{"id":725,"date":"2021-04-23T17:49:14","date_gmt":"2021-04-23T12:19:14","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=725"},"modified":"2022-02-25T12:22:17","modified_gmt":"2022-02-25T06:52:17","slug":"envision-math-grade-6-answer-key-topic-1-3","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-grade-6-answer-key-topic-1-3\/","title":{"rendered":"Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value"},"content":{"rendered":"

Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value<\/h2>\n

Exponents and Place Value<\/strong><\/p>\n

How can you write a number
\nusing exponents?
\nAnswer:
\nEach place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.
\n\"Envision<\/p>\n

Another Example<\/strong>
\nHow do you write the expanded form of a number using exponents?
\nAnswer:
\nStandard form: 562,384
\nExpanded form: (5 \u00d7 100,000) + (6 \u00d7 10,000) + (2 \u00d7 1,000) + (3 \u00d7 100) + (8 \u00d7 10) + 4
\nExpanded form
\nusing exponents: (5 \u00d7 105<\/sup>) + (6 \u00d7 104<\/sup>) + (2 \u00d7 103<\/sup>) + (3 \u00d7 102<\/sup>) + (8 \u00d7 101<\/sup> ) + (4 \u00d7 100<\/sup>)
\nAny number raised to the first power always equals that number. 101<\/sup> = 10.<\/p>\n

Explain It<\/strong><\/p>\n

Question 1.
\nHow many times is 9 used as a factor in the exponent 98?
\nAnswer:
\n8 times
\nExplanation:<\/p>\n

Question 2.
\nWhy does 3 \u00d7 100 = 3?
\nAnswer:
\n100<\/sup> = 1, so 3 \u00d7 100<\/sup> = 3<\/p>\n

Other Examples<\/strong>
\nWrite each in exponential form.
\n100,000 = 105<\/sup> 10 \u00d7 10 \u00d7 10 = 103<\/sup> 1 trillion = 1012<\/sup>
\nEvaluate numbers in exponential form.
\n53<\/sup> = 5 \u00d7 5 \u00d7 5 = 125 34<\/sup> = 3 \u00d7 3 \u00d7 3 \u00d7 3 = 81<\/p>\n

\"Envision
\nYou can write the repeated multiplication of a number in exponential form.
\n\"Envision<\/p>\n

Each place in the place-value chart can be written using an exponent.
\n\"Envision<\/p>\n

Guided Practice<\/strong><\/p>\n

Do you know HOW?<\/strong>
\nQuestion 1.
\nWrite 10,000 as repeated multiplication.
\nAnswer:
\n10,000 = 10 \u00d7 10 \u00d7 10 \u00d7 10
\nExplanation:<\/p>\n

Question 2.
\nWrite 7 \u00d7 7 \u00d7 7 \u00d7 7 in exponential form.
\nAnswer:
\n74<\/sup>
\nExplanation:<\/p>\n

Question 3.
\nWrite 37,169 in expanded form using exponents.
\nAnswer:
\n(3 \u00d7 104<\/sup>) + (7 \u00d7 103<\/sup>) + (1 \u00d7 102<\/sup>) + (6 \u00d7 101<\/sup>) + (9 \u00d7 100<\/sup>)
\nExplanation:<\/p>\n

Question 4.
\nWrite 53<\/sup> in standard form.
\nAnswer:
\n125
\nExplanation:<\/p>\n

Do you UNDERSTAND?<\/strong>
\nQuestion 5.
\nIn the example at the top, why was the number 10 used as the base to write 1,000,000 in exponential form?
\nAnswer:
\nSee margin.
\nExplanation:<\/p>\n

Question 6.
\nUsing the example, how many times would 10 be repeatedly multiplied to equal 100,000?
\nAnswer:
\n5 times. 100,000 = 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 = 10
\nExplanation:<\/p>\n

Question 7.
\nHow many zeros are in 107 when it is written in standard form?
\nAnswer:
\n7
\nExplanation:<\/p>\n

Independent Practice<\/strong><\/p>\n

Leveled Practice What number is the base?
\nQuestion 8.
\n49<\/sup>
\nAnswer:
\n4
\nExplanation:<\/p>\n

Question 9.
\n179<\/sup>
\nAnswer:
\n17
\nExplanation:<\/p>\n

What number is the exponent?
\nQuestion 10.
\n319<\/sup>
\nAnswer:
\n9
\nExplanation:<\/p>\n

Question 11.
\n2100<\/sup>
\nAnswer:
\n100
\nExplanation:<\/p>\n

Write each in exponential form.
\nQuestion 12.
\n1,000
\nAnswer:
\n103<\/sup>
\nExplanation:<\/p>\n

Question 13.
\n1,000,000,000
\nAnswer:
\n109<\/sup>
\nExplanation:<\/p>\n

Question 14.
\n10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10
\nAnswer:
\n105<\/sup>
\nExplanation:<\/p>\n

Write each number in expanded form using exponents.
\nAnswer:
\nSee margin
\nExplanation:<\/p>\n

