{"id":6338,"date":"2022-03-28T14:57:15","date_gmt":"2022-03-28T09:27:15","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6338"},"modified":"2022-04-07T12:50:17","modified_gmt":"2022-04-07T07:20:17","slug":"go-math-grade-8-answer-key-chapter-2-exponents-and-scientific-notation","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-2-exponents-and-scientific-notation\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation"},"content":{"rendered":"<p>Get Free Access to Download Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation PDF from here. Start your preparation with the help of <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a>. It is essential for all the students to learn the concepts of this chapter in-depth. So, make use of the Go Math Grade 8 Chapter 2 Exponents and Scientific Notation Solution Key links and go through the solutions.<\/p>\n<h2>Go Math Grade 8 Chapter 2 Exponents and Scientific Notation Answer Key<\/h2>\n<p>Check out the list of the topics before you start your preparation. You can step by step explanation for all the questions in HMH Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation for free of cost. Quickly download Go Math Grade 8 Chapter 2 Answer Key PDF and fix the timetable to prepare.<\/p>\n<p><strong>Lesson 1: Integer Exponents<\/strong><\/p>\n<ul>\n<li><a href=\"#Integer_Exponents_\u2013_Page_No._36\">Integer Exponents \u2013 Page No. 36<\/a><\/li>\n<li><a href=\"#Integer_Exponents_\u2013_Page_No._37\">Integer Exponents \u2013 Page No. 37<\/a><\/li>\n<li><a href=\"#Integer_Exponents_Lesson_Check_\u2013_Page_No._38\">Integer Exponents Lesson Check \u2013 Page No. 38<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Scientific Notation with Positive Powers of 10<\/strong><\/p>\n<ul>\n<li><a href=\"#Scientific_Notation_with_Positive_Powers_of_10_\u2013_Page_No._42\">Scientific Notation with Positive Powers of 10 \u2013 Page No. 42<\/a><\/li>\n<li><a href=\"#Scientific_Notation_with_Positive_Powers_of_10_\u2013_Page_No._43\">Scientific Notation with Positive Powers of 10 \u2013 Page No. 43<\/a><\/li>\n<li><a href=\"#Scientific_Notation_with_Positive_Powers_of_10_Lesson_Check_\u2013_Page_No._44\">Scientific Notation with Positive Powers of 10 Lesson Check \u2013 Page No. 44<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Scientific Notation with Negative Powers of 10<\/strong><\/p>\n<ul>\n<li><a href=\"#Scientific_Notation_with_Negative_Powers_of_10_\u2013_Page_No._48\">Scientific Notation with Negative Powers of 10 \u2013 Page No. 48<\/a><\/li>\n<li><a href=\"#Scientific_Notation_with_Negative_Powers_of_10_\u2013_Page_No._49\">Scientific Notation with Negative Powers of 10 \u2013 Page No. 49<\/a><\/li>\n<li><a href=\"#Scientific_Notation_with_Negative_Powers_of_10_Lesson_Check_\u2013_Page_No._50\">Scientific Notation with Negative Powers of 10 Lesson Check \u2013 Page No. 50<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Operations with Scientific Notation<\/strong><\/p>\n<ul>\n<li><a href=\"#Operations_with_Scientific_Notation_\u2013_Page_No._54\">Operations with Scientific Notation \u2013 Page No. 54<\/a><\/li>\n<li><a href=\"#Operations_with_Scientific_Notation_\u2013_Page_No._55\">Operations with Scientific Notation \u2013 Page No. 55<\/a><\/li>\n<li><a href=\"#Operations_with_Scientific_Notation_Lesson_Check_\u2013_Page_No._56\">Operations with Scientific Notation Lesson Check \u2013 Page No. 56<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#Integer_Exponents_\u2013_Model_Quiz_\u2013_Page_No._57\">Model Quiz \u2013 Page No. 57<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review<\/strong><\/p>\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._58\">Mixed Review \u2013 Page No. 58<\/a><\/li>\n<\/ul>\n<h3><a id=\"Integer_Exponents_\u2013_Page_No._36\"><\/a>Guided Practice &#8211; Integer Exponents &#8211; Page No. 36<\/h3>\n<p><strong>Find the value of each power.<\/strong><\/p>\n<p>Question 1.<br \/>\n8<sup>\u22121<\/sup> =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 8<br \/>\nExponent = 1<br \/>\n8<sup>\u22121<\/sup> = (1\/8)<sup>1<\/sup> = 1\/8<\/p>\n<p>Question 2.<br \/>\n6<sup>\u22122<\/sup> =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{36}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 6<br \/>\nExponent = 2<br \/>\n6<sup>\u22122<\/sup> = (1\/6)<sup>2<\/sup> = 1\/36<\/p>\n<p>Question 3.<br \/>\n256<sup>0<\/sup> =<br \/>\n______<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\n256<sup>0<\/sup><br \/>\nBase = 256<br \/>\nExponent = 0<br \/>\nAnything raised to the zeroth power is 1.<br \/>\n256<sup>0<\/sup> = 1<\/p>\n<p>Question 4.<br \/>\n10<sup>2<\/sup> =<br \/>\n______<\/p>\n<p>Answer:<br \/>\n100<\/p>\n<p>Explanation:<br \/>\nBase = 10<br \/>\nExponent = 2<br \/>\n10<sup>2<\/sup> = 10 \u00d7 10 = 100<\/p>\n<p>Question 5.<br \/>\n5<sup>4<\/sup> =<br \/>\n______<\/p>\n<p>Answer:<br \/>\n625<\/p>\n<p>Explanation:<br \/>\nBase = 5<br \/>\nExponent = 4<br \/>\n5<sup>4<\/sup> = 5 \u00d7 5 \u00d7 5 \u00d7 5 = 625<\/p>\n<p>Question 6.<br \/>\n2<sup>\u22125<\/sup> =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{32}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 2<br \/>\nExponent = 5<br \/>\n2<sup>\u22125<\/sup> = (1\/2)<sup>5<\/sup> = (1\/2) \u00d7 (1\/2) \u00d7 (1\/2) \u00d7 (1\/2) \u00d7 (1\/2) = 1\/32<\/p>\n<p>Question 7.<br \/>\n4<sup>\u22125<\/sup> =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{1,024}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 4<br \/>\nExponent = 5<br \/>\n4<sup>\u22125<\/sup> = (1\/4)<sup>5<\/sup> = (1\/4) \u00d7 (1\/4) \u00d7 (1\/4) \u00d7 (1\/4) \u00d7 (1\/4) = 1\/1,024<\/p>\n<p>Question 8.<br \/>\n89<sup>0<\/sup> =<br \/>\n______<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\n89<sup>0<\/sup><br \/>\nBase = 89<br \/>\nExponent = 0<br \/>\nAnything raised to the zeroth power is 1.<br \/>\n89<sup>0<\/sup> = 1<\/p>\n<p>Question 9.<br \/>\n11<sup>\u22123<\/sup> =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{1,331}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 11<br \/>\nExponent = 3<br \/>\n11<sup>\u22123<\/sup> = (1\/11)<sup>3<\/sup> = (1\/11) \u00d7 (1\/11) \u00d7 (1\/11) = 1\/1,331<\/p>\n<p><strong>Use properties of exponents to write an equivalent expression.<\/strong><\/p>\n<p>Question 10.<br \/>\n4 \u22c5 4 \u22c5 4 = 4<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n4<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nThe same number 4 is multiplying 3 times.<br \/>\nThe number of times a term is multiplied called the exponent.<br \/>\nSo the base is 4 and the exponent is 3<br \/>\n4 \u22c5 4 \u22c5 4 = 4<sup>3<\/sup><\/p>\n<p>Question 11.<br \/>\n(2 \u22c5 2) \u22c5 (2 \u22c5 2 \u22c5 2) = 2<sup>?<\/sup> \u22c5 2<sup>?<\/sup> = 2<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n2<sup>5<\/sup><\/p>\n<p>Explanation:<br \/>\nThe same number 2 is multiplying 5 times.<br \/>\nThe number of times a term is multiplied called the exponent.<br \/>\nSo the base is 2 and the exponent is 5<br \/>\n(2 \u22c5 2) \u22c5 (2 \u22c5 2 \u22c5 2) = 2<sup>2<\/sup> \u22c5 2<sup>3<\/sup> = 2<sup>5<\/sup><\/p>\n<p>Question 12.<br \/>\n\\(\\frac { { 6 }^{ 7 } }{ { 6 }^{ 5 } } \\) = \\(\\frac{6\u22c56\u22c56\u22c56\u22c56\u22c56\u22c56}{6\u22c56\u22c56\u22c56\u22c56}\\) = 6<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n6<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\n\\(\\frac { { 6 }^{ 7 } }{ { 6 }^{ 5 } } \\) = \\(\\frac{6\u22c56\u22c56\u22c56\u22c56\u22c56\u22c56}{6\u22c56\u22c56\u22c56\u22c56}\\)<br \/>\nCancel the common factors<br \/>\n6.6<br \/>\nBase = 6<br \/>\nExponent = 2<br \/>\n6<sup>2<\/sup><\/p>\n<p>Question 13.<br \/>\n\\(\\frac { { 8 }^{ 12 } }{ { 8 }^{ 9 } } \\) = 8<sup>?-?<\/sup> = 8<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n8<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\n\\(\\frac { { 8 }^{ 12 } }{ { 8 }^{ 9 } } \\)<br \/>\nBases are common. So, the exponents are subtracted<br \/>\n8<sup>12-9<\/sup> = 8<sup>3<\/sup><\/p>\n<p>Question 14.<br \/>\n5<sup>10<\/sup> \u22c5 5 \u22c5 5 = 5<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n5<sup>12<\/sup><\/p>\n<p>Explanation:<br \/>\nBases are common and multiplied. So, the exponents are added<br \/>\nBase = 5<br \/>\nExponents = 10 + 1 + 1 = 12<br \/>\n5<sup>12<\/sup><\/p>\n<p>Question 15.<br \/>\n7<sup>8<\/sup> \u22c5 7<sup>5<\/sup> = 7<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n7<sup>13<\/sup><\/p>\n<p>Explanation:<br \/>\nBases are common and multiplied. So, the exponents are added<br \/>\nBase = 7<br \/>\nExponents = 8 + 5 = 13<br \/>\n7<sup>13<\/sup><\/p>\n<p>Question 16.<br \/>\n(6<sup>2<\/sup>)<sup>4<\/sup> = (6 \u22c5 6)<sup>?<\/sup> = (6 \u22c5 6) \u22c5 (6 \u22c5 6) \u22c5 (? \u22c5 ?) \u22c5 ? = 6<sup>?<\/sup><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n6<sup>8<\/sup><\/p>\n<p>Explanation:<br \/>\n(6<sup>2<\/sup>)<sup>4<\/sup> = (6 \u22c5 6)<sup>4<\/sup> = (6 \u22c5 6) \u22c5 (6 \u22c5 6) \u22c5 (6 \u22c5 6) \u22c5 (6 \u22c5 6) = 6<sup>2<\/sup> \u22c5 6<sup>2<\/sup> . 6<sup>2<\/sup> \u22c5 6<sup>2<\/sup><br \/>\nBases are common and multiplied. So, the exponents are added<br \/>\n= 6<sup>2+2+2+2<br \/>\n<\/sup>6<sup>8<\/sup><\/p>\n<p>Question 17.