\nAnswer: 40,600<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>4<\/sup> =4\u00a0\u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10\u00a0 =\u00a0 40,000<br \/>\n6 \u00d7 10<sup>2<\/sup> \u00a0= 6\u00a0\u00d7 10 \u00d7 10 =\u00a0 600<br \/>\nSo, 40,000 + 600 = 40,600<\/p>\n<p>Question 7.<br \/>\n10,000 + 20 + 3<br \/>\nAnswer:\u00a0 \u00a010023<\/p>\n<p>Explanation:<br \/>\n10,000 + 20 + 3 = 10023.<\/p>\n<p>In 8-10, write each number in expanded form.<\/p>\n<p>Question 8.<br \/>\n5,360<br \/>\nAnswer: (5 \u00d7 10\u00b3) + (3 \u00d7 10\u00b2) + (6 \u00d7 10)<\/p>\n<p>Explanation:<br \/>\n5,360 =\u00a0 5000 + 300 + 60\u00a0 = (5 \u00d7 10\u00b3) + (3 \u00d7 10\u00b2) + (6 \u00d7 10)<\/p>\n<p>Question 9.<br \/>\n102,200<br \/>\nAnswer:\u00a0 10<sup>5<\/sup> + (2 \u00d7 10\u00b3) + ( 2 \u00d7 10\u00b2)<\/p>\n<p>Explanation:<br \/>\n102,200 = 1,00,000 + 2000 + 200 = \u00a010<sup>5<\/sup> + (2 \u00d7 10\u00b3) + ( 2 \u00d7 10\u00b2)<\/p>\n<p>Question 10.<br \/>\n85,000,011<br \/>\nAnswer:\u00a0 (85 \u00d7 \u00a010<sup>6<\/sup>) + 10 + 1<\/p>\n<p>Explanation:<br \/>\n85,000,011 = 85,000,000 + 10 + 1 = (85 \u00d7 \u00a010<sup>6<\/sup>) + 10 + 1<\/p>\n<p>In 11-13, write the values of the given digits.<\/p>\n<p>Question 11.<br \/>\nthe 7s in 6,778<br \/>\nAnswer: 6,000 + 700 + 70 + 8<\/p>\n<p>Explanation:<br \/>\nThe first 7 is on the place of the hundreds, while the second 7 is on the place of the tens.<\/p>\n<p>Question 12.<br \/>\nthe 9s in 990,250<br \/>\nAnswer: 9,00,000 + 90,000 + 200 + 50<\/p>\n<p>Explanation:<br \/>\nThe first 9 is on the place of the hundred thousands, while the second 9 is on the place of the thousands.<\/p>\n<p>Question 13.<br \/>\nthe 1s in 2,011,168<br \/>\nAnswer: 2,000,000 + 11,000 + 100 + 60 + 8<\/p>\n<p>Explanation:<br \/>\nThe first 1 is on the place of the ten thousands, while the second 1 is on the place of the thousands and the third 1 is on the place of hundreds.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 14.<br \/>\nWrite the number name and expanded form for the number of driver ants that could be in two colonies.<\/p>\n<p>Up to 22,000,000 driver ants can live in a single colony.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9162\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.5.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.5\" width=\"320\" height=\"193\" \/><\/p>\n<p>Answer:\u00a0 For 2 colonies\u00a0 44,000,000<br \/>\nThe number name is Forty four million<br \/>\nThe expanded form is (4 \u00d710<sup>6<\/sup>) + (4 \u00d710<sup>6<\/sup>)<\/p>\n<p>Explanation:<br \/>\nGiven , Up to 22,000,000 driver ants can live in a single colony.<br \/>\nFor 2 colonies 22,000,000 + 22,000,000 = 44,000,000<br \/>\nThe expanded form is 40,000,000 + 4,000,000 = (4 \u00d710<sup>6<\/sup>) + (4 \u00d710<sup>6<\/sup>)<\/p>\n<p>Question 15.<br \/>\n<strong>enVision\u00ae STEM<\/strong> A queen ant can produce about nine million ants in her lifetime. Write this number in standard form.<br \/>\nAnswer: The number in standard form is 9,000,000<\/p>\n<p>Explanation:<br \/>\nGiven, A queen ant can produce about nine million ants in her lifetime.<br \/>\nThe number in standard form is 9,000,000.<\/p>\n<p>Question 16.<br \/>\n<strong>Critique Reasoning<\/strong> Paul says that in the number 6,367, one 6 is 10 times as great as the other 6. Is he correct? Explain why or why not.<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\nGiven in the number 6,367, one 6 is 10 times as great as the other 6.<br \/>\nThe first 6 is on the place of the thousands, while the second 6 is on the place of the tens. so the first 6 is a hundred times as great as the second 6.<\/p>\n<p>Question 17.<br \/>\nJorge drew a square that had a side length of 8 inches. What is the perimeter of Jorge&#8217;s square?<br \/>\nRemember, the perimeter of a shape is the distance around it.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9163\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.6.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.6\" width=\"100\" height=\"121\" \/><br \/>\nAnswer: The perimeter of Jorge&#8217;s square is 32 inches.<\/p>\n<p>Explanation:<br \/>\nGiven, Jorge drew a square that had a side length of 8 inches.<br \/>\nSquare has all equal sides, so perimeter of the square P = 4a = 4 \u00d7 8 = 32 inches<\/p>\n<p>Question 18.<br \/>\n<strong>Higher Order Thinking<\/strong><br \/>\nDan wrote (2 \u00d7 10<sup>6<\/sup>) + (3 \u00d7 10<sup>4<\/sup>) + (5 \u00d7 10<sup>3<\/sup>) + 4 for the expanded form of two million, three hundred fifty thousand, four. What error did he make in the expanded form? What is the standard form of the number?<\/p>\n<p>Answer: The standard form of the number is 20,35,004.<br \/>\nThe number name is two million, thirty five thousand and four.<\/p>\n<p>Explanation:<br \/>\n(2 \u00d7 10<sup>6<\/sup>) + (3 \u00d7 10<sup>4<\/sup>) + (5 \u00d7 10<sup>3<\/sup>) + 4<br \/>\n= 2,000,000 + 30,000 + 5,000 + 4<br \/>\n= 20,35,004.<br \/>\nThe standard form of the number is 20,35,004.<br \/>\nThe number name is two million, thirty five thousand and four.<br \/>\nHe made mistake with the three hundred fifty thousand, instead of\u00a0 thirty five thousand<\/p>\n<p><strong>Assessment Practice<\/strong><\/p>\n<p>Question 19.<br \/>\nColleen says she is thinking of a 4-digit number in which all the digits are the same. The value of the digit in the hundreds place is 200.<br \/>\n<strong>Part A<\/strong><br \/>\nWhat is the number? Explain.<\/p>\n<p><strong>Part B<\/strong><br \/>\nDescribe the relationship between the values of the digits in the number.<br \/>\nAnswer:\u00a0 The number is 2,222.<br \/>\nThe first 2 is on the place of the thousands, while the second 2 is on the place of the hundreds, The third 2 is on the place of the tens, and the last 2 is on the place of the ones.<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 Colleen says she is thinking of a 4-digit number in which all the digits are the same. The value of the digit in the hundreds place is 200.<br \/>\nThe number is 2,222.<br \/>\nThe first 2 is on the place of the thousands, while the second 2 is on the place of the hundreds, The third 2 is on the place of the tens, and the last 2 is on the place of the ones.<\/p>\n<h3><a id=\"Lesson_ 1.3_ Decimals_ to_ Thousandths\"><\/a>Lesson 1.3 Decimals to Thousandths<\/h3>\n<p><strong>Solve &amp; Share<\/strong><br \/>\nAt Suzie&#8217;s Sticker City, customers can buy a book of stickers, a page, a strip, or a single sticker. Provide the missing fractions in the boxes below.<\/p>\n<p>How can you use what you know about powers of 10 to help you fill in the boxes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9164\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.7.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.7\" width=\"570\" height=\"374\" \/><\/p>\n<p><strong>Look Back! Use Structure<\/strong> Describe any patterns you notice in the fractions.<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong><br \/>\nHow Can You Read and Write Question Decimals to the Thousandths?<\/p>\n<p><strong>A.<\/strong><br \/>\nA box is filled with 1,000 cubes. Amy picks out 4 cubes. How can you represent 4 out of 1,000 cubes as a decimal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9165\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.8.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.8\" width=\"156\" height=\"198\" \/><\/p>\n<p>You can write 4 out of 1,00 as the fraction \\(\\frac{4}{1,000}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9166\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.9.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.9\" width=\"147\" height=\"272\" \/><\/p>\n<p><strong>B.<\/strong><br \/>\nThe number name for \\(\\frac{4}{1,000}\\) is four thousandths. A decimal place-value chart can help you determine the decimal. Notice that the thousandths place is three places to the right of the decimal point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9167\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.10.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.10\" width=\"307\" height=\"83\" \/><br \/>\nSo, \\(\\frac{4}{1,000}\\) can be represented by the decimal 0.004.<\/p>\n<p><strong>C.<\/strong><br \/>\nHow can \\(\\frac{444}{1,000}\\) be represented by a decimal? \\(\\frac{444}{1,000}\\) is read as four hundred forty-four thousandths and represented by the decimal 0.444.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9168\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-20.11.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 20.11\" width=\"302\" height=\"126\" \/><br \/>\nThe value of the digit 4 in the hundredths place has 10 times the value of the digit 4 in the thousandths place and \\(\\frac{1}{10}\\) the value of the digit 4 in the tenths place.<\/p>\n<p><strong>Convince Me! Reasoning<\/strong> How is 0.004 the same as and different from 0.444?<\/p>\n<p>Answer: 0.004 and 0.444 both have 4 in the thousandth place<\/p>\n<p>Explanation:<br \/>\n0.004 and 0.444 both have 4 in the thousandth place,<br \/>\nboth are in thousandth place<br \/>\ndifferent: 0.444 is greater than 0.004 when divide by 1000<br \/>\n444\/1000 is greater than 4\/1000<br \/>\nif convert to percentage : 0.444 is 44.4% and 0.004 is 0.4%<\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nIf four cubes are pulled from the box on the previous page, how would you write the fraction representing the cubes that are left? the decimal representing the cubes that are left?<br \/>\nAnswer:\u00a0 In decimal form we can write it as 0.996.<\/p>\n<p>Explanation:<br \/>\nGiven, A box is filled with 1,000 cubes, picking out 4 cubes,<br \/>\n1000 &#8211; 4 = 996,<br \/>\nThen \\(\\frac{996}{1000}\\) are the remaining of the cubes which are left in the box<br \/>\nIn decimal form we can write it as 0.996.<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>Question 2.<br \/>\n0.3 is 10 times as great as what decimal? 0.003 is \\(\\frac{1}{10}\\) of what decimal?<br \/>\nAnswer: 0.3 is 10 times as great as 0.03 and 0.003 is \\(\\frac{1}{10}\\) of 0.03<\/p>\n<p>Explanation:<br \/>\n0.3 \u00d7 \\(\\frac{1}{10}\\) = 0.03<br \/>\n0.03 = 0.003 \u00d7 \\(\\frac{1}{10}\\)<br \/>\nSo, 0.3 is 10 times as great as 0.03 and 0.003 is \\(\\frac{1}{10}\\) of 0.03<\/p>\n<p>In 3-6, write each decimal as a fraction.<\/p>\n<p>Question 3.<br \/>\n0.001 =<br \/>\nAnswer: \\(\\frac{1}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.001 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{1}{1000}\\)<\/p>\n<p>Question 4.<br \/>\n0.05 =<br \/>\nAnswer: \\(\\frac{5}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.05 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{5}{100}\\)<\/p>\n<p>Question 5.<br \/>\n0.512 =<br \/>\nAnswer: \\(\\frac{512}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.512 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{512}{1000}\\)<\/p>\n<p>Question 6.<br \/>\n0.309 =<br \/>\nAnswer: \\(\\frac{309}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.309 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{309}{1000}\\)<\/p>\n<p>In 7-10, write each fraction as a decimal.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{2}{1,000}\\) =<br \/>\nAnswer: 0.002<\/p>\n<p>Explanation:<br \/>\nGiven , \\(\\frac{2}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.002<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{34}{100}\\) =<br \/>\nAnswer: 0.34<\/p>\n<p>Explanation:<br \/>\nGiven , \\(\\frac{34}{100}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.34<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{508}{1,000}\\) =<br \/>\nAnswer: 0.508<\/p>\n<p>Explanation:<br \/>\nGiven , \\(\\frac{508}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.508<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{99}{1,000}\\) = =<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nGiven , \\(\\frac{99}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.099<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 11-18, write each decimal as a fraction.<\/p>\n<p>Question 11.<br \/>\n0.007<br \/>\nAnswer: \\(\\frac{7}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.007 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{7}{1000}\\)<\/p>\n<p>Question 12.<br \/>\n0.08<br \/>\nAnswer: \\(\\frac{8}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.08 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{8}{100}\\)<\/p>\n<p>Question 13.<br \/>\n0.065<br \/>\nAnswer: \\(\\frac{65}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.08 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{65}{1000}\\)<\/p>\n<p>Question 14.<br \/>\n0.9<br \/>\nAnswer: \\(\\frac{9}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.9 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{9}{10}\\)<\/p>\n<p>Question 15.