Question 15.
\n841
\nAnswer:<\/p>\n

Question 16.
\n5,832
\nAnswer:<\/p>\n

Question 17.
\n1,874,161
\nAnswer:<\/p>\n

Question 18.
\n22,600,000
\nAnswer:<\/p>\n

Evaluate 19 through 22.
\nQuestion 19.
\n62<\/sup> = \u2610
\nAnswer:
\n36
\nExplanation:<\/p>\n

Question 20.
\n104<\/sup> = \u2610
\nAnswer:
\n10,000
\nExplanation:<\/p>\n

Question 21.
\n43<\/sup> = \u2610
\nAnswer:
\n64
\nExplanation:<\/p>\n

Question 22.
\n27<\/sup> = \u2610
\nAnswer:
\n128
\nExplanation:<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 23.
\nThe population of one U.S. state is approximately 33,871,648. What is this number in expanded form using exponents?
\nAnswer:
\nSee margin
\nExplanation:<\/p>\n

Question 24.
\nReasoning What number raised to both the first power and the second power equals 1?
\nAnswer:
\n1; 11<\/sup> = 1 and 12<\/sup> = 1
\nExplanation:<\/p>\n

Question 25.
\nWriting to Explain Explain how to compare 24 and 42.
\nAnswer:
\n24<\/sup> = 2 \u00d7 2 \u00d7 2 \u00d7 2 = 16; 42<\/sup> = 4 \u00d7 4 = 16; So 24<\/sup> = 42<\/sup>.
\nExplanation:<\/p>\n

Question 26.
\nIn Exercise 23, what is the place of the digit 7?
\nA. hundreds
\nB. thousands
\nC. ten thousands
\nD. millions
\nAnswer:
\nC. ten thousands
\nExplanation:<\/p>\n

Question 27.
\nWriting to Explain Kalesha was asked to write 80,808 in expanded form using exponents. Her response was (8 \u00d7 102<\/sup>) + (8 \u00d7 101<\/sup>) + (8 \u00d7 100<\/sup>). Explain where she made mistakes and write the correct response.
\nAnswer:
\nSee margin
\nExplanation:<\/p>\n

Question 28.
\nThink About the Process You invest $1 in a mutual fund. Every 8 years, your money doubles. If you don\u2019t add more money, which expression shows how much your investment is worth after 48 years?
\nA. 1 48
\nB. 1 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2
\nC. 1 + 2 + 2 + 2 + 2 + 2 + 2
\nD. 1 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2
\nAnswer:
\nExplanation:
\nD. 1 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/p>\n

Question 29.
\nNumber Sense Using the map, write the population of the United States in expanded form using exponents.
\n\"Envision
\nAnswer:
\nSee margin
\nExplanation:<\/p>\n

Question 30.
\nIn 1900, there were 76,803,887 people in the United States. How many more people were there in the United States in a recent year than in 1900?
\nAnswer:
\nSee margin
\nExplanation:<\/p>\n

Algebra Connections<\/strong><\/p>\n

Solution Pairs
\nAn equation is a mathematical sentence that uses an equals sign to show that two expressions are equal. Any values that make an equation true are solutions to the equation.<\/p>\n

An inequality is a mathematical sentence that contains <, >, \u2264, or \u2265. Any value that makes the inequality true is a solution. You can graph the solutions of an inequality on a number line.<\/p>\n

Example:<\/strong> Find two values for each variable that make the equation,
\ny = x + 3, true.
\nIf x = 1, then y = 1 + 3 = 4 is true.
\nIf x = 5, then y = 5 + 3 = 8 is true.
\n(1, 4) and (5, 8) are solution pairs.<\/p>\n

Example:<\/strong> Graph three values that make the inequality, x > 3, true.
\nx = 3.1, x = 4, x = 5
\nDraw a number line. Plot three points that are greater than 3
\n\"Envision<\/p>\n

For 1 through 4, copy the table and find two values for each variable that make the equation true.
\nQuestion 1.
\ny = 4 + x
\nAnswer:
\n\"Envision
\nExplanation:<\/p>\n

Question 2.
\nb = a – 2
\nAnswer:
\n\"Envision
\nExplanation:<\/p>\n

Question 3.
\nt = 3w
\nAnswer:
\n\"Envision
\nExplanation:<\/p>\n

Question 4.
\ny = x \u00f7 2
\nAnswer:
\n\"Envision
\nExplanation:<\/p>\n

Question 5.
\nCopy the number line and graph 3 values that make the inequality, d \u2265 9, true.
\n\"Envision
\nAnswer:
\nAny 3 points right of 9; or 9
\nExplanation:<\/p>\n

Question 6.
\nCopy the number line and graph 3 values that make the inequality,\\(\\frac{x}{3}\\) < 4, true.
\n\"Envision
\nAnswer:
\nAny 3 points to left of 12
\nExplanation:<\/p>\n","protected":false},"excerpt":{"rendered":"

Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value Exponents and Place Value How can you write a number using exponents? Answer: Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/725"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=725"}],"version-history":[{"count":1,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/725\/revisions"}],"predecessor-version":[{"id":27067,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/725\/revisions\/27067"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=725"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=725"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}