<br \/>\n(3<sup>3<\/sup>)<sup>3<\/sup> = (3 \u22c5 3 \u22c5 3)<sup>3<\/sup> = (3 \u22c5 3 \u22c5 3) \u22c5 (? \u22c5 ? \u22c5 ?) \u22c5 ? = 3<sup>?<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3<sup>9<\/sup><\/p>\n<p>Explanation:<br \/>\n(3 \u22c5 3 \u22c5 3) \u22c5 (3 \u22c5 3 \u22c5 3) \u22c5 (3 \u22c5 3 \u22c5 3) = 3<sup>3<\/sup> \u22c5 3<sup>3<\/sup> \u22c5 3<sup>3<\/sup><br \/>\nBases are common and multiplied. So, the exponents are added<br \/>\n3<sup>3 + 3 + 3<br \/>\n<\/sup> 3<sup>9<\/sup><\/p>\n<p><strong>Simplify each expression.<\/strong><\/p>\n<p>Question 18.<br \/>\n(10 \u2212 6)<sup>3<\/sup>\u22c54<sup>2<\/sup> + (10 + 2)<sup>2<\/sup><br \/>\n______<\/p>\n<p>Answer:<br \/>\n1,168<\/p>\n<p>Explanation:<br \/>\n4\u00b3. 4\u00b2 + (12)\u00b2 = 4<sup>5<\/sup> + (12)\u00b2 = 4<sup>5<\/sup> + (12 . 12)\u00b2<br \/>\n4<sup>5<\/sup> + (144) = 1,024 + 144 = 1,168<\/p>\n<p>Question 19.<br \/>\n\\(\\frac { { (12-5) }^{ 7 } }{ { [(3+4)^{ 2 }] }^{ 2 } } \\)<br \/>\n________<\/p>\n<p>Answer:<br \/>\n343<\/p>\n<p>Explanation:<br \/>\n7<sup>7<\/sup> \u00f7 (7\u00b2)\u00b2 = 7<sup>7<\/sup> \u00f7 7<sup>4<\/sup><br \/>\n7<sup>7-4<\/sup><br \/>\n7\u00b3<br \/>\n7 . 7 . 7 = 343<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 20.<br \/>\nSummarize the rules for multiplying powers with the same base, dividing powers with the same base, and raising a power to a power.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe exponent &#8220;product rule&#8221; tells us that, when multiplying two powers that have the same base, you can add the exponents.<br \/>\nThe quotient rule tells us that we can divide two powers with the same base by subtracting the exponents.<br \/>\nThe &#8220;power rule&#8221; tells us that to raise a power to a power, just multiply the exponents.<\/p>\n<h3><a id=\"Integer_Exponents_\u2013_Page_No._37\"><\/a>Independent Practice &#8211; Integer Exponents &#8211; Page No. 37<\/h3>\n<p>Question 21.<br \/>\nExplain why the exponents cannot be added in the product 12<sup>3<\/sup> \u22c5 11<sup>3<\/sup>.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe exponent &#8220;product rule&#8221; tells us that, when multiplying two powers that have the same base, you can add the exponents.<br \/>\nThe bases are not the same in the given problem.<br \/>\n=&gt; (12)\u00b3 x (11)\u00b3<br \/>\nIf we solve this equation following the rule of exponent will get the correct answer:<br \/>\n=&gt; (12 x 12 x 12) x (11 x 11 x 11)<br \/>\n=&gt; 1728 X 1331<br \/>\n=&gt; the answer is 2 299 968<br \/>\nBut if we add the exponent, the answer would be wrong<br \/>\n=&gt; (12)\u00b3 x (11)\u00b3<br \/>\n=&gt; 132^6<br \/>\n=&gt; 5289852801024 which is wrong.<\/p>\n<p>Question 22.<br \/>\nList three ways to express 3<sup>5<\/sup> as a product of powers.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3\u00b9 . 3<sup>4<\/sup><br \/>\n3\u00b2 . 3<sup>3<\/sup><br \/>\n3\u00b3 . 3<sup>2<\/sup><\/p>\n<p>Question 23.<br \/>\nAstronomy<br \/>\nThe distance from Earth to the moon is about 22<sup>4<\/sup> miles. The distance from Earth to Neptune is about 22<sup>7<\/sup> miles. Which distance is the greater distance and about how many times greater is it?<br \/>\n_______ times<\/p>\n<p>Answer:<br \/>\n(22)\u00b3 or 10,648 times<\/p>\n<p>Explanation:<br \/>\nThe distance from Earth to the moon is about 22<sup>4<\/sup> miles. The distance from Earth to Neptune is about 22<sup>7<\/sup> miles.<br \/>\n22<sup>7<\/sup> &#8211; 22<sup>4<\/sup>\u00a0 = (22)\u00b3<br \/>\nThe greatest distance is from Earth to Neptune<br \/>\nThe distance from Earth to Neptune is greater by (22)\u00b3 or 10,648 miles<\/p>\n<p>Question 24.<br \/>\nCritique Reasoning<br \/>\nA student claims that 8<sup>3<\/sup> \u22c5 8<sup>-5<\/sup> is greater than 1. Explain whether the student is correct or not.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n8<sup>3<\/sup> \u22c5 8<sup>-5<\/sup> is = 8<sup>-2<br \/>\n(1\/8)\u00b2<br \/>\n(1\/8) . (1\/8) = 1\/64 = 0.015<br \/>\nThe student is not correct.<\/sup><\/p>\n<p><strong>Find the missing exponent.<\/strong><\/p>\n<p>Question 25.<br \/>\n(b<sup>2<\/sup>)<sup>?<\/sup> = b<sup>-6<\/sup><br \/>\n_______<\/p>\n<p>Answer:<br \/>\n(b<sup>2<\/sup>)<sup>-8<\/sup><\/p>\n<p>Explanation:<br \/>\n(b<sup>2<\/sup>)<sup>?<\/sup> = b<sup>-6<\/sup><br \/>\n(b<sup>-6<\/sup>) = b<sup>2-8<br \/>\n<\/sup>(b<sup>2-8<\/sup>) = b<sup>2<\/sup><span style=\"font-size: 13.3333px;\">\u00a0.<\/span>\u00a0b<sup>-8<br \/>\n<\/sup>(b<sup>2<\/sup>)<sup>-8<\/sup> = b<sup>-6<\/sup><\/p>\n<p>Question 26.<br \/>\nx<sup>?<\/sup> \u22c5 x<sup>6<\/sup> = x<sup>9<\/sup><br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx\u00b3<\/p>\n<p>Explanation:<br \/>\nx<sup>?<\/sup> \u22c5 x<sup>6<\/sup> = x<sup>9<\/sup><br \/>\nx<sup>9<\/sup> = x<sup>3 + 6<br \/>\n<\/sup>x\u00b3 x<sup>6<\/sup><\/p>\n<p>Question 27.<br \/>\n\\(\\frac { { y }^{ 25 } }{ { y }^{ ? } } \\) = y<sup>6<\/sup><br \/>\n_______<\/p>\n<p>Answer:<br \/>\ny25 \u00f7 y16<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { { y }^{ 25 } }{ { y }^{ ? } } \\) = y<sup>6\u00a0<\/sup><br \/>\ny<sup>6<\/sup> = y<sup>25 &#8211; 16<\/sup><br \/>\ny<sup>25<\/sup> \u00f7 y<sup>16<\/sup><\/p>\n<p>Question 28.<br \/>\nCommunicate Mathematical Ideas<br \/>\nWhy do you subtract exponents when dividing powers with the same base?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nTo divide exponents (or powers) with the same base, subtract the exponents. The division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.<\/p>\n<p>Question 29.<br \/>\nAstronomy<br \/>\nThe mass of the Sun is about 2 \u00d7 10<sup>27<\/sup> metric tons, or 2 \u00d7 10<sup>30<\/sup> kilograms. How many kilograms are in one metric ton?<br \/>\n________ kgs in one metric ton<\/p>\n<p>Answer:<br \/>\n1,000 kgs in one metric ton<\/p>\n<p>Explanation:<br \/>\nThe mass of the Sun is about 2 \u00d7 10<sup>27<\/sup> metric tons, or 2 \u00d7 10<sup>30<\/sup> kilograms.<br \/>\n2 \u00d7 10<sup>27<\/sup> metric tons = 2 \u00d7 10<sup>30<\/sup> ki<br \/>\n1 metric ton = 2 \u00d7 10<sup>30<\/sup> ki \u00f7 2 \u00d7 10<sup>27<\/sup> = (10)\u00b3 = 1,000 kgs in one metric ton<\/p>\n<p>Question 30.<br \/>\nRepresent Real-World Problems<br \/>\nIn computer technology, a kilobyte is 2<sup>10<\/sup> bytes in size. A gigabyte is 2<sup>30<\/sup> bytes in size. The size of a terabyte is the product of the size of a kilobyte and the size of a gigabyte. What is the size of a terabyte?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2<sup>40<\/sup>\u00a0bytes<\/p>\n<p>Explanation:<br \/>\nIn computer technology, a kilobyte is 2<sup>10<\/sup> bytes in size. A gigabyte is 2<sup>30<\/sup> bytes in size. The size of a terabyte is the product of the size of a kilobyte and the size of a gigabyte.<br \/>\nterabyte = 2<sup>10<\/sup> bytes \u00d7 2<sup>30<\/sup> bytes = 2<sup>10+30<\/sup> bytes =\u00a02<sup>40<\/sup>\u00a0bytes<\/p>\n<h3><a id=\"Integer_Exponents_Lesson_Check_\u2013_Page_No._38\"><\/a>Integer Exponents &#8211; Page No. 38<\/h3>\n<p>Question 31.<br \/>\nWrite equivalent expressions for x<sup>7<\/sup> \u22c5 x<sup>-2<\/sup> and \\(\\frac { { x }^{ 7 } }{ { x }^{ 2 } } \\). What do you notice? Explain how your results relate to the properties of integer exponents.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx^a * x^b = x^(a+b)<br \/>\nand<br \/>\nx^-a = 1\/x^a<br \/>\nTherefore, x^7 * x^-2 = x^7\/x^2 = x^5<br \/>\nor<br \/>\nx^7 * x^-2 = x^(7-2) = x^5<br \/>\nx^7 \/ x^2 = x^7 * x^-2<\/p>\n<p><strong>A toy store is creating a large window display of different colored cubes stacked in a triangle shape. The table shows the number of cubes in each row of the triangle, starting with the top row.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 1: Integer Exponents img 1\" width=\"491\" height=\"76\" \/><\/p>\n<p>Question 32.<br \/>\nLook for a Pattern<br \/>\nDescribe any pattern you see in the table.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nAs the number of rows increased, the number of cubes in each row by multiple of 3.<\/p>\n<p>Question 33.<br \/>\nUsing exponents, how many cubes will be in Row 6? How many times as many cubes will be in Row 6 than in Row 3?<br \/>\n_______ times more cubes<\/p>\n<p>Answer:<br \/>\n<span style=\"font-size: 13.3333px;\">(3<sup>3<\/sup>) times more cubes<\/span><\/p>\n<p>Explanation:<br \/>\nFor row 6, the number of cubes in each row = (3<sup>6<\/sup>)<span style=\"font-size: 13.3333px;\"><br \/>\n(3<sup>6<\/sup>) \u00f7 (3<sup>3<\/sup>) = (3<sup>6-3<\/sup>) = (3<sup>3<\/sup>)<br \/>\n(3<sup>3<\/sup>) times more cubes<br \/>\n<\/span><\/p>\n<p>Question 34.<br \/>\nJustify Reasoning<br \/>\nIf there are 6 rows in the triangle, what is the total number of cubes in the triangle? Explain how you found your answer.<br \/>\n______ cubes<\/p>\n<p>Answer:<br \/>\n1,092 cubes<\/p>\n<p>Explanation:<br \/>\n<span style=\"font-size: 13.3333px;\">(3<sup>1<\/sup>) + (3<sup>2<\/sup>) + (3<sup>3<\/sup>) + (3<sup>4<\/sup>) + (3<sup>5<\/sup>) + (3<sup>6<\/sup>)<br \/>\n<\/span>3 + 9 + 27 + 81 + 243 + 729 = 1,092<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 35.