<br \/>\n0.832<br \/>\nAnswer: \\(\\frac{832}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.832 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{832}{1000}\\)<\/p>\n<p>Question 16.<br \/>\n0.203<br \/>\nAnswer: \\(\\frac{203}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.203 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{203}{1000}\\)<\/p>\n<p>Question 17.<br \/>\n0.78<br \/>\nAnswer:\u00a0 \\(\\frac{78}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.78 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{78}{100}\\)<\/p>\n<p>Question 18.<br \/>\n0.999<br \/>\nAnswer: \\(\\frac{999}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 0.999 ,<br \/>\nIn fraction form we can write it in to \\(\\frac{999}{1000}\\)<\/p>\n<p>In 19-26, write each fraction as a decimal.<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{434}{1,000}\\) =<br \/>\nAnswer:\u00a0 0.434<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{434}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.0.434<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{3}{10}\\) =<br \/>\nAnswer: 0.3<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{3}{10}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.3<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{873}{1,000}\\) =<br \/>\nAnswer: 0.873<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{873}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.873<\/p>\n<p>Question 22.<br \/>\n\\(\\frac{17}{1,000}\\) =<br \/>\nAnswer:0.017<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{17}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.017<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{309}{1,000}\\) =<br \/>\nAnswer: 0.309<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{309}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.309<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{5}{1,000}\\) =<br \/>\nAnswer: 0.005<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{5}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.005<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{6}{100}\\) =<br \/>\nAnswer: 0.06<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{6}{100}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.06<\/p>\n<p>Question 26.<br \/>\n\\(\\frac{999}{1,000}\\) =<br \/>\nAnswer: 0.999<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{999}{1,000}\\)<br \/>\nIn decimal form we can\u00a0 write it into 0.999<\/p>\n<p>Question 27.<br \/>\nLook at the middle 9 in exercise 18. How is its value related to the value of the 9 to its left? to the value of the 9 to its right?<br \/>\nAnswer: The value of the digit 9 in the hundredths place has 10 times the value of the digit 9 in the thousandths place and \\(\\frac{1}{10}\\)\u00a0the value of the digit 9 in the tenths place.<\/p>\n<p>Explanation:<br \/>\nThe value of the number given in exercise 18 is 0.999,<br \/>\nThe first 9 is on the place of the tenths, while the second 9 is on the place of the hundredths and the second 9 is\u00a0 on the place of thousandths.<br \/>\nSo, The value of the digit 9 in the hundredths place has 10 times the value of the digit 9 in the thousandths place and \\(\\frac{1}{10}\\)\u00a0the value of the digit 9 in the tenths place.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 28.<br \/>\nThe Palmers&#8217; property tax bill for the year is $3,513. In their first installment, they paid $1,757. How much do they still owe on their bill? Write an equation to model your work.<br \/>\nAnswer:\u00a0 They still owe $1,756 on their bill .<\/p>\n<p>Explanation:<br \/>\nGiven, The Palmers&#8217; property tax bill for the year is $3,513.<br \/>\nIn their first installment, they paid $1,757.<br \/>\n$3,513 &#8211; $1,757 = $1,756.<br \/>\nSo, they still have to pay the half amount that is $1,756<br \/>\nThen $1,757 \u00d7 2 = $3,513.<br \/>\nThey still owe $1,756 on their bill .<\/p>\n<p>Question 29.<br \/>\nWrite the fractions \\(\\frac{22}{100}\\) and \\(\\frac{22}{1,000}\\) as decimals. How are the values of the digit 2 related in each of the decimals?<br \/>\nAnswer: 0.22 and 0.022<\/p>\n<p>Explanation:<br \/>\nGiven, \\(\\frac{22}{100}\\)<br \/>\nIn decimal form we can write it as 0.22,<br \/>\nThe value of the digit 2 in the tenths place has 10 times the value of the digit 4 in the hundredths place .<\/p>\n<p>And \\(\\frac{22}{1,000}\\)<br \/>\nIn decimal form we can write it as 0.022,<br \/>\nThe value of the digit 2 in the hundredths place has 10 times the value of the digit 4 in the thousandths place.<\/p>\n<p>Question 30.<br \/>\nSimon scored 4 \u00d7 10<sup>2<\/sup> points in a game. Joe scored 2 \u00d7 10<sup>3<\/sup> points in the same game. Whose score is higher? How much higher?<br \/>\nAnswer: Joe scored 5 times as many as Simon.<\/p>\n<p>Explanation:<br \/>\nGiven, Simon scored 4 \u00d7 10<sup>2<\/sup> points in a game.<br \/>\nJoe scored 2 \u00d7 10<sup>3<\/sup> points in the same game.<br \/>\nNow we have\u00a0 4 \u00d7 10<sup>2<\/sup> =\u00a0 4 \u00d7 10 \u00d7 10 = 400<br \/>\n2 \u00d7 10<sup>3<\/sup> =\u00a0 2 \u00d7 10 \u00d7 10 \u00d7 10 = 2000<br \/>\nFinally, Simon scored 400 point and Joe scored 2000 points<br \/>\nSo, Joe scored 5 times as many as Simon.<\/p>\n<p>Question 31.<br \/>\n<strong>Higher Order Thinking<\/strong> Kelly said that \\(\\frac{97}{1,000}\\) can be written as 0.97. Is she correct? Explain.<br \/>\nAnswer: No , \\(\\frac{97}{1,000}\\)\u00a0 should be 0.097 not 0.97<\/p>\n<p>Explanation:<br \/>\nGiven, Kelly said that \\(\\frac{97}{1,000}\\) can be written as 0.97<br \/>\nThe decimal form can written according to the number of zeros in the denominator<br \/>\nSo , \\(\\frac{97}{1,000}\\)\u00a0 should be 0.097 not 0.97<\/p>\n<p>Question 32.<br \/>\n<strong>Critique Reasoning<\/strong> Frank reasoned that in the number 0.555, the value of the 5 in the thousandths place is ten times as great as the 5 in the hundredths place. Is he correct? Explain.<br \/>\nAnswer: NO<\/p>\n<p>Explanation:<br \/>\nGiven, the number 0.555<br \/>\nThe value of the digit 5 in the hundredths place has 10 times the value of the digit 5 in the thousandths place<\/p>\n<p>Question 33.<br \/>\nHow many cubes are in the box? What fraction of the entire box do the 7 cubes represent? Explain your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9170\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-35.1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 35.1\" width=\"216\" height=\"137\" \/><br \/>\nAnswer: \\(\\frac{7}{1000}\\)<\/p>\n<p>Explanation:<br \/>\nGiven, 10 \u00d7 10 \u00d7 10\u00a0 = 1000<br \/>\nAnd we have the 7 cubes<br \/>\nSo, the fraction will be\u00a0 \\(\\frac{7}{1000}\\)<\/p>\n<p><strong>Assessment Practice<\/strong><\/p>\n<p>Question 34.<br \/>\n0.04 is 10 times as great as which decimal?<br \/>\nA. 0.4<br \/>\nB. 0.1<br \/>\nC. 0.004<br \/>\nD. 0.001<br \/>\nAnswer: C , 0.04 is 10 times as great as 0.004<\/p>\n<p>Explanation:<br \/>\n0.04 \u00d7 \\(\\frac{1}{10}\\) = 0.004<br \/>\nSo, 0.04 is 10 times as great as 0.004<\/p>\n<p>Question 35.<br \/>\n0.009 is o of which decimal?<br \/>\nA. 0.01<br \/>\nB. 0.09<br \/>\nC. 0.1<br \/>\nD. 0.9<br \/>\nAnswer:\u00a0 B, 0.009 is \\(\\frac{1}{10}\\) of 0.09<\/p>\n<p>Explanation:<br \/>\n0.09 \u00d7 \\(\\frac{1}{10}\\) = 0.009<br \/>\nSo, 0.009 is \\(\\frac{1}{10}\\) of 0.09<\/p>\n<h3><a id=\"Lesson_ 1.4_ Understand_ Decimal_ Place_ Value\"><\/a>Lesson 1.4 Understand Decimal Place Value<\/h3>\n<p><strong>Solve &amp; Share<\/strong><\/p>\n<p>A runner won a 100-meter race with a time of 9.85 seconds. How can you use place value to Explain this time? Complete a place-value chart to show this time.<\/p>\n<p><strong>Generalize<\/strong> You can use what you know about whole-number place value to help you think about place value of decimal numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9171\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-36.1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 36.1\" width=\"574\" height=\"346\" \/><\/p>\n<p><strong>Look Back!<\/strong> In the decimal 9.85, what is the value of the 8? What is the value of the 5?<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong> How Can You Represent Decimals?<\/p>\n<p><strong>A.<\/strong><br \/>\nJo picked a seed from her flower. The seed has a mass of 0.245 gram. What are some different ways you can represent 0.245?<\/p>\n<p>You can write the standard form, expanded form, and number name for a decimal just like you can for a whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9172\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-36.2.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 36.2\" width=\"522\" height=\"263\" \/><\/p>\n<p><strong>B.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9173\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-36.3.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 36.3\" width=\"374\" height=\"216\" \/><br \/>\n<strong>Number Name:<\/strong> two hundred forty-five<\/p>\n<p>A place-value chart can help you identify the tenths, hundredths, and thousandths places in a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9174\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-36.4.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 36.4\" width=\"124\" height=\"185\" \/><\/p>\n<p><strong>Convince Me!<\/strong> <strong>Use Structure<\/strong> How many hundredths are in one tenth? How many thousandths are in one hundredth? Tell how you know.<\/p>\n<p><strong>Another example<\/strong><br \/>\nEquivalent decimals name the same amount.<br \/>\nWhat are two other decimals equivalent to 1.4?<br \/>\nOne and four tenths is the same as one and forty hundredths.<br \/>\n1.4 = 1.40<br \/>\nOne and four tenths is the same as one and four hundred thousandths.<br \/>\n1.4 = 1.400.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9175\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answer-Key-Topic-1-Understand-Place-Vale-37.1.png\" alt=\"Envision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Vale 37.1\" width=\"329\" height=\"250\" \/><br \/>\nSo, 1.4 = 1.40 = 1.400.<\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nThe number 3.453 has two 3s. Why does each 3 have a different value?<br \/>\nAnswer: These are different due to the place values. 3 and 0.003<\/p>\n<p>Explanation:<br \/>\nThe given number is 3.453.<br \/>\nThe first 3 that is before the decimal is at ones place, that is 3 \u00d7 1 = 3<br \/>\nBut the second 3 which is after the decimal is at thousandth place, \\(\\frac{3}{1000}\\) = 0.003<br \/>\nHence, you can clearly see the different values of both three&#8217;s. These are different due to the place values.<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>In 2 and 3, write each number in standard form.<\/p>\n<p>Question 2.<br \/>\n4 \u00d7 100 + 7 \u00d7 10 + 6 \u00d7 1 + 6 \u00d7 \\(\\left(\\frac{1}{10}\\right)\\) + 3 \u00d7 \\(\\left(\\frac{1}{100}\\right)\\) + 7 \u00d7 \\(\\left(\\frac{1}{1,000}\\right)\\)<br \/>\nAnswer:\u00a0 The standard form is 476.637.<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n(4 \u00d7 100)+ (7 \u00d7 10) + (6 \u00d7 1) + {6 \u00d7 \\(\\left(\\frac{1}{10}\\right)\\) + 3 \u00d7 \\(\\left(\\frac{1}{100}\\right)\\) + 7 \u00d7 \\(\\left(\\frac{1}{1,000}\\right)\\)}<br \/>\nSolve for the brackets,<br \/>\nwe have 400 + 70 + 6 + [ 0.6 + 0.03 + 0.007]<br \/>\n= 476 + 0.637<br \/>\n= 476.637<br \/>\nThe standard form is 476.637.<\/p>\n<p>Question 3.<br \/>\nfour and sixty-eight thousandths<br \/>\nAnswer: The standard form is 0.468.<\/p>\n<p>Explanation:<br \/>\nGiven, four and sixty-eight thousandths<br \/>\nThe expanded form is 4 \u00d7 \\(\\left(\\frac{1}{10}\\right)\\) + 6 \u00d7 \\(\\left(\\frac{1}{100}\\right)\\) + 8 \u00d7 \\(\\left(\\frac{1}{1,000}\\right)\\)<br \/>\nThen, 0.4 + 0.06 + 0.008 = 0.468<br \/>\nSo, the standard form is 0.468<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 4-6, write each number in standard form.<\/p>\n<p>Question 4.<br \/>\n(2 \u00d7 1) + (6 \u00d7 \\(\\frac{1}{1,000}\\))<br \/>\nAnswer: The standard form is 2.006<\/p>\n<p>Explanation:<br \/>\nGiven, (2 \u00d7 1) + (6 \u00d7 \\(\\frac{1}{1,000}\\))<br \/>\n= 2 + 0.006<br \/>\n= 2.006<br \/>\nThe standard form is 2.006<\/p>\n<p>Question 5.<br \/>\n(3 \u00d7 1) + (3 \u00d7 \\(\\frac{1}{10}\\)) + (9 \u00d7 \\(\\frac{1}{1,000}\\))<br \/>\nAnswer: The standard form is 3.309<\/p>\n<p>Explanation:<br \/>\nGiven, (3 \u00d7 1) + (3 \u00d7 \\(\\frac{1}{10}\\)) + (9 \u00d7 \\(\\frac{1}{1,000}\\))<br \/>\n= 3 + 0.3 + 0.009<br \/>\n= 3.309<br \/>\nSo, The standard form is 3.309<\/p>\n<p>Question 6.<br \/>\nnine and twenty hundredths<br \/>\nAnswer: The standard form is 0.920.<\/p>\n<p>Explanation:<br \/>\nGiven, nine and twenty hundredths<br \/>\nThe expanded form is (9 \u00d7 \\(\\frac{1}{10}\\)) + (20 \u00d7 \\(\\frac{1}{100}\\))<br \/>\n= 0.9 + 0.020<br \/>\n= 0.920<br \/>\nThe standard form is 0.920<\/p>\n<p>In 7-10, write two decimals that are equivalent to the given decimal.