<br \/>\nCritique Reasoning<br \/>\nA student simplified the expression \\(\\frac { { 6 }^{ 2 } }{ { 36 }^{ 2 } } \\) as \\(\\frac{1}{3}\\). Do you agree with this student? Explain why or why not.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n\\(\\frac { { 6 }^{ 2 } }{ { 36 }^{ 2 } } \\)<br \/>\n<span style=\"font-size: 13.3333px;\">(6<sup>2<\/sup>) \u00f7 (6<sup>2<\/sup>)\u00b2<br \/>\n<\/span><span style=\"font-size: 13.3333px;\">(6<sup>2<\/sup>) \u00f7 (6<sup>4<\/sup>)<br \/>\n<\/span><span style=\"font-size: 13.3333px;\">(6<sup>2 &#8211; 4<\/sup>)<br \/>\n<\/span><span style=\"font-size: 13.3333px;\">(6<sup>-2<\/sup>) = 1\/36<br \/>\n<\/span>I don&#8217;t agree with the student<\/p>\n<p>Question 36.<br \/>\nDraw Conclusions<br \/>\nEvaluate \u2013a<sup>n<\/sup> when a = 3 and n = 2, 3, 4, and 5. Now evaluate (\u2013a)<sup>n<\/sup> when a = 3 and n = 2, 3, 4, and 5. Based on this sample, does it appear that \u2013a<sup>n<\/sup> = (\u2013a)<sup>n<\/sup>? If not, state the relationships, if any, between \u2013a<sup>n<\/sup> and (\u2013a)<sup>n<\/sup>.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n\u2013a<sup>n<\/sup> when a = 3 and n = 2, 3, 4, and 5.<br \/>\n-3<sup>n<\/sup><br \/>\n-(3<sup>2<\/sup> )= -9<br \/>\n(\u2013a)<sup>n<\/sup> = -3 . -3 = 9<br \/>\n\u2013a<sup>n<\/sup> = (\u2013a)<sup>n<\/sup> are not equal.<\/p>\n<p>Question 37.<br \/>\nPersevere in Problem Solving<br \/>\nA number to the 12th power divided by the same number to the 9th power equals 125. What is the number?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nLet&#8217;s call our number a.<br \/>\n(a<sup>12<\/sup> ) \u00f7 (a<sup>9<\/sup>\u00a0)<br \/>\n(a<sup>12-9<\/sup> ) = (a<sup>3<\/sup> )<br \/>\n(a<sup>3<\/sup> ) = 125<br \/>\na = (125)<sup>1\/3<\/sup><br \/>\na = 5<\/p>\n<h3><a id=\"Scientific_Notation_with_Positive_Powers_of_10_\u2013_Page_No._42\"><\/a>Guided Practice &#8211; Scientific Notation with Positive Powers of 10 &#8211; Page No. 42<\/h3>\n<p><strong>Write each number in scientific notation.<\/strong><\/p>\n<p>Question 1.<br \/>\n58,927<br \/>\n(Hint: Move the decimal left 4 places)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5.8927 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n58,927<br \/>\nMove the decimal left 4 places<br \/>\n5.8927 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 2.<br \/>\n1,304,000,000<br \/>\n(Hint: Move the decimal left 9 places.)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.304 \u00d7 (10)<sup>9<\/sup><\/p>\n<p>Explanation:<br \/>\n1,304,000,000<br \/>\nMove the decimal left 9 places<br \/>\n1.304 \u00d7 (10)<sup>9<\/sup><\/p>\n<p>Question 3.<br \/>\n6,730,000<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n6,730,000<br \/>\nMove the decimal left 6 places<br \/>\n6.73 \u00d7 (10)<sup>6<\/sup><\/p>\n<p>Question 4.<br \/>\n13,300<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n13,300<br \/>\nMove the decimal left 4 places<br \/>\n1.33 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 5.<br \/>\nAn ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n97,700,000,000,000,000,000,000<br \/>\nMove the decimal left 22 places<br \/>\n9.77 \u00d7 (10)<sup>22<\/sup><\/p>\n<p>Question 6.<br \/>\nThe distance from Earth to the Moon is about 384,000 kilometers.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3.84 \u00d7 (10)<sup>6<\/sup><\/p>\n<p>Explanation:<br \/>\n384,000<br \/>\nMove the decimal left 6 places<br \/>\n3.84 \u00d7 (10)<sup>6<\/sup><\/p>\n<p><strong>Write each number in standard notation.<\/strong><\/p>\n<p>Question 7.<br \/>\n4 \u00d7 10<sup>5<\/sup><br \/>\n(Hint: Move the decimal right 5 places.)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n400,000<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>5<\/sup><br \/>\nMove the decimal right 5 places<br \/>\n400,000<\/p>\n<p>Question 8.<br \/>\n1.8499 \u00d7 10<sup>9<\/sup><br \/>\n(Hint: Move the decimal right 9 places.)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1849900000<\/p>\n<p>Explanation:<br \/>\n1.8499 \u00d7 10<sup>9<\/sup><br \/>\nMove the decimal right 9 places<br \/>\n1849900000<\/p>\n<p>Question 9.<br \/>\n6.41 \u00d7 10<sup>3<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6410<\/p>\n<p>Explanation:<br \/>\n6.41 \u00d7 10<sup>3<\/sup><br \/>\nMove the decimal right 3 places<br \/>\n6410<\/p>\n<p>Question 10.<br \/>\n8.456 \u00d7 10<sup>7<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n84560000<\/p>\n<p>Explanation:<br \/>\n8.456 \u00d7 10<sup>7<br \/>\n<\/sup>Move the decimal right 7 places<br \/>\n84560000<\/p>\n<p>Question 11.<br \/>\n8 \u00d7 10<sup>5<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n800,000<\/p>\n<p>Explanation:<br \/>\n8 \u00d7 10<sup>5<\/sup><br \/>\nMove the decimal right 5 places<br \/>\n800,000<\/p>\n<p>Question 12.<br \/>\n9 \u00d7 10<sup>10<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n90000000000<\/p>\n<p>Explanation:<br \/>\n9 \u00d7 10<sup>10<\/sup><br \/>\nMove the decimal right 10 places<br \/>\n90000000000<\/p>\n<p>Question 13.<br \/>\nDiana calculated that she spent about 5.4 \u00d7 10<sup>4<\/sup> seconds doing her math homework during October. Write this time in standard notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5400<\/p>\n<p>Explanation:<br \/>\nDiana calculated that she spent about 5.4 \u00d7 10<sup>4<\/sup> seconds doing her math homework during October.<br \/>\n5.4 \u00d7 10<sup>4<br \/>\nMove the decimal right 4 places<\/sup><br \/>\n5400<\/p>\n<p>Question 14.<br \/>\nThe town recycled 7.6 \u00d7 10<sup>6<\/sup> cans this year. Write the number of cans in standard notation<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n7600000<\/p>\n<p>Explanation:<br \/>\nThe town recycled 7.6 \u00d7 10<sup>6<\/sup> cans this year.<br \/>\n7.6 \u00d7 10<sup>6<\/sup><br \/>\nMove the decimal right 10 places<br \/>\n7600000<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 15.<br \/>\nDescribe how to write 3,482,000,000 in scientific notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3.482 \u00d7 (10)<sup>9<\/sup><\/p>\n<p>Explanation:<br \/>\n3,482,000,000<br \/>\nMove the decimal left 9 places<br \/>\n3.482 \u00d7 (10)<sup>9<\/sup><\/p>\n<h3><a id=\"Scientific_Notation_with_Positive_Powers_of_10_\u2013_Page_No._43\"><\/a>Independent Practice &#8211; Scientific Notation with Positive Powers of 10 &#8211; Page No. 43<\/h3>\n<p><strong>Paleontology<\/strong><\/p>\n<p><strong>Use the table for problems 16\u201321. Write the estimated weight of each dinosaur in scientific notation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 2: Scientific Notation with Positive Powers of 10 img 2\" width=\"371\" height=\"284\" \/><\/p>\n<p>Question 16.<br \/>\nApatosaurus ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6.6 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n66,000<br \/>\nMove the decimal left 4 places<br \/>\n6.6 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 17.<br \/>\nArgentinosaurus ___________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2.2 \u00d7 (10)<sup>5<\/sup><\/p>\n<p>Explanation:<br \/>\n220,000<br \/>\nMove the decimal left 5 places<br \/>\n2.2 \u00d7 (10)<sup>5<\/sup><\/p>\n<p>Question 18.<br \/>\nBrachiosaurus ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1 \u00d7 (10)<sup>5<\/sup><\/p>\n<p>Explanation:<br \/>\n100,000<br \/>\nMove the decimal left 5 places<br \/>\n1 \u00d7 (10)<sup>5<\/sup><\/p>\n<p>Question 19.<br \/>\nCamarasaurus ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n40,000<br \/>\nMove the decimal left 4 places<br \/>\n4 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 20.<br \/>\nCetiosauriscus ____________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.985 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n19,850<br \/>\nMove the decimal left 4 places<br \/>\n1.985 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 21.<br \/>\nDiplodocus _____________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n50,000<br \/>\nMove the decimal left 4 places<br \/>\n5 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 22.<br \/>\nA single little brown bat can eat up to 1,000 mosquitoes in a single hour. Express in scientific notation how many mosquitoes a little brown bat might eat in 10.5 hours.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.05 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n(1000 x 10.5) = 10500.<br \/>\nThe little brown bat can eat 10500 mosquitoes in 10.5 hours.<br \/>\n1.05 \u00d7 (10)<sup>4<\/sup><\/p>\n<p>Question 23.<br \/>\nMultistep<br \/>\nSamuel can type nearly 40 words per minute. Use this information to find the number of hours it would take him to type 2.6 \u00d7 10<sup>5<\/sup> words.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nSamuel can type 40 words per minute.<br \/>\nThen how many hours will it take for him to type 2.6 words times 10 to the power of five words<br \/>\n2.6 words time 10 to the power of 5<br \/>\n2.6 \u00d7 (10)<sup>4<\/sup><br \/>\n2.6 x 100 000 = 260 000 words in all.<br \/>\nNow, we need to find the number of words Samuel can type in an hour<br \/>\n40 words\/minutes, in 1 hour there are 60 minutes<br \/>\n40 x 60<br \/>\n2,400 words \/hour<br \/>\nNow, let\u2019s divide the total of words he needs to type to the number of words he can type in an hour<br \/>\n260 000 \/ 2 400<br \/>\n108.33 hours.<\/p>\n<p>Question 24.<br \/>\nEntomology<br \/>\nA tropical species of mite named Archegozetes longisetosus is the record holder for the strongest insect in the world. It can lift up to 1.182 \u00d7 10<sup>3<\/sup> times its own weight.<br \/>\na. If you were as strong as this insect, explain how you could find how many pounds you could lift.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNumber of pounds you can lift by 1.182 \u00d7 10<sup>3<\/sup> by your weight<\/p>\n<p>Question 24.<br \/>\nb. Complete the calculation to find how much you could lift, in pounds, if you were as strong as an Archegozetes longisetosus mite. Express your answer in both scientific notation and standard notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nscientific notation: 1.182 \u00d7 10<sup>5<\/sup><br \/>\nstandard notation: 118200<\/p>\n<p>Explanation:<br \/>\n1.182 \u00d7 10<sup>3<\/sup> \u00d7 10<sup>2<\/sup><br \/>\n1.182 \u00d7 10<sup>5<\/sup><br \/>\n118200<\/p>\n<p>Question 25.<br \/>\nDuring a discussion in science class, Sharon learns that at birth an elephant weighs around 230 pounds. In four herds of elephants tracked by conservationists, about 20 calves were born during the summer. In scientific notation, express approximately how much the calves weighed all together.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.6 \u00d7 10<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nDuring a discussion in science class, Sharon learns that at birth an elephant weighs around 230 pounds. In four herds of elephants tracked by conservationists, about 20 calves were born during the summer.<br \/>\nTotal weight of the claves = 230 \u00d7 20 = 4600<br \/>\nMove the decimal left 3 places<br \/>\n4.6 \u00d7 10<sup>3<\/sup><\/p>\n<p>Question 26.<br \/>\nClassifying Numbers<br \/>\nWhich of the following numbers are written in scientific notation?<br \/>\n0.641 \u00d7 10<sup>3<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9.999 \u00d7 10<sup>4<\/sup><br \/>\n2 \u00d7 10<sup>1<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04.38 \u00d7 5<sup>10<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.641 \u00d7 10<sup>3<\/sup><br \/>\n4.38 \u00d7 5<sup>10<\/sup><\/p>\n<h3><a id=\"Scientific_Notation_with_Positive_Powers_of_10_Lesson_Check_\u2013_Page_No._44\"><\/a>Scientific Notation with Positive Powers of 10 &#8211; Page No. 44<\/h3>\n<p>Question 27.<br \/>\nExplain the Error<br \/>\nPolly\u2019s parents\u2019 car weighs about 3500 pounds. Samantha, Esther, and Polly each wrote the weight of the car in scientific notation. Polly wrote 35.0 \u00d7 10<sup>2<\/sup>, Samantha wrote 0.35 \u00d7 10<sup>4<\/sup>, and Esther wrote 3.5 \u00d7 10<sup>4<\/sup>.<br \/>\na. Which of these girls, if any, is correct?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNone of the girls is correct<\/p>\n<p>Question 27.<br \/>\nb. Explain the mistakes of those who got the question wrong.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPolly did not express the number such first part is greater than or equal to 1 and less than 10<br \/>\nSamantha did not express the number such first part is greater than or equal to 1 and less than 10<br \/>\nEsther did not express the exponent of 10 correctly<\/p>\n<p>Question 28.<br \/>\nJustify Reasoning<br \/>\nIf you were a biologist counting very large numbers of cells as part of your research, give several reasons why you might prefer to record your cell counts in scientific notation instead of standard notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nIt is easier to comprehend the magnitude of large numbers when in scientific notation as multiple zeros in the number are removed and express as an exponent of 10.<br \/>\nIt is easier to compare large numbers when in scientific notation as numbers are be expressed as a product of a number greater than or equal to 1 and less than 10<br \/>\nIt is easier to multiply the numbers in scientific notation.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 29.<br \/>\nDraw Conclusions<br \/>\nWhich measurement would be least likely to be written in scientific notation: number of stars in a galaxy, number of grains of sand on a beach, speed of a car, or population of a country? Explain your reasoning.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nspeed of a car<\/p>\n<p>Explanation:<br \/>\nAs we know scientific notation is used to express measurements that are extremely large or extremely small.<br \/>\nThe first two are extremely large, then, they could be expressed in scientific notation.<br \/>\nIf we compare the speed of a car and the population of a country, it is clear that the larger will be the population of a country.<br \/>\nTherefore, it is more likely to express that in scientific notation, so the answer is the speed of a car.<\/p>\n<p>Question 30.<br \/>\nAnalyze Relationships<br \/>\nCompare the two numbers to find which is greater. Explain how you can compare them without writing them in standard notation first.<br \/>\n4.5 \u00d7 10<sup>6<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.1 \u00d7 10<sup>8<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2.1 \u00d7 10<sup>8<\/sup><\/p>\n<p>Explanation:<br \/>\n2.1 \u00d7 10<sup>8 <\/sup>is greater because the power of 10 is greater in \u00a02.1 \u00d7 10<sup>8<\/sup><\/p>\n<p>Question 31.<br \/>\nCommunicate Mathematical Ideas<br \/>\nTo determine whether a number is written in scientific notation, what test can you apply to the first factor, and what test can you apply to the second factor?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe first term must have one number before the decimal point<br \/>\nthe second term (factor) must be 10 having some power.<\/p>\n<h3><a id=\"Scientific_Notation_with_Negative_Powers_of_10_\u2013_Page_No._48\"><\/a>Guided Practice &#8211; Scientific Notation with Negative Powers of 10 &#8211; Page No. 48<\/h3>\n<p><strong>Write each number in scientific notation.<\/strong><\/p>\n<p>Question 1.<br \/>\n0.000487<br \/>\nHint: Move the decimal right 4 places.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.87 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000487<br \/>\nMove the decimal right 4 places<br \/>\n4.87 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Question 2.<br \/>\n0.000028<br \/>\nHint: Move the decimal right 5 places<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2.8 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000028<br \/>\nMove the decimal right 5 places<br \/>\n2.8 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Question 3.<br \/>\n0.000059<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5.9 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000059<br \/>\nMove the decimal right 5 places<br \/>\n5.9 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Question 4.<br \/>\n0.0417<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.17 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0417<br \/>\nMove the decimal right 2 places<br \/>\n4.17 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Question 5.<br \/>\nPicoplankton can be as small as 0.00002 centimeters.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n0.00002<br \/>\nMove the decimal right 5 places<br \/>\n2 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Question 6.<br \/>\nThe average mass of a grain of sand on a beach is about 0.000015 gram.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.5 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000015<br \/>\nMove the decimal right 5 places<br \/>\n1.5 \u00d7 10<sup>-5<\/sup><\/p>\n<p><strong>Write each number in standard notation.<\/strong><\/p>\n<p>Question 7.<br \/>\n2 \u00d7 10<sup>-5<\/sup><br \/>\nHint: Move the decimal left 5 places.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.00002<\/p>\n<p>Explanation:<br \/>\n2 \u00d7 10<sup>-5<\/sup><br \/>\nMove the decimal left 5 places<br \/>\n0.00002<\/p>\n<p>Question 8.<br \/>\n3.582 \u00d7 10<sup>-6<\/sup><br \/>\nHint: Move the decimal left 6 places.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.000003582<\/p>\n<p>Explanation:<br \/>\n3.582 \u00d7 10<sup>-6<\/sup><br \/>\nMove the decimal left 6 places<br \/>\n0.000003582<\/p>\n<p>Question 9.<br \/>\n8.3 \u00d7 10<sup>-4<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.00083<\/p>\n<p>Explanation:<br \/>\n8.3 \u00d7 10<sup>-4<\/sup><br \/>\nMove the decimal left 4 places<br \/>\n0.00083<\/p>\n<p>Question 10.<br \/>\n2.97 \u00d7 10<sup>-2<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.0297<\/p>\n<p>Explanation:<br \/>\n2.97 \u00d7 10<sup>-2<\/sup><br \/>\nMove the decimal left 2 places<br \/>\n0.0297<\/p>\n<p>Question 11.<br \/>\n9.06 \u00d7 10<sup>-5<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.0000906<\/p>\n<p>Explanation:<br \/>\n9.06 \u00d7 10<sup>-5<\/sup><br \/>\nMove the decimal left 5 places<br \/>\n0.0000906<\/p>\n<p>Question 12.<br \/>\n4 \u00d7 10<sup>-5<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.00004<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>-5<\/sup><br \/>\nMove the decimal left 5 places<br \/>\n0.00004<\/p>\n<p>Question 13.