<\/p>\n<p>Question 7.<br \/>\n2.200<br \/>\nAnswer: The two decimals that are equivalent to the given decimal are 2.2 and 2.20<\/p>\n<p>Explanation:<br \/>\nGiven, 2.200<br \/>\nTwo and two tenths is the same as two and twenty hundredths.<br \/>\n2.2 = 2.20<br \/>\nTwo and Two tenths is the same as two and twenty tenths.<br \/>\n2.2 = 2.2.<br \/>\nSo, The two decimals that are equivalent to the given decimal are 2.2 and 2.20<\/p>\n<p>Question 8.<br \/>\n8.1<br \/>\nAnswer: The two decimals that are equivalent to the given decimal are 8.10 and 8.100<\/p>\n<p>Explanation:<br \/>\nGiven, 8.1<br \/>\nEight and one tenths is the same as eight and one hundredths.<br \/>\n8.1 = 8.10<br \/>\nEight and one tenths is the same as eight and one hundred thousandths.<br \/>\n8.1 = 8.100.<br \/>\nSo, The two decimals that are equivalent to the given decimal are 8.10 and 8.100<\/p>\n<p>Question 9.<br \/>\n9.50<br \/>\nAnswer: The two decimals that are equivalent to the given decimal are 9.5 and 9.500<\/p>\n<p>Explanation:<br \/>\nGiven, 9.50<br \/>\nNine and five tenths is the same as nine and\u00a0 fifty tenths.<br \/>\n9.50 = 9.5.<br \/>\nNine and five tenths is the same as nine and fifty hundred thousandths.<br \/>\n9.50 = 9.500.<br \/>\nSo, The two decimals that are equivalent to the given decimal are 9.5 and 9.500<\/p>\n<p>Question 10.<br \/>\n4.200<br \/>\nAnswer: The two decimals that are equivalent to the given decimal are 4.2 and 4.20<\/p>\n<p>Explanation:<br \/>\nGiven, 4.200<br \/>\nFour and two tenths is the same as four and twenty hundredths.<br \/>\n4.200 = 4.20<br \/>\nFour and two tenths is the same as two and twenty tenths.<br \/>\n4.200 = 4.2.<br \/>\nSo, The two decimals that are equivalent to the given decimal are 4.2 and 4.20<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 11.<br \/>\nThe annual fundraising goal of a charity is $100,000. So far $63,482 has been raised. How much more money is needed to reach the goal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9177\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-40.1.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 40.1\" width=\"293\" height=\"70\" \/><br \/>\nAnswer: To reach the goal they need $36,518.<\/p>\n<p>Explanation:<br \/>\nGiven, The annual fundraising goal of a charity is $100,000.<br \/>\nSo far $63,482 has been raised.<br \/>\nThen, $100,000 &#8211; $63,482 = $36,518.<br \/>\nSo, To reach the goal they need $36,518.<\/p>\n<p>Question 12.<br \/>\nSantiago has a rope that measures 205.95 centimeters. Write this number in expanded form.<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nGiven, Santiago has a rope that measures 205.95 centimeters<br \/>\nThe standard form is 205.95<br \/>\nThen, The expanded form is (2 \u00d7 100) + (5 \u00d7 1) + (9 \u00d7 \\(\\frac{1}{10}\\)) + (5 \u00d7 \\(\\frac{1}{100}\\))<br \/>\n= 200 + 5 +[ 0.9 + 0.05 ]<br \/>\n= 205 + 0.95<br \/>\n= 205.95<br \/>\nSo, The expanded form is (2 \u00d7 100) + (5 \u00d7 1) + (9 \u00d7 \\(\\frac{1}{10}\\)) + (5 \u00d7 \\(\\frac{1}{100}\\))<\/p>\n<p>Question 13.<br \/>\nHow can you tell that 7.630 and 7.63 are equivalent decimals?<br \/>\nAnswer: The two decimals that are equivalent to both the numbers<\/p>\n<p>Explanation:<br \/>\nGiven, 7.630 and 7.63<br \/>\nSeven and sixty three tenths is the same as Seven and sixty three hundredths.<br \/>\n7.63 = 7.630<br \/>\nSo, The two decimals that are equivalent to both the numbers<\/p>\n<p>Question 14.<br \/>\nIn Justin&#8217;s school, 0.825 of the students participate in a sport. If there are one thousand students in Justin&#8217;s school, how many participate in a sport?<br \/>\nAnswer: Totally 825 students are participating in the school.<\/p>\n<p>Explanation:<br \/>\nGiven, In Justin&#8217;s school, 0.825 of the students participate in a sport.<br \/>\nSince, there are 1 thousand students, and the decimal is 0.825,<br \/>\nSo, there are 825 students participating.<\/p>\n<p><span class=\"copyright-span\"><br \/>\n<\/span>Question 15.<br \/>\n<strong>Be Precise<\/strong> Maria incorrectly placed the decimal point when she wrote 0.65 inch for the width of her tablet computer. What is the correct decimal number for the width?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9178\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-40.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 40.2\" width=\"300\" height=\"150\" \/><br \/>\nAnswer: The correct decimal number for the width is 6.5.<\/p>\n<p>Explanation:<br \/>\nGiven, Maria incorrectly placed the decimal point when she wrote 0.65 inch for the width of her tablet computer.<br \/>\nAs shown in the figure, the scale placed there to measure the width , as per the scale the width is 6.5.<br \/>\nSo, The correct decimal number for the width is 6.5.<\/p>\n<p>Question 16.<br \/>\n<strong>Higher Order Thinking<\/strong> Three boys cut out hundredths decimal models. Derrick does not shade any of his models. Ari shades half of one model. Wesley shades two models and one tenth of another model. What decimal represents the amount each boy shades?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9179\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-42.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 42.2\" width=\"275\" height=\"88\" \/><br \/>\nAnswer: Derrick&#8217;s value = 0,<br \/>\nAri&#8217;s value = 0.5,<br \/>\nWesley&#8217;s value = 2.1 ,<\/p>\n<p>Explanation:<br \/>\nGiven, Derrick does not shade any of his models. Ari shades half of one model. Wesley shades two models and one tenth of another model.<br \/>\nDerrick doesn&#8217;t shade anything, so his value is 0.<br \/>\nAri shades half of one model, so 1\/2 = 0.5 is his value Wesley shades 2 full models, plus 1\/10 = 0.1 of another one, leading to 2+0.1 = 2.1 as his value.\u00a0<span class=\"copyright-span\"><br \/>\n<\/span>Derrick&#8217;s value = 0,<br \/>\nAri&#8217;s value = 0.5,<br \/>\nWesley&#8217;s value = 2.1 ,<\/p>\n<p><strong>Assessment Practice<\/strong><\/p>\n<p>Question 17.<br \/>\nFind two decimals that are equivalent to (4 \u00d7 10) + (7 \u00d7 \\(\\frac{1}{100}\\)). Write the decimals in the box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9180\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-42.3.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 42.3\" width=\"312\" height=\"91\" \/><br \/>\nAnswer:\u00a0 The two decimals that are equivalent to the 40.07 are 40.070 and 40.07<\/p>\n<p>Explanation:<br \/>\nGiven, (4 \u00d7 10) + (7 \u00d7 \\(\\frac{1}{100}\\)).<br \/>\n= 40 + 0.07<br \/>\n= 40.07<br \/>\nThe standard form is 40.07<br \/>\nThe two decimals that are equivalent to the 40.07 are 40.070 and 40.07 , from the given box of decimals.<\/p>\n<h3><a id=\"Lesson_ 1.5_ Compare_ Decimals\"><\/a>Lesson 1.5 Compare Decimals<\/h3>\n<p><strong>Activity<\/strong><\/p>\n<p><strong>Solve &amp; Share<\/strong><\/p>\n<p>The lengths of three ants were measured in a laboratory. The lengths were 0.521 centimeter, 0.498 centimeter, and 0.550 centimeter. Which ant was the longest? Which ant was the shortest?<\/p>\n<p>How can you use the math you know to compare and order the decimals? Tell how you decided.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9181\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-42.4.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 42.4\" width=\"674\" height=\"371\" \/><\/p>\n<p><strong>Look Back! Be Precise<\/strong> What are the lengths of the ants in order from least to greatest?<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong> How Can You Compare Decimals?<\/p>\n<p><strong>A.<\/strong><br \/>\nScientists collected and measured the lengths of different cockroach species. Which cockroach had the greater length, the American or the Oriental cockroach?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9182\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-42.5.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 42.5\" width=\"675\" height=\"226\" \/><br \/>\nComparing decimals is like comparing whole numbers!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9183\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-42.6.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 42.6\" width=\"107\" height=\"285\" \/><\/p>\n<p><strong>B.<\/strong><br \/>\n<strong>Step 1<\/strong><br \/>\nLine up the decimal points.<br \/>\nStart at the left.<br \/>\nCompare digits of the same place value.<br \/>\n3.576<br \/>\n3.432<\/p>\n<p><strong>C.<\/strong><br \/>\n<strong>Step 2<\/strong><br \/>\nFind the first place where the digits are different.<br \/>\n3.576<br \/>\n3.432<\/p>\n<p><strong>D.<\/strong><br \/>\n<strong>Step 3<\/strong><br \/>\nCompare.<br \/>\n5 &gt; 4<br \/>\n0.5 &gt; 0.4<br \/>\nSo, 3.576 &gt; 3.432.<br \/>\nThe American cockroach is longer than the Oriental cockroach.<\/p>\n<p><strong>Convince Me!<\/strong> Critique Reasoning Valerie said, \u201c12.68 is greater than 12.8 because 68 is greater than 8.&#8221; Is she correct? Explain.<\/p>\n<p>Answer: No, 12.8 is greater than 12.68<\/p>\n<p>Explanation:<br \/>\nGiven \u00a0: 12.68 is greater than 12.8<br \/>\nWe have given 12.68 and 12.8<br \/>\nIn 12.68,<br \/>\nTens place is 1,<br \/>\nOnes place is 2,<br \/>\nTenth place is 6,<br \/>\nHundredth place is 8.<br \/>\nIn 12.8,<br \/>\nTens place is 1 .<br \/>\nOnes place is 2,<br \/>\nTenth place is 8,<br \/>\nSo, We can see Tens place and ones place of both number are same but tenth place of 12.8 is greater than 12.68.<br \/>\nTherefore, 12.8 is greater than 12.68 .\u00a0<span class=\"copyright-span\"><br \/>\n<\/span><\/p>\n<p><strong>Another example<\/strong><br \/>\nOrder the cockroaches from least to greatest length.<br \/>\n<strong>Step 1<\/strong><br \/>\nWrite the numbers, lining up the decimal points. Start at the left. Compare digits of the same place value.<br \/>\n3.576<br \/>\n3.582<br \/>\n3.432 is the least.<\/p>\n<p><strong>Step 2<\/strong><br \/>\nWrite the remaining numbers, lining up the decimal points. Start at the left. Compare.<br \/>\n3.576<br \/>\n3.582<br \/>\n3.582 is greater than 3.576.<\/p>\n<p><strong>Step 3<\/strong><br \/>\nWrite the numbers from least to greatest.<br \/>\n3.432 3.576 3.582<br \/>\nFrom least to greatest lengths are the Oriental, the American, and the Australian.<\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nScientists measured a Madeira cockroach and found it to be 3.44 centimeters long. Toby says that the Madeira is shorter than the Oriental because 3.44 has fewer digits than 3.432. Is he correct? Explain.<br \/>\nAnswer: 3.44cm cockroach is the longest.<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 3.44\u00a0 and\u00a0 3.432<br \/>\n3.44<br \/>\n3.432<br \/>\nComparing the numbers after decimals,<br \/>\n4 &gt; 3<br \/>\nSo, 3.44cm cockroach is the longest.<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>In 2 and 3, write &gt;, &lt;, or = for each <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/>.<\/p>\n<p>Question 2.<br \/>\n3.692 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/> 3.697<br \/>\nAnswer: 3.692 &lt; 3.697<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 3.692\u00a0 and\u00a0 3.697<br \/>\n3.692<br \/>\n3.697<br \/>\nComparing the numbers after decimals, we have<br \/>\n2 &lt; 7<br \/>\nSo, 3.692 &lt; 3.697.<\/p>\n<p>Question 3.<br \/>\n7.216 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/> 7.203<br \/>\nAnswer:\u00a0 7.216 &gt; 7.203.<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 7.216\u00a0 and\u00a0 7.203<br \/>\n7.216<br \/>\n7.203<br \/>\nComparing the numbers after decimals, we have<br \/>\n1 &gt; 0<br \/>\nSo, 7.216 &gt; 7.203.<\/p>\n<p>In 4 and 5, order the decimals from least to greatest.<\/p>\n<p>Question 4.<br \/>\n5.540, 5.631, 5.625<br \/>\nAnswer: The order from least to greatest is\u00a0 5.540, 5.625, 5.631.<\/p>\n<p>Explanation:<br \/>\nGiven, 5.540, 5.631, 5.625<br \/>\nlining up the decimal points.<br \/>\n5.540, is the least<br \/>\n5.631,<br \/>\n5.625,<br \/>\nComparing the numbers after decimals, we have<br \/>\n5.631,<br \/>\n5.625,<br \/>\nCompare digits of the same place value.<br \/>\n3 &gt; 2<br \/>\n5.631 is the greatest<br \/>\nSo, The order from least to greatest is\u00a0 5.540, 5.625, 5.631.<\/p>\n<p>Question 5.<br \/>\n0.675, 1.529, 1.35, 0.693<br \/>\nAnswer: The order from least to greatest is 0.675, 0.693, 1.35, 1.529.<\/p>\n<p>Explanation:<br \/>\nGiven, 0.675, 1.529, 1.35, 0.693<br \/>\nlining up the decimal points.<br \/>\n0.675,<br \/>\n1.529,<br \/>\n1.35,<br \/>\n0.693<br \/>\nComparing the numbers after decimals, we have<br \/>\n0.675,<br \/>\n0.693,<br \/>\nCompare digits of the same place value.<br \/>\n7 &lt; 9<br \/>\n0.675 is the less than 0.693<br \/>\nThen 1.529,<br \/>\n1.35,<br \/>\nCompare digits of the same place value.