<br \/>\nThe average length of a dust mite is approximately 0.0001 meters. Write this number in scientific notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Explanation:<br \/>\nThe average length of a dust mite is approximately 0.0001 meters.<br \/>\n0.0001<br \/>\nMove the decimal right 4 places<br \/>\n1 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Question 14.<br \/>\nThe mass of a proton is about 1.7 \u00d7 10<sup>-24<\/sup> grams. Write this number in standard notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n0.000000000000000000000017<\/p>\n<p>Explanation:<br \/>\nThe mass of a proton is about 1.7 \u00d7 10<sup>-24<\/sup> grams.<br \/>\n1.7 \u00d7 10<sup>-24<\/sup><br \/>\nMove the decimal left 24 places<br \/>\n0.000000000000000000000017<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 15.<br \/>\nDescribe how to write 0.0000672 in scientific notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6.72 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0000672<br \/>\nMove the decimal right 5 places<br \/>\n6.72 \u00d7 10<sup>-5<\/sup><\/p>\n<h3><a id=\"Scientific_Notation_with_Negative_Powers_of_10_\u2013_Page_No._49\"><\/a>Independent Practice &#8211; Scientific Notation with Negative Powers of 10 &#8211; Page No. 49<\/h3>\n<p><strong>Use the table for problems 16\u201321. Write the diameter of the fibers in scientific notation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 3: Scientific Notation with Negative Powers of 10 img 3\" width=\"368\" height=\"241\" \/><\/p>\n<p>Question 16.<br \/>\nAlpaca _______<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2.77 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Explanation:<br \/>\n0.00277<br \/>\nMove the decimal right 3 places<br \/>\n2.77 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Question 17.<br \/>\nAngora rabbit _____________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.3 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0013<br \/>\nMove the decimal right 3 places<br \/>\n1.3 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Question 18.<br \/>\nLlama ____________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3.5 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0035<br \/>\nMove the decimal right 3 places<br \/>\n3.5 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Question 19.<br \/>\nAngora goat ____________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.5 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0045<br \/>\nMove the decimal right 3 places<br \/>\n4.5 \u00d7 10<sup>-3<\/sup><\/p>\n<p>Question 20.<br \/>\nOrb web spider ___________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.5 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Explanation:<br \/>\n0.015<br \/>\nMove the decimal right 2 places<br \/>\n1.5 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Question 21.<br \/>\nVicu\u00f1a __________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n8 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0008<br \/>\nMove the decimal right 4 places<br \/>\n8 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Question 22.<br \/>\nMake a Conjecture<br \/>\nWhich measurement would be least likely to be written in scientific notation: the thickness of a dog hair, the radius of a period on this page, the ounces in a cup of milk? Explain your reasoning.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe ounces in a cup of milk would be least likely to be written in scientific notation. The ounces in a cup of milk is correct.<br \/>\nScientific notation is used for either very large or extremely small numbers.<br \/>\nThe thickness of dog hair is very small as the hair is thin. Hence can be converted to scientific notation.<br \/>\nThe radius of a period on this page is also pretty small. Hence can be converted to scientific notation.<br \/>\nThe ounces in a cup of milk. There are 8 ounces in a cup, so this is least likely to be written in scientific notation.<\/p>\n<p>Question 23.<br \/>\nMultiple Representations<br \/>\nConvert the length 7 centimeters to meters. Compare the numerical values when both numbers are written in scientific notation<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n7 centimeters convert to meters<br \/>\nIn every 1 meter, there are 100 centimeters = 7\/100 = 0.07<br \/>\nTherefore, in 7 centimeters there are 0.07 meters.<br \/>\n7 cm is a whole number while 0.07 m is a decimal number<br \/>\nScientific Notation of each number<br \/>\n7 cm = 7 x 10\u00b0<br \/>\n7 m = 1 x 10\u00af\u00b2<br \/>\nScientific notation, by the way, is an expression used by the scientist to make a large number of very small number easy to handle.<\/p>\n<p>Question 24.<br \/>\nDraw Conclusions<br \/>\nA graphing calculator displays 1.89 \u00d7 10<sup>12<\/sup> as 1.89E12. How do you think it would display 1.89 \u00d7 10<sup>-12<\/sup>? What does the E stand for?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.89E-12. E= Exponent<\/p>\n<p>Explanation:<\/p>\n<p>Question 25.<br \/>\nCommunicate Mathematical Ideas<br \/>\nWhen a number is written in scientific notation, how can you tell right away whether or not it is greater than or equal to 1?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nA number written in scientific notation is of the form<br \/>\na \u00d7 10<sup>-n<\/sup><span id=\"MathJax-Element-3-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-11\" class=\"mjx-math\"><span id=\"MJXc-Node-12\" class=\"mjx-mrow\"><span id=\"MJXc-Node-13\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-14\" class=\"mjx-mrow\"><span id=\"MJXc-Node-17\" class=\"mjx-msup\"><span class=\"mjx-sup\"><span id=\"MJXc-Node-19\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u00a0where 1 \u2264 a &lt; 10 and n is an integer<br \/>\nThe number is greater than or equal to one if n \u2265 0.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 26.<br \/>\nThe volume of a drop of a certain liquid is 0.000047 liter. Write the volume of the drop of liquid in scientific notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.7 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\nThe volume of a drop of a certain liquid is 0.000047 liter.<br \/>\nMove the decimal right 5 places<br \/>\n4.7 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Question 27.<br \/>\nJustify Reasoning<br \/>\nIf you were asked to express the weight in ounces of a ladybug in scientific notation, would the exponent of the 10 be positive or negative? Justify your response.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNegative<\/p>\n<p>Explanation:<br \/>\nScientific notation is used to express very small or very large numbers.<br \/>\nVery small numbers are written in scientific notation using negative exponents.<br \/>\nVery large numbers are written in scientific notation using positive exponents.<br \/>\nSince a ladybug is very small, we would use the very small scientific notation, which uses negative exponents.<\/p>\n<h3><a id=\"Scientific_Notation_with_Negative_Powers_of_10_Lesson_Check_\u2013_Page_No._50\"><\/a>Physical Science &#8211; Scientific Notation with Negative Powers of 10 &#8211; Page No. 50<\/h3>\n<p><strong>The table shows the length of the radii of several very small or very large items. Complete the table.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 3: Scientific Notation with Negative Powers of 10 img 4\" width=\"704\" height=\"263\" \/><\/p>\n<p>Question 28.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.74 \u00d7 (10)<sup>6<\/sup><\/p>\n<p>Explanation:<br \/>\nThe moon = 1,740,000<br \/>\nMove the decimal left 6 places<br \/>\n1.74 \u00d7 (10)<sup>6<\/sup><\/p>\n<p>Question 29.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.25e-10<\/p>\n<p>Explanation:<br \/>\n1.25 \u00d7 (10)<sup>-10<br \/>\n<\/sup>Move the decimal left 10 places<br \/>\n1.25e-10<\/p>\n<p>Question 30.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2.8 \u00d7 (10)<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\n0.0028<br \/>\nMove the decimal left 3 places<br \/>\n2.8 \u00d7 (10)<sup>3<\/sup><\/p>\n<p>Question 31.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n71490000<\/p>\n<p>Explanation:<br \/>\n7.149 \u00d7 (10)<sup>7<br \/>\nMove the decimal left 7 places<br \/>\n71490000<br \/>\n<\/sup>Question 32.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.82 \u00d7 (10)<sup>-10<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000000000182<br \/>\nMove the decimal right 10 places<br \/>\n1.82 \u00d7 (10)<sup>-10<\/sup><\/p>\n<p>Question 33.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3397000<\/p>\n<p>Explanation:<br \/>\n3.397 \u00d7 (10)<sup>6<br \/>\n<\/sup>Move the decimal left 6 places<br \/>\n3397000<\/p>\n<p>Question 34.<br \/>\nList the items in the table in order from the smallest to the largest.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.82 \u00d7 (10)<sup>-10<\/sup><br \/>\n1.25 \u00d7 (10)<sup>-10<\/sup><br \/>\n2.8 \u00d7 (10)<sup>3<\/sup><br \/>\n1.74 \u00d7 (10)<sup>6<\/sup><br \/>\n3.397 \u00d7 (10)<sup>6<\/sup><br \/>\n7.149 \u00d7 (10)<sup>7<\/sup><\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 35.