<br \/>\n5 &gt; 3<br \/>\n1.529 is greater than 1.35<br \/>\nSo, The order from least to greatest is 0.675, 0.693, 1.35, 1.529.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 6-8, compare the two numbers. Write &gt;, &lt;, or = for each <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/>.<\/p>\n<p>Question 6.<br \/>\n0.890 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/> 0.890<br \/>\nAnswer: 0.890 = 0.890<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 0.890\u00a0 and 0.890<br \/>\n0.890<br \/>\n0.890<br \/>\nComparing the numbers after decimals, we have<br \/>\nAll the numbers are equal<br \/>\nSo, 0.890 = 0.890.<\/p>\n<p>Question 7.<br \/>\n5.733 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/> 5.693<br \/>\nAnswer: 5.733 &gt; 5.693.<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 5.733\u00a0 and\u00a0 5.693<br \/>\n5.733<br \/>\n5.693<br \/>\nComparing the numbers after decimals, we have<br \/>\n7 &gt; 6<br \/>\nSo, 5.733 &gt; 5.693.<\/p>\n<p>Question 8.<br \/>\n9.707 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9184\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-55.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 55\" width=\"29\" height=\"31\" \/> 9.717<br \/>\nAnswer: 9.707 &lt; 9.717<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 9.707\u00a0 and\u00a0 9.717<br \/>\nlining up the decimal points<br \/>\n9.707<br \/>\n9.717<br \/>\nComparing the numbers after decimals, we have, Compare digits of the same place value.<br \/>\n0 &lt; 1<br \/>\nSo, 9.707 &lt; 9.717.<\/p>\n<p>In 9 and 10, order the decimals from greatest to least.<\/p>\n<p>Question 9.<br \/>\n878.403, 887.304,887.043<br \/>\nAnswer: The order from least to greatest is 878.403 ,887.043 , 887.304.<\/p>\n<p>Explanation:<br \/>\nGiven, 878.403, 887.304,887.043<br \/>\nlining up the decimal points.<br \/>\n878.403, is the least<br \/>\n887.304,<br \/>\n887.043<br \/>\nComparing the numbers after decimals, we have<br \/>\n887.304,<br \/>\n887.043<br \/>\nCompare digits of the same place value.<br \/>\n3 &gt; 0<br \/>\n887.304 is greater than 887.043<br \/>\nSo, The order from least to greatest is 878.403 ,887.043 , 887.304.<\/p>\n<p>Question 10.<br \/>\n435.566, 436.565, 435.665<br \/>\nAnswer: The order from least to greatest is 435.566, 435.665 , 436.565.<\/p>\n<p>Explanation:<br \/>\nGiven, 435.566, 436.565, 435.665<br \/>\nlining up the decimal points.<br \/>\n435.566,<br \/>\n436.565, is the greatest<br \/>\n435.665<br \/>\nComparing the numbers after decimals, we have<br \/>\n435.566,<br \/>\n435.665<br \/>\nCompare digits of the same place value.<br \/>\n5 &lt; 6<br \/>\n435.566 is less than 435.665<br \/>\nSo, The order from least to greatest is 435.566, 435.665 , 436.565.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 11.<br \/>\n<strong>Critique Reasoning<\/strong> Explain why it is not reasonable to say that 4.23 is less than 4.135 because 4.23 has fewer digits after the decimal point than 4.135.<br \/>\nAnswer: 4.23 is greater than 4.135.<\/p>\n<p>Explanation:<br \/>\nGiven, 4.23 and 4.135<br \/>\nlining up the decimal points.<br \/>\n4.23,<br \/>\n4.135<br \/>\nComparing the numbers after decimals, we have ,Compare digits of the same place value.<br \/>\n2 &lt; 1<br \/>\nSo, 4.23 is greater than 4.135.<\/p>\n<p>Question 12.<br \/>\n<strong>Number Sense<\/strong> Carlos wrote three numbers between 0.33 and 0.34. What numbers could Carlos have written?<br \/>\nAnswer: there can be any three numbers mentioned Below between 0.33 and 0.34.<\/p>\n<p>Explanation:<br \/>\nGiven, three numbers between 0.33 and 0.34<br \/>\nThe numbers between the 0.33 and 0.34 are 0.331, 0.332, 0.333, 0.334, 0.335, 0.336, 0.337, 0.338 and 0.339,<br \/>\nThen the next number will be 0.340 that is same as 0.34<br \/>\nSo, there can be any three numbers mentioned above between 0.33 and 0.34.<\/p>\n<p>Question 13.<br \/>\n<strong>Vocabulary<\/strong> Draw lines to match each decimal on the left to its equivalent decimal on the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9185\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-58.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 58.2\" width=\"154\" height=\"94\" \/><br \/>\nAnswer: The given decimals are compared to its nearest decimals by place value method.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21277\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.9.png\" alt=\"\" width=\"176\" height=\"100\" \/><\/p>\n<p>Question 14.<br \/>\nIs 0.5 greater than or less than \\(\\frac{6}{10}\\)? Draw a number line to show your answer.<br \/>\nAnswer: 0.5 is &lt; 0.6<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21281\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.10.png\" alt=\"\" width=\"598\" height=\"112\" \/><br \/>\nGiven,\u00a0 0.5 and \\(\\frac{6}{10}\\)<br \/>\nWe can write \\(\\frac{6}{10}\\) as 0.6 in decimal form,<br \/>\nCompare digits of the same place value.<br \/>\n5 &lt; 6<br \/>\nSo, 0.5 is &lt; 0.6<\/p>\n<p>Question 15.<br \/>\n<strong>Higher Order Thinking<\/strong> Ana&#8217;s gymnastics scores were posted on the scoreboard in order from highest to lowest score. One digit in her floor score is not visible. List all the possible digits for the missing number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9186\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-58.3.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 58.3\" width=\"245\" height=\"277\" \/><br \/>\nAnswer: The possible digits are 1 , 2 , 3 , 4<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe floor score must be higher than 15.133 and lower than 15.500<br \/>\nThen all the possible scores are: 15.166 , 15.266 , 15.366 and 15.466<br \/>\nBecause 15.166 &gt; 15.133 and 15.466 &lt; 15.500<br \/>\nThen all the possible digits are 1 , 2 , 3 , 4\u00a0<span class=\"copyright-span\"><br \/>\n<\/span><\/p>\n<p>Question 16.<br \/>\nMarcia&#8217;s vault score is 15.050. How does it compare to Ana&#8217;s vault score?<br \/>\nAnswer: Marcia&#8217;s vault score is less than Ana&#8217;s vault score<\/p>\n<p>Explanation:<br \/>\nGiven, Marcia&#8217;s vault score is 15.050<br \/>\nAna&#8217;s vault score is 15.500<br \/>\nLining up the decimal points.<br \/>\n15.050<br \/>\n15.500<br \/>\nComparing the numbers after decimals, we have ,Compare digits of the same place value.<br \/>\n0 &lt; 5<br \/>\nSo, 15.050 is less than 15.500.<br \/>\nFinally, Marcia&#8217;s vault score is less than Ana&#8217;s vault score<\/p>\n<p><strong>Assessment Practice<\/strong><\/p>\n<p>Question 17.<br \/>\nWhich statements correctly compare two numbers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9188\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59\" width=\"34\" height=\"34\" \/> 0.1 &lt;0.125<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9188\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59\" width=\"34\" height=\"34\" \/> 0.2 &lt; 0.125<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9188\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59\" width=\"34\" height=\"34\" \/> 125 &gt; 0.13<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9188\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59\" width=\"34\" height=\"34\" \/> 0.125 &gt; 0.12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9188\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59\" width=\"34\" height=\"34\" \/> 0.126 &lt; 0.125<br \/>\nAnswer: 0.1 &lt; 0.125 , 125 &gt; 0.13 , 0.125 &gt; 0.12 .<\/p>\n<p>Explanation:<br \/>\nCompare digits of the same place value.<br \/>\n0.1 &lt; 0.125 , because 0 &lt; 2<br \/>\n125 &gt; 0.13 , because .0 &gt; 0.<br \/>\n0.125 &gt; 0.12 . because 5 &gt; 0<\/p>\n<p>Question 18.<br \/>\nCara weighed 4.16 pounds of apples at the grocery store. Which numbers make the statement true? <img loading=\"lazy\" class=\"alignnone size-full wp-image-9194\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60\" width=\"28\" height=\"31\" \/> &gt; 4.16<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9187\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59.2\" width=\"27\" height=\"29\" \/> 04.15<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9187\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59.2\" width=\"27\" height=\"29\" \/> 04.19<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9187\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59.2\" width=\"27\" height=\"29\" \/> 4.2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9187\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59.2\" width=\"27\" height=\"29\" \/> 4.09<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9187\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-59.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 59.2\" width=\"27\" height=\"29\" \/> 4.1<br \/>\nAnswer: 04.15<\/p>\n<p>Explanation:<br \/>\nGiven, Cara weighed 4.16 pounds of apples at the grocery store<br \/>\n4.16 and 04.15 are the closest decimals<br \/>\nCompare digits of the same place value.<br \/>\n5 &lt; 6<br \/>\nSo, the immediate number of 4.16 is 04.15.<\/p>\n<h3><a id=\"Lesson_ 1.6_ Round_ Decimals\"><\/a>Lesson 1.6 Round Decimals<\/h3>\n<p><strong>Activity<\/strong><\/p>\n<p><strong>Solve &amp; Share<\/strong><\/p>\n<p>In science class, Marci recorded numbers from an experiment as 12.87, 12.13, 12.5, and 12.08. Which numbers are closer to 12? Which are closer to 13? How can you tell?<\/p>\n<p>You can use structure to help determine what number is halfway between two whole numbers. Show your work!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9189\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.1.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60.1\" width=\"672\" height=\"338\" \/><\/p>\n<p><strong>Look Back!<\/strong> What is the halfway point between 12 and 13? Is that point closer to 12 or 13?<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong> How Can You Round Decimals?<\/p>\n<p><strong>A.<\/strong><br \/>\nRounding replaces one number with another number that tells about how many or about how much. Round 2.36 to the nearest tenth. Is 2.36 closer to 2.3 or 2.4?<\/p>\n<p>A number line can help you round a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9190\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60.2\" width=\"675\" height=\"203\" \/><\/p>\n<p><strong>B.<\/strong><br \/>\n<strong>Step 1<\/strong><br \/>\nFind the rounding place. Look at the digit to the right of the rounding place.<br \/>\n2.<u>3<\/u>6<\/p>\n<p><strong>C.<\/strong><br \/>\n<strong>Step 2<\/strong><br \/>\nIf the digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5, leave the rounding digit alone.<br \/>\nSince 6 &gt;5, add 1 to the 3.<\/p>\n<p><strong>D.<\/strong><br \/>\n<strong>Step 3<\/strong><br \/>\nDrop the digits to the right of the rounding digit.<br \/>\n2.36 rounds to 2.4<\/p>\n<p>Rounding can help (you find which tenth or hundredth a decimal is closest to.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9191\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.3.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60.3\" width=\"99\" height=\"255\" \/><\/p>\n<p><strong>Convince Me!<\/strong> <strong>Critique Reasoning<\/strong> Carrie said, &#8220;448 rounds to 500 because 448 rounds to 450 and 450 rounds to 500.&#8221; Is she correct? Explain. Use the number line in your explanation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9192\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.4.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60.4\" width=\"499\" height=\"73\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nGiven, 448 rounds to 500 because 448 rounds to 450 and 450 rounds to 500.&#8221;<br \/>\nThe nearest number to 448 is 450 and that is correct but,<br \/>\n450 is not near the number 500 ,<br \/>\nThe difference between these numbers is 50 ,<br \/>\nSo, Carrie is wrong.<\/p>\n<p><strong>Another example<\/strong><br \/>\nRound 3.2 to the nearest whole number. Is 3.2 closer to 3 or 4?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9193\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-60.5.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 60.5\" width=\"236\" height=\"78\" \/><\/p>\n<p><strong>Step 1<\/strong><br \/>\nFind the rounding place. Look at the digit to the right of the rounding place.<br \/>\n<u>3<\/u>.2<br \/>\n<strong>Step 2<\/strong><br \/>\nIf the digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5, leave the rounding digit alone. Since 2 &lt; 5, leave 3 the same.<br \/>\n<strong>Step 3<\/strong><br \/>\nDrop the digits to the right of the decimal point. Drop the decimal point.<br \/>\n3.2 rounds to 3.<\/p>\n<p><strong>Guided Practice<\/strong><\/p>\n<p><strong>Do You Understand?<\/strong><\/p>\n<p>Question 1.