<br \/>\nAnalyze Relationships<br \/>\nWrite the following diameters from least to greatest. 1.5 \u00d7 10<sup>-2<\/sup>m ; 1.2 \u00d7 10<sup>2<\/sup> m ; 5.85 \u00d7 10<sup>-3<\/sup> m ; 2.3 \u00d7 10<sup>-2<\/sup> m ; 9.6 \u00d7 10<sup>-1<\/sup> m.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5.85 \u00d7 10<sup>-3<\/sup> m, 1.5 \u00d7 10<sup>-2<\/sup>m, 2.3 \u00d7 10<sup>-2<\/sup> m, 9.6 \u00d7 10<sup>-1<\/sup> m, 1.2 \u00d7 10<sup>2<\/sup> m<\/p>\n<p>Explanation:<br \/>\n1.5 \u00d7 10<sup>-2<\/sup>m = 0.015<br \/>\n1.2 \u00d7 10<sup>2<\/sup> m = 120<br \/>\n5.85 \u00d7 10<sup>-3<\/sup> m = 0.00585<br \/>\n2.3 \u00d7 10<sup>-2<\/sup> m = 0.023<br \/>\n9.6 \u00d7 10<sup>-1<\/sup> m = 0.96<br \/>\n0.00585, 0.015, 0.023, 0.96, 120<\/p>\n<p>Question 36.<br \/>\nCritique Reasoning<br \/>\nJerod\u2019s friend Al had the following homework problem:<br \/>\nExpress 5.6 \u00d7 10<sup>-7<\/sup> in standard form.<br \/>\nAl wrote 56,000,000. How can Jerod explain Al\u2019s error and how to correct it?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n5.6 \u00d7 10<sup>-7<\/sup> in<br \/>\n0.000000056<br \/>\nAl wrote 56,000,000. AI wrote the zeroes to the right side of the 56 which is not correct. As the exponent of 10 is negative zero&#8217;s need to add to the left of the number.<\/p>\n<p>Question 37.<br \/>\nMake a Conjecture<br \/>\nTwo numbers are written in scientific notation. The number with a positive exponent is divided by the number with a negative exponent. Describe the result. Explain your answer.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nWhen the division is performed, the denominator exponent is subtracted from the numerator exponent. Subtracting a negative value from the numerator exponent will increase its value.<\/p>\n<h3><a id=\"Operations_with_Scientific_Notation_\u2013_Page_No._54\"><\/a>Guided Practice &#8211; Operations with Scientific Notation &#8211; Page No. 54<\/h3>\n<p><strong>Add or subtract. Write your answer in scientific notation.<\/strong><\/p>\n<p>Question 1.<br \/>\n4.2 \u00d7 10<sup>6<\/sup> + 2.25 \u00d7 10<sup>5<\/sup> + 2.8 \u00d7 10<sup>6<\/sup><br \/>\n4.2 \u00d7 10<sup>6<\/sup> + ? \u00d7 10 ? + 2.8 \u00d7 10<sup>6<\/sup><br \/>\n4.2 + ? + ?<br \/>\n? \u00d7 10?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.2 \u00d7 10<sup>6<\/sup> + 0.225 \u00d7 10 \u00d7 10<sup>5<\/sup> + 2.8 \u00d7 10<sup>6<\/sup><br \/>\nRewrite 2.25 = 0.225 \u00d7 10<br \/>\n(4.2 + 0.225 + 2.8) \u00d7 10<sup>6<\/sup><br \/>\n7.225 \u00d7 10<sup>6<\/sup><\/p>\n<p>Question 2.<br \/>\n8.5 \u00d7 10<sup>3<\/sup> \u2212 5.3 \u00d7 10<sup>3<\/sup> \u2212 1.0 \u00d7 10<sup>2<\/sup><br \/>\n8.5 \u00d7 10<sup>3<\/sup> \u2212 5.3 \u00d7 10<sup>3<\/sup> \u2212 ? \u00d7 10?<br \/>\n? \u2212 ? \u2212 ?<br \/>\n? \u00d7 10<sup>?<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n8.5 \u00d7 10<sup>3<\/sup> \u2212 5.3 \u00d7 10<sup>3<\/sup> \u2212 0.1 \u00d7 10<sup>3<\/sup><br \/>\n(8.5 \u2212 5.3 \u2212 0.1) \u00d7 10<sup>3<\/sup><br \/>\n(3.1) \u00d7 10<sup>3<\/sup><\/p>\n<p>Question 3.<br \/>\n1.25 \u00d7 10<sup>2<\/sup> + 0.50 \u00d7 10<sup>2<\/sup> + 3.25 \u00d7 10<sup>2<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.25 \u00d7 10<sup>2<\/sup> + 0.50 \u00d7 10<sup>2<\/sup> + 3.25 \u00d7 10<sup>2<\/sup><br \/>\n(1.25 + 0.50 + 3.25) \u00d7 10<sup>2<\/sup><br \/>\n5 \u00d7 10<sup>2<\/sup><\/p>\n<p>Question 4.<br \/>\n6.2 \u00d7 10<sup>5<\/sup> \u2212 2.6 \u00d7 10<sup>4<\/sup> \u2212 1.9 \u00d7 10<sup>2<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6.2 \u00d7 10<sup>5<\/sup> \u2212 2.6 \u00d7 10<sup>4<\/sup> \u2212 1.9 \u00d7 10<sup>2<\/sup><br \/>\n6.2 \u00d7 10<sup>5<\/sup> \u2212 0.26 \u00d7 10<sup>5<\/sup> \u2212 0.0019 \u00d7 10<sup>5<\/sup><br \/>\n(6.2 &#8211; 0.26 &#8211; 0.0019) \u00d7 10<sup>5<\/sup><br \/>\n5.9381 \u00d7 10<sup>5<\/sup><\/p>\n<p><strong>Multiply or divide. Write your answer in scientific notation.<\/strong><\/p>\n<p>Question 5.<br \/>\n(1.8 \u00d7 10<sup>9<\/sup>)(6.7 \u00d7 10<sup>12<\/sup>)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n12.06 \u00d7 10<sup>21<\/sup><\/p>\n<p>Explanation:<br \/>\n(1.8 \u00d7 10<sup>9<\/sup>)(6.7 \u00d7 10<sup>12<\/sup>)<br \/>\n1.8 \u00d7 6.7 = 12.06<br \/>\n10<sup>9+12<\/sup>\u00a0= 10<sup>21<br \/>\n<\/sup>12.06 \u00d7 10<sup>21<\/sup><\/p>\n<p>Question 6.<br \/>\n\\(\\frac { { 3.46\u00d710 }^{ 17 } }{ { 2\u00d710 }^{ 9 } } \\)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.73 \u00d7 10<sup>8<\/sup><\/p>\n<p>Explanation:<br \/>\n3.46\/2 = 1.73<br \/>\n10<sup>17<\/sup>\/10<sup>9<\/sup>\u00a0= 10<sup>17-9<\/sup>\u00a0= 10<sup>8<\/sup><br \/>\n1.73 \u00d7 10<sup>8<\/sup><\/p>\n<p>Question 7.<br \/>\n(5 \u00d7 10<sup>12<\/sup>)(3.38 \u00d7 10<sup>6<\/sup>)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n16.9 \u00d7 10<sup>18<\/sup><\/p>\n<p>Explanation:<br \/>\n(5 \u00d7 10<sup>12<\/sup>)(3.38 \u00d7 10<sup>6<\/sup>)<br \/>\n5 \u00d7 3.38 = 16.9<br \/>\n10<sup>6+12<\/sup> = 10<sup>18<br \/>\n<\/sup>16.9 \u00d7 10<sup>18<\/sup><\/p>\n<p>Question 8.<br \/>\n\\(\\frac { { 8.4\u00d710 }^{ 21 } }{ { 4.2\u00d710 }^{ 14 } } \\)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\n8.4\/4.2 = 2<br \/>\n10<sup>21<\/sup>\/10<sup>14<\/sup> = 10<sup>21-14<\/sup> = 10<sup>7<\/sup><br \/>\n2 \u00d7 10<sup>7<\/sup><\/p>\n<p><strong>Write each number using calculator notation.<\/strong><\/p>\n<p>Question 9.<br \/>\n3.6 \u00d7 10<sup>11<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3.6e11<\/p>\n<p>Question 10.<br \/>\n7.25 \u00d7 10<sup>-5<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n7.25e-5<\/p>\n<p>Question 11.<br \/>\n8 \u00d7 10<sup>-1<\/sup><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n8e-1<\/p>\n<p><strong>Write each number using scientific notation.<\/strong><\/p>\n<p>Question 12.<br \/>\n7.6E \u2212 4<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n7.6 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Question 13.<br \/>\n1.2E16<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.2 \u00d7 10<sup>16<\/sup><\/p>\n<p>Question 14.<br \/>\n9E1<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n9 \u00d7 10<sup>1<\/sup><\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 15.<br \/>\nHow do you add, subtract, multiply, and divide numbers written in scientific notation?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNumbers with exponents can be added and subtracted only when they have the same base and exponent.<br \/>\nTo multiply two numbers in scientific notation, multiply their coefficients and add their exponents.<br \/>\nTo divide two numbers in scientific notation, divide their coefficients, and subtract their exponents.<\/p>\n<h3><a id=\"Operations_with_Scientific_Notation_\u2013_Page_No._55\"><\/a>Independent Practice &#8211; Operations with Scientific Notation &#8211; Page No. 55<\/h3>\n<p>Question 16.<br \/>\nAn adult blue whale can eat 4.0 \u00d7 10<sup>7<\/sup> krill in a day. At that rate, how many krill can an adult blue whale eat in 3.65 \u00d7 10<sup>2<\/sup> days?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n14.6 \u00d7 10<sup>9<\/sup><\/p>\n<p>Explanation:<br \/>\n(4.0 \u00d7 10<sup>7<\/sup> )(3.65 \u00d7 10<sup>2<\/sup> )<br \/>\n4.0 \u00d7 3.65 = 14.6<br \/>\n10<sup>7+2<\/sup>\u00a0 =\u00a0 10<sup>9<\/sup><br \/>\n14.6 \u00d7 10<sup>9<\/sup><\/p>\n<p>Question 17.<br \/>\nA newborn baby has about 26,000,000,000 cells. An adult has about 4.94 \u00d7 10<sup>13<\/sup> cells. How many times as many cells does an adult have than a newborn? Write your answer in scientific notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.9 \u00d7 10<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\n26,000,000,000 = 2.6 \u00d7 10<sup>10<\/sup><br \/>\n4.94 \u00d7 10<sup>13<\/sup><br \/>\n(4.94 \u00d7 10<sup>13<\/sup> )\/(2.6 \u00d7 10<sup>10<\/sup>\u00a0)<br \/>\n1.9 \u00d7 10<sup>3<\/sup><\/p>\n<p><strong>Represent Real-World Problems<\/strong><\/p>\n<p><strong>The table shows the number of tons of waste generated and recovered (recycled) in 2010.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 4: Operations with Scientific Notation img 5\" width=\"394\" height=\"331\" \/><\/p>\n<p>Question 18.<br \/>\nWhat is the total amount of paper, glass, and plastic waste generated?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n11.388 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\n7.131 \u00d7 10<sup>7<\/sup>\u00a0+ 1.153 \u00d7 10<sup>7<\/sup>\u00a0+ 3.104 \u00d7 10<sup>7<\/sup><br \/>\n11.388 \u00d7 10<sup>7<\/sup><\/p>\n<p>Question 19.<br \/>\nWhat is the total amount of paper, glass, and plastic waste recovered?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n5.025 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\n4.457 \u00d7 10<sup>7<\/sup>\u00a0 + 0.313 \u00d7 10<sup>7<\/sup>\u00a0 + 0.255 \u00d7 10<sup>7<\/sup><br \/>\n5.025 \u00d7 10<sup>7<\/sup><\/p>\n<p>Question 20.<br \/>\nWhat is the total amount of paper, glass, and plastic waste not recovered?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6.363 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\n(11.388 \u00d7 10<sup>7<\/sup> )\u00a0 &#8211; (5.025 \u00d7 10<sup>7<\/sup>)<br \/>\n6.363 \u00d7 10<sup>7<\/sup><\/p>\n<p>Question 21.