<br \/>\nTo round 74.58 to the nearest tenth, which digit do you look at? What is 74.58 rounded to the nearest tenth?<br \/>\nAnswer: the nearest tenth to 74.58 is 74.6<\/p>\n<p>Explanation:<br \/>\nGiven, To round 74.58 to the nearest tenth,<br \/>\nFind the rounding place. Look at the digit to the right of the rounding place.<br \/>\n8 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point.<br \/>\n74.6<br \/>\nSo, the nearest tenth to 74.58 is 74.6<\/p>\n<p>Question 2.<br \/>\nA car-rental service charges customers for the number of miles they travel, rounded to the nearest whole mile. George travels 40.8 miles. For how many miles will he be charged? Explain.<br \/>\nAnswer: He will be charged for 41 miles<\/p>\n<p>Explanation:<br \/>\nGiven, George travels 40.8 miles.<br \/>\nFind the rounding place. Look at the digit to the right of the rounding place.<br \/>\n8 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point.<br \/>\nThe nearest to 40.8 is 41<br \/>\nSo, He will be charged for 41 miles<\/p>\n<p><strong>Do You Know How?<\/strong><\/p>\n<p>In 3-10, round each number to the place of the underlined digit.<\/p>\n<p>Question 3.<br \/>\n1<u>6<\/u>.5<br \/>\nAnswer: 17<\/p>\n<p>Explanation:<br \/>\nGiven, 1<u>6<\/u>.5<br \/>\n6 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 17<br \/>\nThe rounding number is 17.<\/p>\n<p>Question 4.<br \/>\n5<u>6<\/u>.1<br \/>\nAnswer: 56<\/p>\n<p>Explanation:<br \/>\nGiven, 5<u>6<\/u>.1<br \/>\n6 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 56<br \/>\nThe rounding number is 56.<\/p>\n<p>Question 5.<br \/>\n1.<u>3<\/u>2<br \/>\nAnswer: 1.3<\/p>\n<p>Explanation:<br \/>\nGiven, 1.<u>3<\/u>2<br \/>\n3 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1.3<br \/>\nThe rounding number is 1.3.<\/p>\n<p>Question 6.<br \/>\n42.<u>7<\/u>8<br \/>\nAnswer: 42.8<\/p>\n<p>Explanation:<br \/>\nGiven, 42.<u>7<\/u>8<br \/>\n7 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 42.8<br \/>\nThe rounding number is 42.8.<\/p>\n<p>Question 7.<br \/>\n1.6<u>5<\/u>2<br \/>\nAnswer: 1.65<\/p>\n<p>Explanation:<br \/>\nGiven, 1.6<u>5<\/u>2<br \/>\n5 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1.65<br \/>\nThe rounding number is 1.65.<\/p>\n<p>Question 8.<br \/>\n582.0<u>4<\/u><br \/>\nAnswer: 582.0<\/p>\n<p>Explanation:<br \/>\nGiven, 582.0<u>4<\/u><br \/>\n4 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 582.0<br \/>\nThe rounding number is 582.0.<\/p>\n<p>Question 9.<br \/>\n80,547.6<u>4<\/u>5<br \/>\nAnswer: 80,547.65<\/p>\n<p>Explanation:<br \/>\nGiven, 80,547.6<u>4<\/u>5<br \/>\n4 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 80,547.65<br \/>\nThe rounding number is 80,547.65.<\/p>\n<p>Question 10.<br \/>\n135,701.<u>9<\/u>49<br \/>\nAnswer: 135,701.9<\/p>\n<p>Explanation:<br \/>\nGiven, 135,701.<u>9<\/u>49<br \/>\n9 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 135,701.9<br \/>\nThe rounding number is 135,701.9.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p>In 11-14, round each decimal to the nearest whole number.<\/p>\n<p>Question 11.<br \/>\n4.5<br \/>\nAnswer: 5<\/p>\n<p>Explanation:<br \/>\nGiven, 4.5<br \/>\n4 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 5<br \/>\nThe rounding number is 5.<\/p>\n<p>Question 12.<br \/>\n57.3<br \/>\nAnswer: 57<\/p>\n<p>Explanation:<br \/>\nGiven, 57.3<br \/>\n7 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 57<br \/>\nThe rounding number is 57.<\/p>\n<p>Question 13.<br \/>\n34.731<br \/>\nAnswer: 34.73<\/p>\n<p>Explanation:<br \/>\nGiven, 34.731<br \/>\n3 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 34.73<br \/>\nThe rounding number is 34.73.<\/p>\n<p>Question 14.<br \/>\n215.39<br \/>\nAnswer: 215.4<\/p>\n<p>Explanation:<br \/>\nGiven,215.39<br \/>\n3 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 215.4<br \/>\nThe rounding number is 215.4.<\/p>\n<p>In 15-18, round each number to the place of the underlined digit.<\/p>\n<p>Question 15.<br \/>\n7.<u>1<\/u>58<br \/>\nAnswer: 7.2<\/p>\n<p>Explanation:<br \/>\nGiven, 7.<u>1<\/u>58<br \/>\n1 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 7.2<br \/>\nThe rounding number is 7.2.<\/p>\n<p>Question 16.<br \/>\n0.7<u>5<\/u>8<br \/>\nAnswer: 0.76<\/p>\n<p>Explanation:<br \/>\nGiven, 0.7<u>5<\/u>8<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 0.76<br \/>\nThe rounding number is 0.76.<\/p>\n<p>Question 17.<br \/>\n6.4<u>3<\/u>82<br \/>\nAnswer: 6.44<\/p>\n<p>Explanation:<br \/>\nGiven, 6.4<u>3<\/u>82<br \/>\n3 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 6.44<br \/>\nThe rounding number is 6.44.<\/p>\n<p>Question 18.<br \/>\n84.<u>7<\/u>32<br \/>\nAnswer: 84.7<\/p>\n<p>Explanation:<br \/>\nGiven, 84.<u>7<\/u>32<br \/>\n7 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 84.7<br \/>\nThe rounding number is 84.7.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 19.<br \/>\nThe picture at the right shows the length of an average American alligator. What is the length of the alligator rounded to the nearest tenth?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9195\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-62.1.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 62.1\" width=\"365\" height=\"121\" \/><br \/>\nAnswer: 4.4 is the length of the alligator rounded to the nearest tenth.<\/p>\n<p>Explanation:<br \/>\nGiven, 4.39<br \/>\n3 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 4.4<br \/>\nThe rounding number is 4.4.<br \/>\nSo,4.4\u00a0 is the length of the alligator rounded to the nearest tenth<\/p>\n<p>Question 20.<br \/>\nName two different numbers that round to 8.21 when rounded to the nearest hundredth.<br \/>\nAnswer: 8.211 and 8.212<\/p>\n<p>Explanation:<br \/>\nGiven, 8.21 rounded to the nearest hundredth,<br \/>\n2 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 8.211 and 8.212<br \/>\nThe rounding number is 8.211 and 8.212.<\/p>\n<p>Question 21.<br \/>\n<strong>Number Sense<\/strong> To the nearest hundred, what is the greatest whole number that rounds to 2,500? the least whole number?<br \/>\nAnswer: 2,499 and 2,491.<\/p>\n<p>Explanation:<br \/>\nGiven, 2,500<br \/>\nThe greatest whole number to nearest hundred of 2,500 is 2,499<br \/>\nAnd, The less whole number to nearest hundred of 2,500 is 2,491<\/p>\n<p>Question 22.<br \/>\nDraw all of the lines of symmetry in the figure shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9196\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-62.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 62.2\" width=\"93\" height=\"129\" \/><br \/>\nAnswer: There are 2 line lines of symmetry.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21291\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.11.png\" alt=\"\" width=\"178\" height=\"223\" \/><br \/>\nThe given figure is in the form of a Rectangle<br \/>\nSo, it has 2 lines of symmetry.<\/p>\n<p>Question 23.<br \/>\n<strong>Higher Order Thinking<\/strong> Emma needs 2 pounds of ground meat to make a meatloaf. She has one package with 2.36 pounds of ground meat and another package with 2.09 pounds of ground meat. She uses rounding and finds that both packages are close to 2 pounds. Explain how Emma can choose the package closer to 2 pounds.<br \/>\nAnswer: She can use the package of 2.09 because it is close to 2 pounds.<\/p>\n<p>Explanation:<br \/>\nGiven, 2.09 and 2.36<br \/>\nFor 2.09 , 0\u00a0is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point. 2.1<br \/>\nFor 2.36, 3\u00a0is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point. 2.4<br \/>\nSo, She can use the package of 2.09 because it is close to 2 pounds.<\/p>\n<p>Question 24.<br \/>\n<strong>Make Sense and Persevere<\/strong> Robert slices a large loaf of bread to make 12 sandwiches. He makes 3 turkey sandwiches and 5 veggie sandwiches. The rest are ham sandwiches. What fraction of the sandwiches Robert makes are ham?<br \/>\nAnswer: \\(\\frac{3}{12}\\), \\(\\frac{5}{12}\\), \\(\\frac{4}{12}\\).<\/p>\n<p>Explanation:<br \/>\nGiven, Robert slices a large loaf of bread to make 12 sandwiches,<br \/>\nHe makes 3 turkey sandwiches and 5 veggie sandwiches<br \/>\nThe rest are ham sandwiches.<br \/>\nThe number of turkey sandwiches are \\(\\frac{3}{12}\\),<br \/>\nThe number of veggie sandwiches are \\(\\frac{5}{12}\\),<br \/>\nThe number of ham sandwiches are \\(\\frac{4}{12}\\),<br \/>\nTotal 12 sandwiches are there made by Robert.<\/p>\n<p>Question 25.<br \/>\n<strong>Algebra<\/strong> After buying school supplies, Ruby had $32 left over. She spent $4 on notebooks, $18 on a backpack, and $30 on a new calculator. How much money, m, did Ruby start with? Write an equation to show your work.<br \/>\nAnswer: Ruby started with $84.<\/p>\n<p>Explanation:<br \/>\nGiven, Ruby had $32 left over.<br \/>\nShe spent $4 on notebooks, $18 on a backpack, and $30 on a new calculator.<br \/>\nThe total money spent =\u00a0 $4 + $18\u00a0 +\u00a0 $30\u00a0 = $52<br \/>\nAdd the money she had left over and money she had spent<br \/>\nwe have, $52 + $32 = $84<br \/>\nSo, Ruby started with $84.<\/p>\n<p><strong>Assessment Practice<\/strong><\/p>\n<p>Question 26.<br \/>\nFind two numbers that round to 35.4 when rounded to the nearest tenth. Write the numbers in the box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9197\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-63.1.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 63.1\" width=\"323\" height=\"83\" \/><br \/>\nAnswer: 35.45 and 35.391<\/p>\n<p>Explanation:<br \/>\nGiven, 35.40<br \/>\n4 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 35.45<br \/>\nif the digit is 5 or greater, add 1 to the rounding digit. 35.391<br \/>\nThe rounding number is 35.45 and 35.391.<\/p>\n<h3><a id=\"Lesson_ 1.7_ Look_ For_ and_ Use_ Structure\"><\/a>Lesson 1.7 Look For and Use Structure<\/h3>\n<p><strong>Problem Solving<\/strong><\/p>\n<p><strong>Activity<\/strong><\/p>\n<p><strong>Solve &amp; Share<\/strong><br \/>\nAngie volunteers in the school library after school. The librarian gave her a stack of books and told her to use the number on each book to shelve it where it belongs.<br \/>\nHow can Angie arrange the books in order from least to greatest to make shelving them easier?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9198\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-63.2.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 63.2\" width=\"219\" height=\"214\" \/><\/p>\n<p><strong>Thinking Habits<\/strong><br \/>\nBe a good thinker! These questions can help you.<br \/>\n\u2022 What patterns can I see and describe?<br \/>\n\u2022 How can I use the patterns to solve the problem?<br \/>\n\u2022 Can I see expressions and objects in different ways?<br \/>\n\u2022 What equivalent expressions can I use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9199\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-63.3.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 63.3\" width=\"179\" height=\"153\" \/><\/p>\n<p><strong>Look Back! Use Structure<\/strong> Explain why 323.202 is less than 323.21 even though 202 is greater than 21.<\/p>\n<p>Answer: Because , when rounding the decimals we have to look for the place values to decide which is greater or least.<\/p>\n<p>Explanation:<br \/>\nGiven, 323.202<br \/>\n0 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 323.21<br \/>\nThe rounding number is 323.21.<\/p>\n<p><strong>Visual Learning Bridge<\/strong><\/p>\n<p><strong>Essential Question<\/strong><br \/>\nHow Can You Use Structure to Solve Problems?<\/p>\n<p><strong>A.<\/strong><br \/>\nAnalyze the chart. What do you notice that can help you complete the chart?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9200\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-63.4.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 63.4\" width=\"350\" height=\"149\" \/><br \/>\nWhat do I need to do to solve this problem?<\/p>\n<p>I can use the structure of the decimal place-value system to complete the chart.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9203\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.5.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.5\" width=\"146\" height=\"123\" \/><br \/>\nYou can look for patterns to find the missing numbers.<\/p>\n<p><strong>B.<\/strong><br \/>\nHow can I make use of structure to solve this problem?<br \/>\nI can<br \/>\n\u2022 find and describe patterns.<br \/>\n\u2022 use the patterns to see how the numbers are organized.<br \/>\n\u2022 analyze patterns to see the structure in the table.<br \/>\n\u2022 break the problem into simpler parts.<\/p>\n<p><strong>C.<\/strong><br \/>\nSolve<br \/>\nHere&#8217;s my thinking&#8230;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9204\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.6.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.6\" width=\"112\" height=\"176\" \/><br \/>\nAs you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same, except for the last number, while the hundredths increase by 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9205\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.7.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.7\" width=\"347\" height=\"224\" \/><\/p>\n<p><strong>Convince Me!<\/strong> <strong>Use Structure<\/strong> Write the missing numbers. Explain how you can use structure to find the last number in the bottom row.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9201\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Topic-1-Understand-Place-Vale-63.8.png\" alt=\"Envision Math Common Core 5th Grade Answers Topic 1 Understand Place Vale 63.8\" width=\"347\" height=\"140\" \/><\/p>\n<p>Answer:\u00a0 \u00a0<img loading=\"lazy\" class=\"alignnone size-full wp-image-21294\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.12.png\" alt=\"\" width=\"346\" height=\"147\" \/><\/p>\n<p>Explanation:<br \/>\nBecause, down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1.<\/p>\n<p><strong>Guided Practice<\/strong><br \/>\nUse Structure Each of these grids is a part of a decimal number chart similar to the one on page 30.<\/p>\n<p>You can use what you know about place value when you look for patterns with decimals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9207\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.9.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.9\" width=\"125\" height=\"347\" \/><\/p>\n<p>Question 1.<br \/>\nDescribe the pattern for moving from a pink square to a green square. Then write the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9208\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.10.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.10\" width=\"232\" height=\"190\" \/><br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-21295\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.13.png\" alt=\"\" width=\"234\" height=\"208\" \/><\/p>\n<p>Explanation:<br \/>\nBecause, down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1.<\/p>\n<p>Question 2.<br \/>\nHow can you use patterns to find the number that would be in the box below 0.52?<br \/>\nAnswer: the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1. and completing the pattern.<\/p>\n<p><strong>Independent Practice<\/strong><\/p>\n<p><strong>Use Structure<\/strong> Pamela is hiking. When she returns to camp, she passes the mile markers shown at the right.<\/p>\n<p>Question 3.<br \/>\nExplain how you can use structure to find the decimal numbers that will be shown on the next four mile markers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9209\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.11.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.11\" width=\"234\" height=\"299\" \/><br \/>\nAnswer:\u00a0 the next four mile markers will be 2.2 , 2.1 , 2.0 , 1.9<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21297\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.14.png\" alt=\"\" width=\"784\" height=\"125\" \/><br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1<br \/>\nSo, the next four mile markers will be 2.2 , 2.1 , 2.0 , 1.9<\/p>\n<p>Question 4.<br \/>\nPamela stops at the 1.8 mile marker. Where will she be if she walks one tenth of a mile towards camp? one mile towards camp? Explain.<br \/>\nAnswer: she will be on 0.18 if she walks one tenth of a mile towards camp and 1.7 if she walks one mile towards the camp.<\/p>\n<p>Explanation:<br \/>\nGiven, 1.8<br \/>\n8 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 1.7<br \/>\nThe reducing mile as reaching out for camp is 1.7<br \/>\nIf she will be on 0.18 if she walks one tenth of a mile towards camp, That is 1.8 \u00d7 \\(\\frac{1}{10}\\)<br \/>\nFinally, she will be on 0.18 if she walks one tenth of a mile towards camp and 1.7 if she walks one mile towards the camp.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Thousandths Chart<\/strong><br \/>\nThe students in Ms. Lowell&#8217;s class wrote a thousandths decimal chart on the board. Some of the numbers got erased.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9210\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-63.12.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 63.12\" width=\"622\" height=\"148\" \/><br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-21480\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.15.png\" alt=\"\" width=\"627\" height=\"162\" \/><\/p>\n<p>Explanation:<br \/>\nBecause, down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1.<\/p>\n<p>Question 5.<br \/>\n<strong>Use Structure<\/strong> Describe the pattern for moving across a row from left to right.<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-21482\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.16.png\" alt=\"\" width=\"612\" height=\"37\" \/><\/p>\n<p>Explanation:<br \/>\nMoving from left to right in the rows, tenths stay the same, except for the last number, while the hundredths increase by 1.<\/p>\n<p>You can use structure to decide if decimal numbers are following a pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9211\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-69.9.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 69.9\" width=\"125\" height=\"333\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-21482\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.16.png\" alt=\"\" width=\"612\" height=\"37\" \/><\/p>\n<p>Explanation:<br \/>\nAbove question has the figure, we have the decimal numbers following a pattern of\u00a0 tenths stay the same, except for the last number, while the hundredths increase by 1.<\/p>\n<p>Question 6.<br \/>\n<strong>Be Precise<\/strong> How does the pattern change in the last square of each row?<br \/>\nAnswer: As you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21483\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.17.png\" alt=\"\" width=\"40\" height=\"142\" \/><br \/>\nAs you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<\/p>\n<p>Question 7.<br \/>\n<strong>Use Structure<\/strong> Describe the pattern for moving down a column.<br \/>\nAnswer: As you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21483\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.17.png\" alt=\"\" width=\"40\" height=\"142\" \/><br \/>\nAs you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<\/p>\n<p>Question 8.<br \/>\n<strong>Use Repeated Reasoning<\/strong> Write the missing numbers in the decimal chart above.<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-21480\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.15.png\" alt=\"\" width=\"627\" height=\"162\" \/><\/p>\n<p>Explanation:<br \/>\nBecause, down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1.<\/p>\n<p>Question 9.<br \/>\n<strong>Use Structure<\/strong> Suppose the students add to the chart. Write the missing numbers in the row and the column below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9212\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-70.1.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 70.1\" width=\"690\" height=\"148\" \/><br \/>\nAnswer:\u00a0 The complete chart is as follows,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21484\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.18.png\" alt=\"\" width=\"694\" height=\"149\" \/><\/p>\n<p>Explanation:<br \/>\nBecause, down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same,<br \/>\nexcept for the last number, while the hundredths increase by 1.<\/p>\n<h3><a id=\"Topic_ 1_ Fluency_ Review\"><\/a>Topic 1 Fluency Review<\/h3>\n<p><strong>Activity<\/strong><\/p>\n<p><strong>Find a Match<\/strong><\/p>\n<p>Work with a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box above the match. Find a match for every clue.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9213\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-70.2.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 70.2\" width=\"99\" height=\"209\" \/><\/p>\n<p><strong>Clues<\/strong><br \/>\nA The sum is between 15,000 and 20,000.<br \/>\nB The difference is less than 10,000.<br \/>\nC The difference is between 41,000 and 42,000.<br \/>\nD The sum is exactly 52,397.<br \/>\nE The difference is between 82,000 and 84,000.<br \/>\nF The sum is greater than 79,000.<br \/>\nG The sum is exactly 52,407,<br \/>\nH The difference is exactly 42,024.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-9214\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-70.3.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 70.3\" width=\"647\" height=\"360\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21485\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.19.png\" alt=\"\" width=\"640\" height=\"360\" \/><\/p>\n<p><strong>Topic 1 Vocabulary Review<\/strong><\/p>\n<p><strong>Understand Vocabulary<\/strong><\/p>\n<p><strong>Glossary<\/strong><\/p>\n<p><strong>Word List<br \/>\n<\/strong>\u2022 base<br \/>\n\u2022 equivalent decimals<br \/>\n\u2022 expanded form<br \/>\n\u2022 exponent<br \/>\n\u2022 power<br \/>\n\u2022 thousandths<br \/>\n\u2022 value<\/p>\n<p>Choose the best term from the Word List. Write it on the blank.<\/p>\n<p>Question 1.<br \/>\nDecimal numbers that name the same part of a whole or the same point on a number line are called ____<br \/>\nAnswer: Decimal numbers that name the same part of a whole or the same point on a number line are called Equivalent decimals<\/p>\n<p>Question 2.<br \/>\nThe ____ of a digit in a number depends on its place in the number.<br \/>\nAnswer: The value of a digit in a number depends on its place in the number.<\/p>\n<p>Question 3.<br \/>\nThe product that results from multiplying the same number over and over is a(n) ____ of that number.<br \/>\nAnswer:\u00a0 The product that results from multiplying the same number over and over is a(n) POWER of that number.<\/p>\n<p>Question 4.<br \/>\nA digit in the hundredths place has ten times the value of the same digit in the ___ place.<br \/>\nAnswer: A digit in the hundredths place has ten times the value of the same digit in the thousandths place.<\/p>\n<p>Question 5.<br \/>\nIn 10<sup>5<\/sup>, the number 10 is the _____.<br \/>\nAnswer: In 10<sup>5<\/sup>, the number 10 is the BASE.<\/p>\n<p>Draw a line from each number in Column A to the same number in Column B.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-9215\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-Grade-5-Answers-Topic-1-Understand-Place-Vale-72.3.png\" alt=\"Envision Math Common Core Grade 5 Answers Topic 1 Understand Place Vale 72.3\" width=\"506\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21486\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.20.png\" alt=\"\" width=\"504\" height=\"144\" \/><\/p>\n<p><strong>Use Vocabulary in Writing<\/strong><\/p>\n<p>Question 10.<br \/>\nExplain why each 8 in the number 8.888 has a different value. Use one or more terms from the Word List in your explanation.<br \/>\nAnswer:\u00a0 Because of its place value.<\/p>\n<p>Explanation:<br \/>\nGiven, 8.888<br \/>\nThe first 8 has the place value of tenths, The second 8 has the place value of hundredths and the final 8 has the place value of thousandths.<\/p>\n<p><strong>Set A<\/strong><br \/>\npages 5-8<br \/>\nHow can you write 7,000 using exponents?<br \/>\n7,000 = 7 \u00d7 10 \u00d7 10 \u00d7 10 = 7 \u00d7 10<sup>3<\/sup><br \/>\nSo, using exponents, you can write 7,000 as 7 \u00d7 10<sup>3<\/sup><\/p>\n<p><strong>Remember<\/strong> the number of zeros in the product is the same as the exponent.<\/p>\n<p>Find each product.<\/p>\n<p>Question 1.<br \/>\n9 \u00d7 10<sup>1<\/sup><br \/>\nAnswer: 90<\/p>\n<p>Explanation:<br \/>\n9 \u00d7 10<sup>1 <\/sup>= 9 \u00d7 10 = 90<\/p>\n<p>Question 2.<br \/>\n8 \u00d7 1,000<br \/>\nAnswer: 8,000<\/p>\n<p>Explanation:<br \/>\n8 \u00d7 10 \u00d7 10 \u00d7 10 = 8,000<\/p>\n<p>Question 3.<br \/>\n5 \u00d7 10<sup>2<\/sup><br \/>\nAnswer: 5 \u00d7 10<sup>2<\/sup>\u00a0= 500<\/p>\n<p>Explanation:<br \/>\n5 \u00d7 10<sup>2<\/sup>\u00a0=\u00a0 5\u00a0\u00d7 10 \u00d7 10\u00a0 = 500<\/p>\n<p>Question 4.<br \/>\n2 \u00d7 10<sup>5<\/sup><br \/>\nAnswer: 2\u00a0\u00d7 10<sup>5<\/sup> \u00a0= 2,00,000<\/p>\n<p>Explanation:<br \/>\n2 \u00d7 10<sup>5<\/sup> \u00a0= 2 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 = 2,00,000<\/p>\n<p><strong>Set B<\/strong><br \/>\npages 9-12<br \/>\nWrite the number name and tell the value of the underlined digit for 93<u>0<\/u>,365.<br \/>\nNine hundred thirty thousand, three hundred sixty-five<br \/>\nSince the 0 is in the thousands place, its value is 0 thousands, or 0.<br \/>\nUse digital tools to solve these and other problems.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9217\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-76.9.