<br \/>\nWhich type of waste has the lowest recovery ratio?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPlastics<\/p>\n<p>Explanation:<br \/>\n7.131 \u00d7 10<sup>7<\/sup>\u00a0 &#8211; 4.457 \u00d7 10<sup>7<\/sup> = 2.674 \u00d7 10<sup>7<\/sup><br \/>\n1.153 \u00d7 10<sup>7<\/sup>\u00a0 &#8211; 0.313 \u00d7 10<sup>7<\/sup> = 0.84 \u00d7 10<sup>7<\/sup><br \/>\n3.104 \u00d7 10<sup>7<\/sup>\u00a0 &#8211; 0.255 \u00d7 10<sup>7<\/sup> = 2.849 \u00d7 10<sup>7<\/sup><br \/>\nPlastics has the lowest recovery ratio<\/p>\n<p><strong>Social Studies<\/strong><\/p>\n<p><strong>The table shows the approximate populations of three countries.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-2-Exponents-and-Scientific-Notation-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation Lesson 4: Operations with Scientific Notation img 6\" width=\"353\" height=\"70\" \/><\/p>\n<p>Question 22.<br \/>\nHow many more people live in France than in Australia?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4.33 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\n(6.48 \u00d7 10<sup>7<\/sup> )\u00a0 &#8211; (2.15\u00d7 10<sup>7<\/sup>)<br \/>\n4.33 \u00d7 10<sup>7<\/sup><\/p>\n<p>Question 23.<br \/>\nThe area of Australia is 2.95 \u00d7 10<sup>6<\/sup> square miles. What is the approximate average number of people per square mile in Australia?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nAbout 7 people per square mile<\/p>\n<p>Explanation:<br \/>\n2.95 \u00d7 10<sup>6<\/sup> square miles = (2.15\u00d7 10<sup>7<\/sup>)<br \/>\n1 square mile = (2.15\u00d7 10<sup>7<\/sup>)\/(2.95 \u00d7 10<sup>6<\/sup>) = 7.288<\/p>\n<p>Question 24.<br \/>\nHow many times greater is the population of China than the population of France? Write your answer in standard notation.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n20.52; there are about 20 people in china for every 1 person in France.<\/p>\n<p>Question 25.<br \/>\nMia is 7.01568 \u00d7 10<sup>6<\/sup> minutes old. Convert her age to more appropriate units using years, months, and days. Assume each month to have 30.5 days.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n13 years 3 months 22.5 days<\/p>\n<p>Explanation:<br \/>\n7.01568 \u00d7 10<sup>6<\/sup> minutes<br \/>\n(7.01568 \u00d7 10<sup>6<\/sup> minutes) \u00f7 (6 \u00d7 10<sup>1<\/sup>)(2.4\u00a0\u00d7 10<sup>1<\/sup>)(1.2\u00a0\u00d7 10<sup>1<\/sup>)(3.05 \u00d7 10<sup>1<\/sup>)<br \/>\n= (1.331 \u00d7 10<sup>1<\/sup>)<br \/>\n= 13 years 3 months 22.5 days<\/p>\n<h3><a id=\"Operations_with_Scientific_Notation_Lesson_Check_\u2013_Page_No._56\"><\/a>Operations with Scientific Notation &#8211; Page No. 56<\/h3>\n<p>Question 26.<br \/>\nCourtney takes 2.4 \u00d7 10<sup>4<\/sup> steps during her a long-distance run. Each step covers an average of 810 mm. What total distance (in mm) did Courtney cover during her run? Write your answer in scientific notation. Then convert the distance to the more appropriate unit kilometers. Write that answer in standard form.<br \/>\n______ km<\/p>\n<p>Answer:<br \/>\n19.4 km<\/p>\n<p>Explanation:<br \/>\nCourtney takes 2.4 \u00d7 10<sup>4<\/sup> steps during her a long-distance run. Each step covers an average of 810 mm.<br \/>\n(2.4 \u00d7 10<sup>4<\/sup> steps) \u00d7 810mm<br \/>\n(2.4 \u00d7 10<sup>4<\/sup> ) \u00d7 (8.1 \u00d7 10<sup>2<\/sup> )<br \/>\nThe total distance covered = (19.44 \u00d7 10<sup>6<\/sup> )<br \/>\nConvert to unit kilometers:<br \/>\n(19.44 \u00d7 10<sup>6<\/sup> ) \u00d7 (1 \u00d7 10<sup>-6<\/sup> )<br \/>\n(1.94 \u00d7 10<sup>1<\/sup> )<br \/>\n19.4 km<\/p>\n<p>Question 27.<br \/>\nSocial Studies<br \/>\nThe U.S. public debt as of October 2010 was $9.06 \u00d7 10<sup>12<\/sup>. What was the average U.S. public debt per American if the population in 2010 was 3.08 \u00d7 10<sup>8<\/sup> people?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\n$29,400 per American<\/p>\n<p>Explanation:<br \/>\n($9.06 \u00d7 10<sup>12<\/sup>.)\/(3.08 \u00d7 10<sup>8<\/sup> )<br \/>\n($2.94 \u00d7 10<sup>4<\/sup>.) = $29,400 per American<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 28.<br \/>\nCommunicate Mathematical Ideas<br \/>\nHow is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nWhen you multiply or divide in scientific notation, you just add or subtract the exponents. When you add or subtract in scientific notation, you have to make the exponents the same before you can do anything else.<\/p>\n<p>Question 29.<br \/>\nExplain the Error<br \/>\nA student found the product of 8 \u00d7 10<sup>6<\/sup> and 5 \u00d7 10<sup>9<\/sup> to be 4 \u00d7 10<sup>15<\/sup>. What is the error? What is the correct product?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe error student makes is he multiply the terms instead of addition.<\/p>\n<p>Explanation:<br \/>\nproduct of 8 \u00d7 10<sup>6<\/sup> and 5 \u00d7 10<sup>9<\/sup><br \/>\n40 \u00d7 10<sup>15<\/sup><br \/>\n4 \u00d7 10<sup>16<\/sup><br \/>\nThe student missed the 10 while multiplying the product of 8 \u00d7 10<sup>6<\/sup> and 5 \u00d7 10<sup>9<\/sup><\/p>\n<p>Question 30.<br \/>\nCommunicate Mathematical Ideas<br \/>\nDescribe a procedure that can be used to simplify \\(\\frac { { (4.87\u00d710 }^{ 12 }) &#8211; { (7\u00d710 }^{ 10 }) }{ { (3\u00d710 }^{ 7 })-{ (6.1\u00d710 }^{ 8 }) } \\). Write the expression in scientific notation in simplified form.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n\\(\\frac { { (4.87\u00d710 }^{ 12 }) &#8211; { (7\u00d710 }^{ 10 }) }{ { (3\u00d710 }^{ 7 })-{ (6.1\u00d710 }^{ 8 }) } \\)<br \/>\n\\(\\frac { { (487\u00d710 }^{ 10 }) &#8211; { (7\u00d710 }^{ 10 }) }{ { (3\u00d710 }^{ 7 })-{ (61\u00d710 }^{ 7 }) } \\)<br \/>\n(480 \u00d7 10<sup>10<\/sup>\u00a0)\/(64 \u00d7 10<sup>7<\/sup>\u00a0)<br \/>\n7.50 \u00d7 10\u00b3<\/p>\n<h3><a id=\"Integer_Exponents_\u2013_Model_Quiz_\u2013_Page_No._57\"><\/a>2.1 Integer Exponents &#8211; Model Quiz &#8211; Page No. 57<\/h3>\n<p><strong>Find the value of each power.<\/strong><\/p>\n<p>Question 1.<br \/>\n3<sup>-4<\/sup><br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{81}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 3<br \/>\nExponent = 4<br \/>\n3<sup>-4<\/sup> = (1\/3)<sup>4<\/sup> = 1\/81<\/p>\n<p>Question 2.<br \/>\n35<sup>0<\/sup><br \/>\n______<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\n35<sup>0<\/sup><br \/>\nBase = 35<br \/>\nExponent = 0<br \/>\nAnything raised to the zeroth power is 1.<br \/>\n35<sup>0<\/sup> = 1<\/p>\n<p>Question 3.<br \/>\n4<sup>4<\/sup><br \/>\n______<\/p>\n<p>Answer:<br \/>\n256<\/p>\n<p>Explanation:<br \/>\nBase = 4<br \/>\nExponent = 4<br \/>\n4<sup>4<\/sup> = 4 . 4 . 4 . 4 = 2561<\/p>\n<p><strong>Use the properties of exponents to write an equivalent expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n8<sup>3<\/sup> \u22c5 8<sup>7<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n8<sup>10<\/sup><\/p>\n<p>Explanation:<br \/>\n8<sup>3<\/sup> \u22c5 8<sup>7<br \/>\n<\/sup>8<sup>3+7<br \/>\n<\/sup>8<sup>10<\/sup><\/p>\n<p>Question 5.<br \/>\n\\(\\frac { 12^{ 6 } }{ 12^{ 2 } } \\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n12<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n12<sup>6<\/sup> \u00f7 12<sup>2<br \/>\n<\/sup>12<sup>6-2<br \/>\n<\/sup> 12<sup>4<\/sup><\/p>\n<p>Question 6.<br \/>\n(10<sup>3<\/sup>)<sup>5<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n10<sup>8<\/sup><\/p>\n<p>Explanation:<br \/>\n(10<sup>3<\/sup>)<sup>5<\/sup><br \/>\n(10<sup>3+5<\/sup>)<br \/>\n(10<sup>8<\/sup>)<\/p>\n<p><strong>2.2 Scientific Notation with Positive Powers of 10<\/strong><\/p>\n<p><strong>Convert each number to scientific notation or standard notation.<\/strong><\/p>\n<p>Question 7.<br \/>\n2,000<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2 \u00d7 (10<sup>3<\/sup>)<\/p>\n<p>Explanation:<br \/>\n2 \u00d7 1,000<br \/>\nMove the decimal left 3 places<br \/>\n2 \u00d7 (10<sup>3<\/sup>)<\/p>\n<p>Question 8.<br \/>\n91,007,500<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n9.10075 \u00d7 (10<sup>7<\/sup>)<\/p>\n<p>Explanation:<br \/>\n91,007,500<br \/>\nMove the decimal left 7 places<br \/>\n9.10075 \u00d7 (10<sup>7<\/sup>)<\/p>\n<p>Question 9.<br \/>\n1.0395 \u00d7 10<sup>9<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n1039500000<\/p>\n<p>Explanation:<br \/>\n1.0395 \u00d7 10<sup>9<\/sup><br \/>\nMove the decimal right 9 places<br \/>\n1039500000<\/p>\n<p>Question 10.<br \/>\n4 \u00d7 10<sup>2<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n400<\/p>\n<p>Explanation:<br \/>\n4 \u00d7 10<sup>2<\/sup><br \/>\nMove the decimal right 2 places<br \/>\n400<\/p>\n<p><strong>2.3 Scientific Notation with Negative Powers of 10<\/strong><\/p>\n<p><strong>Convert each number to scientific notation or standard notation.<\/strong><\/p>\n<p>Question 11.<br \/>\n0.02<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Explanation:<br \/>\n0.02<br \/>\nMove the decimal right 2 places<br \/>\n2 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Question 12.<br \/>\n0.000701<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n7.01 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Explanation:<br \/>\n0.000701<br \/>\nMove the decimal right 4 places<br \/>\n7.01 \u00d7 10<sup>-4<\/sup><\/p>\n<p>Question 13.<br \/>\n8.9 \u00d7 10<sup>-5<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n0.000089<\/p>\n<p>Explanation:<br \/>\n8.9 \u00d7 10<sup>-5<\/sup><br \/>\nMove the decimal left 5 places<br \/>\n0.000089<\/p>\n<p>Question 14.<br \/>\n4.41 \u00d7 10<sup>-2<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n0.0441<\/p>\n<p>Explanation:<br \/>\n4.41 \u00d7 10<sup>-2<\/sup><br \/>\nMove the decimal left 2 places<br \/>\n0.0441<\/p>\n<p><strong>2.4 Operations with Scientific Notation<\/strong><\/p>\n<p><strong>Perform the operation. Write your answer in scientific notation.<\/strong><\/p>\n<p>Question 15.<br \/>\n7 \u00d7 10<sup>6<\/sup> \u2212 5.3 \u00d7 10<sup>6<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n1.7 \u00d7 10<sup>6<\/sup><\/p>\n<p>Explanation:<br \/>\n7 \u00d7 10<sup>6<\/sup> \u2212 5.3 \u00d7 10<sup>6<\/sup><br \/>\n(7 &#8211; 5.3) \u00d7 10<sup>6<\/sup><br \/>\n1.7 \u00d7 10<sup>6<\/sup><\/p>\n<p>Question 16.<br \/>\n3.4 \u00d7 10<sup>4<\/sup> + 7.1 \u00d7 10<sup>5<\/sup><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n7.44 \u00d7 10<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\n3.4 \u00d7 10<sup>4<\/sup> + 7.1 \u00d7 10<sup>5<\/sup><br \/>\n0.34 \u00d7 10<sup>5<\/sup> + 7.1 \u00d7 10<sup>5<\/sup><br \/>\n(0.34 + 7.1) \u00d7 10<sup>5<br \/>\n<\/sup>7.44 \u00d7 10<sup>5<\/sup><\/p>\n<p>Question 17.<br \/>\n(2 \u00d7 10<sup>4<\/sup>)(5.4 \u00d7 10<sup>6<\/sup>)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n10.8 \u00d7 10<sup>10<\/sup><\/p>\n<p>Explanation:<br \/>\n(2 \u00d7 10<sup>4<\/sup>)(5.4 \u00d7 10<sup>6<\/sup>)<br \/>\n(2 \u00d7 5.4)(10<sup>4<\/sup> \u00d7 10<sup>6<\/sup>)<br \/>\n10.8 \u00d7 10<sup>10<\/sup><\/p>\n<p>Question 18.<br \/>\n\\(\\frac { 7.86\u00d710^{ 9 } }{ 3\u00d710^{ 4 } } \\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2.62 \u00d7 10<sup>5<\/sup><\/p>\n<p>Explanation:<br \/>\n7.86\/3 = 2.62<br \/>\n10<sup>9<\/sup>\/10<sup>4<\/sup>\u00a0= 10<sup>5<\/sup><br \/>\n2.62 \u00d7 10<sup>5<\/sup><\/p>\n<p>Question 19.<br \/>\nNeptune\u2019s average distance from the Sun is 4.503\u00d710<sup>9<\/sup> km. Mercury\u2019s average distance from the Sun is 5.791 \u00d7 10<sup>7<\/sup> km. About how many times farther from the Sun is Neptune than Mercury? Write your answer in scientific notation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n(0.7776 \u00d7 10<sup>2<\/sup> km) = 77.76 times<\/p>\n<p>Explanation:<br \/>\nAs Neptune\u2019s average distance from the sun is 4.503\u00d710<sup>9<\/sup> km and Mercury is 5.791 \u00d7 10<sup>7<\/sup> km<br \/>\n(4.503\u00d710<sup>9<\/sup> km)\/(5.791 \u00d7 10<sup>7<\/sup> km)<br \/>\n(0.7776 \u00d7 10<sup>9-7<\/sup> km)<br \/>\n(0.7776 \u00d7 10<sup>2<\/sup> km)<br \/>\n<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-108\" class=\"mjx-math\"><span id=\"MJXc-Node-109\" class=\"mjx-mrow\"><span id=\"MJXc-Node-110\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">77.76<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0times<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 20.<br \/>\nHow is scientific notation used in the real world?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nScientific notation is used to write very large or very small numbers using less digits.<\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._58\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 58<\/h3>\n<p>Question 1.<br \/>\nWhich of the following is equivalent to 6<sup>-3<\/sup>?<br \/>\nOptions:<br \/>\na. 216<br \/>\nb. \\(\\frac{1}{216}\\)<br \/>\nc. \u2212\\(\\frac{1}{216}\\)<br \/>\nd. -216<\/p>\n<p>Answer:<br \/>\nb. \\(\\frac{1}{216}\\)<\/p>\n<p>Explanation:<br \/>\nBase = 6<br \/>\nExponent = 3<br \/>\n6<sup>3<\/sup> = (1\/6)<sup>3<\/sup> = 1\/216<\/p>\n<p>Question 2.<br \/>\nAbout 786,700,000 passengers traveled by plane in the United States in 2010. What is this number written in scientific notation?<br \/>\nOptions:<br \/>\na. 7,867 \u00d7 10<sup>5<\/sup> passengers<br \/>\nb. 7.867 \u00d7 10<sup>2<\/sup> passengers<br \/>\nc. 7.867 \u00d7 10<sup>8<\/sup> passengers<br \/>\nd. 7.867 \u00d7 10<sup>9<\/sup> passengers<\/p>\n<p>Answer:<br \/>\nc. 7.867 \u00d7 10<sup>8<\/sup> passengers<\/p>\n<p>Explanation:<br \/>\n786,700,000<br \/>\nMove the decimal left 8 places<br \/>\n7.867 \u00d7 10<sup>8<\/sup> passengers<\/p>\n<p>Question 3.<br \/>\nIn 2011, the population of Mali was about 1.584 \u00d7 10<sup>7<\/sup> people. What is this number written in standard notation?<br \/>\nOptions:<br \/>\na. 1.584 people<br \/>\nb. 1,584 people<br \/>\nc. 15,840,000 people<br \/>\nd. 158,400,000 people<\/p>\n<p>Answer:<br \/>\nc. 15,840,000 people<\/p>\n<p>Explanation:<br \/>\n1.584 \u00d7 10<sup>7<\/sup><br \/>\nMove the decimal right 7 places<br \/>\n15,840,000 people<\/p>\n<p>Question 4.<br \/>\nThe square root of a number is between 7 and 8. Which could be the number?<br \/>\nOptions:<br \/>\na. 72<br \/>\nb. 83<br \/>\nc. 51<br \/>\nd. 66<\/p>\n<p>Answer:<br \/>\nc. 51<\/p>\n<p>Explanation:<br \/>\n7\u00b2= 49<br \/>\n8\u00b2=64<br \/>\n(49+64)\/2<br \/>\n56.5<\/p>\n<p>Question 5.<br \/>\nEach entry-level account executive in a large company makes an annual salary of $3.48 \u00d7 10<sup>4<\/sup>. If there are 5.2 \u00d7 10<sup>2<\/sup> account executives in the company, how much do they make in all?<br \/>\nOptions:<br \/>\na. $6.69 \u00d7 10<sup>1<\/sup><br \/>\nb. $3.428 \u00d7 10<sup>4<\/sup><br \/>\nc. $3.532 \u00d7 10<sup>4<\/sup><br \/>\nd. $1.8096 \u00d7 10<sup>7<\/sup><\/p>\n<p>Answer:<br \/>\nd. $1.8096 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\nEach entry-level account executive in a large company makes an annual salary of $3.48 \u00d7 10<sup>4<\/sup>. If there are 5.2 \u00d7 10<sup>2<\/sup> account executives in the company,<br \/>\n($3.48 \u00d7 10<sup>4<\/sup>)( 5.2 \u00d7 10<sup>2<\/sup>)<br \/>\n$1.8096 \u00d7 10<sup>7<\/sup><\/p>\n<p>Question 6.<br \/>\nPlace the numbers in order from least to greatest.<br \/>\n0.24,4 \u00d7 10<sup>-2<\/sup>, 0.042, 2 \u00d7 10<sup>-4<\/sup>, 0.004<br \/>\nOptions:<br \/>\na. 2 \u00d7 10<sup>-4<\/sup>, 4 \u00d7 10<sup>-2<\/sup>, 0.004, 0.042, 0.24<br \/>\nb. 0.004, 2 \u00d7 10<sup>-4<\/sup>, 0.042, 4 \u00d7 10<sup>-2<\/sup>, 0.24<br \/>\nc. 0.004, 2 \u00d7 10<sup>-4<\/sup>, 4 \u00d7 10<sup>-2<\/sup>, 0.042, 0.24<br \/>\nd. 2 \u00d7 10<sup>-4<\/sup>, 0.004, 4 \u00d7 10<sup>-2<\/sup>, 0.042, 0.24<\/p>\n<p>Answer:<br \/>\nd. 2 \u00d7 10<sup>-4<\/sup>, 0.004, 4 \u00d7 10<sup>-2<\/sup>, 0.042, 0.24<\/p>\n<p>Explanation:<br \/>\n2 \u00d7 10<sup>-4<\/sup>\u00a0= 0.0002<br \/>\n4 \u00d7 10<sup>-2<\/sup>\u00a0= 0.04<\/p>\n<p>Question 7.<br \/>\nGuillermo is 5 \\(\\frac{5}{6}\\) feet tall. What is this number of feet written as a decimal?<br \/>\nOptions:<br \/>\na. 5.7 feet<br \/>\nb. 5.\\(\\bar{7}\\) feet<br \/>\nc. 5.83 feet<br \/>\nd. 5.8\\(\\bar{3}\\) feet<\/p>\n<p>Answer:<br \/>\nc. 5.83 feet<\/p>\n<p>Question 8.<br \/>\nA human hair has a width of about 6.5 \u00d7 10<sup>-5<\/sup> meters. What is this width written in standard notation?<br \/>\nOptions:<br \/>\na. 0.00000065 meter<br \/>\nb. 0.0000065 meter<br \/>\nc. 0.000065 meter<br \/>\nd. 0.00065 meter<\/p>\n<p>Answer:<br \/>\nc. 0.000065 meter<\/p>\n<p>Explanation:<br \/>\n6.5 \u00d7 10<sup>-5<\/sup> meter = 0.000065<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 9.<br \/>\nConsider the following numbers: 7000, 700, 70, 0.7, 0.07, 0.007<br \/>\na. Write the numbers in scientific notation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n7000 = 7 \u00d7 10\u00b3<br \/>\n700 = 7 \u00d7 10\u00b2<br \/>\n70 = 7 \u00d7 10\u00b9<br \/>\n0.7 = 7 \u00d7 10\u00af\u00b9<br \/>\n0.07 = 7 \u00d7 10\u00af\u00b2<br \/>\n0.007 = 7 \u00d7 10\u00af\u00b3<\/p>\n<p>Question 9.<br \/>\nb. Look for a pattern in the given list and the list in scientific notation. Which numbers are missing from the lists?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIn the given list the decimal is moving to the left by one place. From the scientific notation, numbers are decreasing by 10. The number missing is 7<\/p>\n<p>Question 9.<br \/>\nc. Make a conjecture about the missing numbers.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe numbers will continue to decrease by 10 in the given list.<\/p>\n<h3>Conclusion:<\/h3>\n<p>We wish the information provided in the Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation for all the students. Go through the solved examples to have a complete grip on the subject and also on the way of solving each problem. Go Math Grade 8 Chapter 2 Exponents and Scientific Notation Key will help the students to score the highest marks in the exam.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Get Free Access to Download Go Math Grade 8 Answer Key Chapter 2 Exponents and Scientific Notation PDF from here. Start your preparation with the help of Go Math Grade 8 Answer Key. It is essential for all the students to learn the concepts of this chapter in-depth. 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