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 76.9\" width=\"82\" height=\"110\" \/><\/p>\n<p><strong>Remember<\/strong> you can find the value of a digit by its place in a number.<\/p>\n<p>Write the number name and tell the value of the underlined digit.<\/p>\n<p>Question 1.<br \/>\n<u>9<\/u>,000,000<br \/>\nAnswer: Nine million<\/p>\n<p>Explanation:<br \/>\nthe value of the underlined digit is in millions place.<\/p>\n<p>Question 2.<br \/>\n4<u>8<\/u>5,002,000<br \/>\nAnswer: four hundred and eighty five million and two thousands<\/p>\n<p>Explanation:<br \/>\nthe value of the underlined digit is in millions place.<\/p>\n<p>Question 3.<br \/>\n2<u>5<\/u>,678<br \/>\nAnswer: Twenty five thousand and six hundred and seventy eight<\/p>\n<p>Explanation:<br \/>\nthe value of the underlined digit is in thousands place.<\/p>\n<p>Question 4.<br \/>\n<u>1<\/u>7,874,000<br \/>\nAnswer: seventeen million and eight hundred and seventy four thousand<\/p>\n<p>Explanation:<br \/>\nthe value of the underlined digit is in ten millions place.<\/p>\n<p><strong>Set C<\/strong><br \/>\npages 13-16, 17-20<br \/>\nA place-value chart can help you write the standard form, expanded form, and number name for a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9218\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-76.10.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 76.10\" width=\"230\" height=\"73\" \/><br \/>\nStandard form: 8.026<br \/>\nexpanded form: 8 + 2 \u00d7 \\(\\frac{1}{100}\\) + 6 \u00d7 \\(\\frac{1}{1,000}\\)<br \/>\nNumber name: Eight and twenty-six thousandths<\/p>\n<p><strong>Remember<\/strong> the word and is written for the decimal point.<\/p>\n<p>Question 1.<br \/>\nHow can you write 0.044 as a fraction?<br \/>\nHow are the values of the two 4s related in 0.044?<br \/>\nAnswer: \\(\\frac{44}{1,000}\\) and The first 4 is in hundredths place and last 4 is in thousandths place<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{44}{1,000}\\) = 0.044,<br \/>\nThe first 4 is in hundredths place and last 4 is in thousandths place<\/p>\n<p>Write each number in standard form.<\/p>\n<p>Question 2.<br \/>\neight and fifty-nine hundredths<br \/>\nAnswer: 8.59<\/p>\n<p>Question 3.<br \/>\nseven and three thousandths + 4. 3 + 2 \u00d7 \\(\\frac{1}{10}\\) + 4 \u00d7 \\(\\frac{1}{1000}\\)<br \/>\nAnswer: 11.507<\/p>\n<p>Explanation:<br \/>\nGiven, seven and three thousandths + 4. 3 + 2 \u00d7 \\(\\frac{1}{10}\\) + 4 \u00d7 \\(\\frac{1}{1000}\\)<br \/>\n7.003 + 4.3 + [ 0.2 + 0.004]<br \/>\n= 11.303 + 0.204<br \/>\n= 11.507<\/p>\n<p><strong>Set D<\/strong><br \/>\npages 21-24 Compare. Write &gt;, &lt;, or =.<\/p>\n<p>8. 45 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 8.47<br \/>\nLine up the decimal points. Start at the left to compare. Find the first place where the digits are different.<br \/>\n8.4<u>5<\/u><br \/>\n8.4<u>7<\/u> 0.05 &lt; 0.07<br \/>\nSo, 8.45 &lt; 8.47.<\/p>\n<p><strong>Remember<\/strong> that equivalent decimals, such as 0.45 and 0.450, can help you compare numbers.<br \/>\nCompare. Write &gt;, &lt;, or =.<\/p>\n<p>Question 1.<br \/>\n0.584 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 0.58<br \/>\nAnswer: 0.584 &gt; 0.58<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 0.584 and 0.58<br \/>\n0.584<br \/>\n0.58<br \/>\nComparing the numbers after decimals,<br \/>\n4 &gt; 0<br \/>\nSo, 0.584 &gt; 0.58<\/p>\n<p>Question 2.<br \/>\n9.327 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 9.236<br \/>\nAnswer: 9.327 &gt; 9.236<\/p>\n<p>Explanation:<br \/>\nGiven, 9.327 and 9.236<br \/>\n9.327<br \/>\n9.236<br \/>\nComparing the numbers after decimals,<br \/>\n3 &gt; 2<br \/>\nSo, 9.327 &gt; 9.236<\/p>\n<p>Question 3.<br \/>\n5.2 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 5.20<br \/>\nAnswer: 5.2 = 5.20<\/p>\n<p>Explanation:<br \/>\nGiven, 5.2 and 5.20<br \/>\n5.2<br \/>\n5.20<br \/>\nComparing the numbers after decimals, we have<br \/>\nAll the numbers are equal<br \/>\nSo, 5.2 = 5.20<\/p>\n<p>Question 4.<br \/>\n5.643 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 5.675<br \/>\nAnswer: 5.643 &lt;\u00a05.675<\/p>\n<p>Explanation:<br \/>\nGiven, 5.643 and 5.675<br \/>\n5.643<br \/>\n5.675<br \/>\nComparing the numbers after decimals, we have<br \/>\n4 &lt; 7<br \/>\nSo, 5.643 &lt; 5.675<\/p>\n<p>Question 5.<br \/>\n0.07 <img loading=\"lazy\" class=\"alignnone size-full wp-image-9219\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-88.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 88\" width=\"26\" height=\"34\" \/> 0.08<br \/>\nAnswer: 0.07 &lt; 0.08.<\/p>\n<p>Explanation:<br \/>\nGiven,\u00a0 0.07 and 0.08<br \/>\n0.07<br \/>\n0.08<br \/>\nComparing the numbers after decimals, we have<br \/>\n7 &lt; 8<br \/>\nSo, 0.07 &lt; 0.08.<\/p>\n<p><strong>Set E<\/strong><br \/>\npages 25-28<br \/>\nRound 12.0<u>8<\/u>7 to the place of the underlined digit.<br \/>\n12.0<u>8<\/u>7 Look at the digit following the underlined digit. Look at 7.<br \/>\nRound to the next greater number of hundredths because 7 &gt; 5.<br \/>\n12.087 rounded to the nearest hundredth is 12.09.<\/p>\n<p><strong>Remember<\/strong> that rounding a number means replacing it with a number that tells about how many or how much.<br \/>\nRound each number to the place of the underlined digit.<\/p>\n<p>Question 1.<br \/>\n10.<u>2<\/u>45<br \/>\nAnswer: 10.2<\/p>\n<p>Explanation:<br \/>\nGiven, 10.<u>2<\/u>45<br \/>\n2 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 10.2<br \/>\nThe rounding number is 10.2.<\/p>\n<p>Question 2.<br \/>\n<u>7<\/u>3.4<br \/>\nAnswer: 73<\/p>\n<p>Explanation:<br \/>\nGiven, 73.4<br \/>\n7 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 73<br \/>\nThe rounding number is 73.<\/p>\n<p>Question 3.<br \/>\n0.1<u>4<\/u>5<br \/>\nAnswer: 0.1<\/p>\n<p>Explanation:<br \/>\nGiven, 0.145<br \/>\n1 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 0.1<br \/>\nThe rounding number is 0.1.<\/p>\n<p>Question 4.<br \/>\n3.<u>9<\/u>99<br \/>\nAnswer: 4<\/p>\n<p>Explanation:<br \/>\nGiven, 3.<u>9<\/u>99<br \/>\n9 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 4<br \/>\nThe rounding number is 4.<\/p>\n<p>Question 5.<br \/>\n13.0<u>2<\/u>3<br \/>\nAnswer: 13<\/p>\n<p>Explanation:<br \/>\n2 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 13<br \/>\nThe rounding number is 13.<\/p>\n<p>Question 6.<br \/>\n45.<u>3<\/u>98<br \/>\nAnswer: 45<\/p>\n<p>Explanation:<br \/>\n3 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 45<br \/>\nThe rounding number is 45.<\/p>\n<p><strong>Set F<\/strong><br \/>\npages 29-32<br \/>\nThink about these questions to help you look for and use structure to understand and Explain patterns with decimal numbers.<\/p>\n<p><strong>Thinking Habits<\/strong><br \/>\n\u2022 What patterns can I see and describe?<br \/>\n\u2022 How can I use the patterns to solve the problem?<br \/>\n\u2022 Can I see expressions and objects in different ways?<br \/>\n\u2022 What equivalent expressions can I use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9220\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-89.1.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 89.1\" width=\"133\" height=\"144\" \/><\/p>\n<p><strong>Remember<\/strong> to check that all of your answers follow a pattern.<br \/>\nEach grid is part of a decimal number chart. Write the missing numbers to complete the grids.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9221\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-89.2.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 89.2\" width=\"116\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21490\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.21.png\" alt=\"\" width=\"128\" height=\"131\" \/><\/p>\n<p>Explanation:<br \/>\nAs you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same, except for the last number, while the hundredths increase by 1.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9222\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-89.3.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 89.3\" width=\"178\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21491\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.22.png\" alt=\"\" width=\"191\" height=\"123\" \/><\/p>\n<p>Explanation:<br \/>\nAs you move down the columns, tenths increase by 1 while the Column 1 hundredths stay the same.<br \/>\nMoving from left to right in the rows, tenths stay the same, except for the last number, while the hundredths increase by 1.<\/p>\n<h3><a id=\"Topic_ 1_ Assessment_ Practice\"><\/a>Topic 1 Assessment Practice<\/h3>\n<p>Question 1.<br \/>\nComplete the sentences to make true statements.<br \/>\n6 is 100 times ____.<br \/>\n0.06 is 10 times ______.<br \/>\n60 is \\(\\frac{1}{100}\\) of ____.<br \/>\nAnswer: 600, 0.6, 0.6<\/p>\n<p>Explanation:<br \/>\n6 \u00d7 100 = 600<br \/>\n0.06 \u00d7 10 = 0.6<br \/>\n60 \u00d7 \\(\\frac{1}{100}\\) = 0.6<\/p>\n<p>Question 2.<br \/>\nA national park has eighty thousand, nine-hundred twenty-three and eighty-six hundredths acres of land. Which shows this in standard form?<br \/>\nA. 80,923.086<br \/>\nB. 80,923.68<br \/>\nC. 80,923.806<br \/>\nD. 80,923.86<br \/>\nAnswer: A , that is 80,923.086<\/p>\n<p>Explanation:<br \/>\nBecause, the number name of 80,923.086 is eighty thousand, nine-hundred twenty-three and eighty-six hundredths<\/p>\n<p>Question 3.<br \/>\nWhich numbers have a digit in the ones place that is \\(\\frac{1}{10}\\) the value of the digit in the tens place? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9223\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-90.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 90\" width=\"28\" height=\"28\" \/> 9,077<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9223\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-90.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 90\" width=\"28\" height=\"28\" \/> 9,884<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9223\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-90.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 90\" width=\"28\" height=\"28\" \/> 1,303<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9223\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-90.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 90\" width=\"28\" height=\"28\" \/> 1,055<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9223\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-90.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 90\" width=\"28\" height=\"28\" \/> 3,222<br \/>\nAnswer: 9,884 and\u00a0 3,222<\/p>\n<p>Explanation:<br \/>\nThese numbers 9,884 and\u00a0 3,222 have a digit in the ones place that is \\(\\frac{1}{10}\\) the value of the digit in the tens place<\/p>\n<p>Question 4.<br \/>\nMrs. Martin has $7,000 in her savings account. Alonzo has \\(\\frac{1}{10}\\) to as much money in his account as Mrs. Martin. How much money does Alonzo have in his account?<br \/>\nAnswer: Amount Alonzo has is $ 700<\/p>\n<p>Explanation:<br \/>\nhe amount Martin has in her account is $ 7000<br \/>\nAlonzo has 1\/10th the amount Martin has<br \/>\nTherefore Alonzo has \\(\\frac{1}{10}\\) of 7000 ;<br \/>\n= 7000\/10 = $ 700<br \/>\nAmount Alonzo has is $ 700 .<\/p>\n<p>Question 5.<br \/>\nSelect all the comparisons that are true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9225\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91\" width=\"23\" height=\"27\" \/> 04.15 &gt; 4.051<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9225\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91\" width=\"23\" height=\"27\" \/> 1.054 &gt; 1.45<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9225\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91\" width=\"23\" height=\"27\" \/> 5.14 &lt; 5.041<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9225\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91\" width=\"23\" height=\"27\" \/> 5.104 &lt; 5.41<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9225\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91\" width=\"23\" height=\"27\" \/> 5.014 &lt; 5.41<br \/>\nAnswer:\u00a0 04.15 &gt; 4.051, 5.104 &lt; 5.41 and 5.014 &lt; 5.41<\/p>\n<p>Explanation:<br \/>\nBecause of their place value ,<br \/>\n04.15 &gt; 4.051<br \/>\n1 &gt; 0<br \/>\nSo, 04.15 &gt; 4.051<\/p>\n<p>5.104 &lt; 5.41<br \/>\n1 &lt; 4<br \/>\nSo, 5.104 &lt; 5.41<\/p>\n<p>5.014 &lt; 5.41<br \/>\n0 &lt; 4<br \/>\nSo, 5.014 &lt; 5.41<\/p>\n<p>Question 6.<br \/>\nLuke shaded 20 squares on his hundredths grid. Bekka shaded 30 squares on her hundredths grid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9224\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-91.1.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 91.1\" width=\"204\" height=\"96\" \/><br \/>\nA. Whose grid represents the larger decimal?<br \/>\nB. Write two decimals equivalent to Luke&#8217;s decimal.<br \/>\nAnswer: 0.2 &lt; 0.3, The two decimals equivalent to Luke&#8217;s decimal are 0.20 and 0.21<\/p>\n<p>Explanation:<br \/>\nGiven, Luke shaded 20 squares on his hundredths grid, \\(\\frac{20}{100}\\) that is 0.2<br \/>\nBekka shaded 30 squares on her hundredths grid. \\(\\frac{30}{100}\\)that is 0.3<br \/>\nBekka has largest decimal.<\/p>\n<p>The two decimals equivalent to Luke&#8217;s decimal are 0.20 and 0.21<\/p>\n<p>Question 7.<br \/>\nWhich statements about the values of 2.044 and 20.44 are true? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9226\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-93.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 93\" width=\"30\" height=\"31\" \/> 2.044 is \\(\\frac{1}{10}\\) of 20.44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9226\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-93.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 93\" width=\"30\" height=\"31\" \/> 2.044 is \\(\\frac{1}{100}\\) of 20.44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9226\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-93.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 93\" width=\"30\" height=\"31\" \/> 20.44 is 10 times 2.044.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9226\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-93.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 93\" width=\"30\" height=\"31\" \/> 20.44 is 100 times 2.044.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9226\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-93.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 93\" width=\"30\" height=\"31\" \/> 2.044 is 10 times 20.44.<br \/>\nAnswer:\u00a0 20.44 is 10 times 2.044.<\/p>\n<p>Explanation:<br \/>\nGiven, 20.44 is 10 times 2.044.<br \/>\n20.44 \u00d7 10 = 2.044.<\/p>\n<p>Question 8.<br \/>\nThe weight of Darrin&#8217;s phone is 3.405 ounces. What is 3.405 written in expanded form?<br \/>\nA. 3 \u00d7 1 + 4 \u00d7 \\(\\frac{1}{10}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)<br \/>\nB. 3 \u00d7 10 + 4 \u00d7 \\(\\frac{1}{10}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)<br \/>\nC. 3 \u00d7 10 + 4 \u00d7 \\(\\frac{1}{10}\\) + 5 \u00d7 \\(\\frac{1}{100}\\)<br \/>\nD. 3 \u00d7 1 + 4 \u00d7 \\(\\frac{1}{100}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)<br \/>\nAnswer:\u00a0 D<\/p>\n<p>Explanation:<br \/>\nGiven, 3.405<br \/>\nThe expanded form, 3 \u00d7 1 + 4 \u00d7 \\(\\frac{1}{100}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)<br \/>\n= 3 +0.04 + 0.005<br \/>\n= 3.405<\/p>\n<p>Question 9.<br \/>\nElaine has a piece of wire that is 2.16 meters long. Dikembe has a piece of wire that is 2.061 meters long. Whose piece of wire is longer? How can you tell?<br \/>\nAnswer: Dikembe has the longest wire.<\/p>\n<p>Explanation:<br \/>\nGiven, 2.16 and 2.061<br \/>\n2.16<br \/>\n2.061<br \/>\nComparing the place values of the digits after decimal<br \/>\n1 &gt; 0<br \/>\nSo, 2.16 &gt; 2.061<br \/>\nDikembe has the longest wire.<\/p>\n<p>Question 10.<br \/>\nIn a basketball tournament, Dimitri averaged 12.375 rebounds per game. What is 12.375 written in expanded form? How is it written with number names?<br \/>\nAnswer: The expanded form is (12 \u00d7 1) + {3 \u00d7 \\(\\frac{1}{10}\\) + 7 \u00d7 \\(\\frac{1}{100}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)}<\/p>\n<p>Explanation:<br \/>\nGiven, 12.375<br \/>\nThe expanded form is (12 \u00d7 1) + {3 \u00d7 \\(\\frac{1}{10}\\) + 7 \u00d7 \\(\\frac{1}{100}\\) + 5 \u00d7 \\(\\frac{1}{1,000}\\)}<br \/>\n12 + 0.3 + 0.07 + 0.005<br \/>\n= 12.375.<br \/>\nThe number name is twelve thousand and three hundred and seventy five.<\/p>\n<p>Question 11.<br \/>\nThe numbers below follow a pattern.<br \/>\n0.006 0.06 0.6 6 ____ _____<br \/>\nA. What are the next two numbers in the pattern?<br \/>\nB. What is the relationship between the terms in the pattern?<br \/>\nAnswer:\u00a0 60 and 600 , The terms relate to each other in that the next term is 10 times the previous term.<\/p>\n<p>Explanation:<br \/>\nRelationship between term: The next term is ten times the previous term.<br \/>\n0.006 = 6\/1000<br \/>\n0.06 = 6\/100<br \/>\n0.6 = 6\/10<br \/>\n6 = 6\/1<br \/>\nThis is a geometric sequence, where the common ratio is 10. 0.6\/0.06 = 6\/0.6 = 0.06\/0.006 = 10<br \/>\nTo get next number we simply multiply the previous number by 10.<br \/>\nThe terms relate to each other in that the next term is 10 times the previous term.\u00a0<span class=\"copyright-span\"><br \/>\n<\/span><\/p>\n<p>Question 12.<br \/>\nKendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? Explain how you decided.<br \/>\nAnswer: The rounding number is 16.<\/p>\n<p>Explanation:<br \/>\nGiven, 15.839<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 16<br \/>\nThe rounding number is 16.<\/p>\n<h3><a id=\"Topic_ 1_ Performance_ Task\"><\/a>Topic 1 Performance Task<\/h3>\n<p><strong>Fruits and Vegetables<\/strong><br \/>\nHenry recorded how many pounds of fruits and vegetables his family bought during the past two months.<\/p>\n<p>Question 1.<br \/>\nPick four fruits and list them in the table below.<br \/>\n<strong>Part A<\/strong><br \/>\nRound each fruit&#8217;s weight to the nearest 0.1 pound. Write the rounded weight in the next column.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9227\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-94.1.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 94.1\" width=\"669\" height=\"241\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21495\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.23.png\" alt=\"\" width=\"412\" height=\"141\" \/><\/p>\n<p><strong>Part B<\/strong><br \/>\nExplain how you rounded the weights of the fruits.<br \/>\nAnswer:\u00a0 detailed explanation is given below.<\/p>\n<p>Explanation:<br \/>\nFor Apples, given 2.068<br \/>\n5 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 2<br \/>\nThe rounding number is 2.<\/p>\n<p>For Blueberries 1.07<br \/>\n0 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 1.1<br \/>\nThe rounding number is 1.1.<\/p>\n<p>For lemons 1.031<br \/>\n0 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1<br \/>\nThe rounding number is 1.<\/p>\n<p>For oranges 3.502<br \/>\n0 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 3.5<br \/>\nThe rounding number is 3.5.<\/p>\n<p>For peaches 2.608<br \/>\n0 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 2.6<br \/>\nThe rounding number is 2.6.<\/p>\n<p>For pears 3.592<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 3.6<br \/>\nThe rounding number is 3.6.<\/p>\n<p>Question 2.<br \/>\nPick four vegetables and list them in the table below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9228\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-94.2.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 94.2\" width=\"227\" height=\"247\" \/><\/p>\n<p><strong>Part A<\/strong><br \/>\nRound each vegetable&#8217;s weight to the nearest 0.01 pound. Write the rounded weight in the next column.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-9229\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-95.2.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 95.2\" width=\"412\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21496\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-1-Understand-Place-Value-.24.png\" alt=\"\" width=\"409\" height=\"130\" \/><\/p>\n<p><strong>Part B<\/strong><br \/>\nExplain how you rounded the weights of the vegetables.<br \/>\nAnswer: Detailed explanation is given below<\/p>\n<p>Explanation:<\/p>\n<p>For Beets 1.862<br \/>\n6 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1.86<br \/>\nThe rounding number is 1.86.<\/p>\n<p>For Celery 1.402<br \/>\n0 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1.4<br \/>\nThe rounding number is 1.4.<\/p>\n<p>For Corn 2.556<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 2.56<br \/>\nThe rounding number is 2.56.<\/p>\n<p>For potatoes 3.441<br \/>\n4 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 3.44<br \/>\nThe rounding number is 3.44.<\/p>\n<p>Question 3.<br \/>\nUse &lt;, &gt;, or= to compare the weights of blueberries and lemons.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhen rounded to the nearest hundredth, two items will round to the same decimal. What two items are they?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nHow does writing the weight for potatoes in expanded form show why the same digit can have different values?<br \/>\nAnswer: Because of the place value of the numbers in the decimals<\/p>\n<p>Explanation:<br \/>\nFor potatoes 3.441<br \/>\n4 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 3.44<br \/>\nThe rounding number is 3.44.<\/p>\n<p>The first 4 has the place value of tenths and the last 4 has the place value of hundredths.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-9230\" src=\"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/Envision-Math-Common-Core-5th-Grade-Answer-Key-Topic-1-Understand-Place-Vale-100.png\" alt=\"Envision Math Common Core 5th Grade Answer Key Topic 1 Understand Place Vale 100\" width=\"136\" height=\"468\" \/><\/p>\n<p>Question 6.<br \/>\nWhat is the relationship between the values of the two 4s in the weight of the potatoes?<br \/>\nAnswer: The first 4 has the place value of tenths and the last 4 has the place value of hundredths. and the first 4 is ten times the value of second 4.<\/p>\n<p>Explanation:<\/p>\n<p>For potatoes 3.441<br \/>\n4 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 3.44<br \/>\nThe rounding number is 3.44.<\/p>\n<p>The first 4 has the place value of tenths and the last 4 has the place value of hundredths.<br \/>\nand the first 4 is ten times the value of second 4.<\/p>\n<p>Question 7.<br \/>\nWrite the number of pounds of celery Henry&#8217;s family bought using number names and in expanded form.<br \/>\nAnswer: The number name is 1.4 pounds<br \/>\nThe expanded form is 14 \u00d7 \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nFor Celery 1.402<br \/>\n0 is the rounding place, the digit is less than 5, leave the rounding digit alone.<br \/>\nDrop the digits to the right of the decimal point, that is 1.4<br \/>\nThe rounding number is 1.4.<\/p>\n<p>The number name is 1.4 pounds<br \/>\nThe expanded form is 14 \u00d7 \\(\\frac{1}{10}\\)<\/p>\n<p>Question 8.<br \/>\nThe store where Henry&#8217;s family shops sold 103 times as many pounds of corn as Henry&#8217;s family bought.<br \/>\nAnswer:263.68 pounds have sold.<\/p>\n<p>Explanation:<br \/>\nFor Corn 2.556<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 2.56<br \/>\nThe rounding number is 2.56.<\/p>\n<p>Given, Henry&#8217;s family shops sold 103 times as many pounds of corn as Henry&#8217;s family bought.<br \/>\n2.56 \u00d7 103 = 263.68<\/p>\n<p><strong>Part A<\/strong><br \/>\nHow many pounds of corn did the store sell? Write your answer in standard form and with number names.<\/p>\n<p>Answer: The number form is twenty six thousand and three hundred and sixty eight.<\/p>\n<p>Explanation:<br \/>\nStore has sold 263.68<br \/>\nThe number form is twenty six thousand and three hundred and sixty eight.<\/p>\n<p><strong>Part B<\/strong><br \/>\nExplain how you found your answer.<br \/>\nAnswer:\u00a0 detailed explanation is given below<\/p>\n<p>Explanation:<br \/>\nFor Corn 2.556<br \/>\n5 is the rounding place, the digit is 5 or greater, add 1 to the rounding digit.<br \/>\nDrop the digits to the right of the decimal point, that is 2.56<br \/>\nThe rounding number is 2.56.<\/p>\n<p>Given, Henry&#8217;s family shops sold 103 times as many pounds of corn as Henry&#8217;s family bought.<br \/>\n2.56 \u00d7 103 = 263.68<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Practice with the help of enVision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Value regularly and improve your accuracy in solving questions. enVision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value Envision Math Common Core 5th Grade Answers Key Topic 1 Understand Place Value has all the &#8230; <a title=\"enVision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Value\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/envision-math-common-core-grade-5-answer-key-topic-1\/\" aria-label=\"More on enVision Math Common Core Grade 5 Answer Key Topic 1 Understand Place Value\">Read more<\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/90112"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=90112"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/90112\/revisions"}],"predecessor-version":[{"id":90115,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/90112\/revisions\/90115"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=90112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=90112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=90112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}