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Now that we know multiplying a number by 10 can be accomplished by moving all the digits one place to the left, explain why you can multiply a number by 1000 by moving all the digits 3 places to the left.

Now that we know multiplying a number by 10 can be accomplished by moving all the digits one place to the left, explain why you can multiply a number by 1000 by moving all the digits 3 places to the left.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 7:** Now that we know multiplying a number by 10 can be accomplished by moving all the digits one place to the left, explain why you can multiply a number by 1000 by moving all the digits 3 places to the left. **Explanation:** When you multiply a number by 10, you effectively increase its place value by one digit as each digit shifts one place to the left. This is because multiplying by 10 increases the value of each digit tenfold. For example, multiplying 25 by 10 results in 250. Similarly, multiplying a number by 1000 involves increasing its place value by three digits as each digit shifts three places to the left. This is because multiplying by 1000 increases the value of each digit a thousandfold. For example, multiplying 25 by 1000 results in 25000. Thus, moving digits 3 places to the left when multiplying by 1000 is analogous to moving digits 1 place to the left when multiplying by 10.
Transcribed Image Text:**Question 7:** Now that we know multiplying a number by 10 can be accomplished by moving all the digits one place to the left, explain why you can multiply a number by 1000 by moving all the digits 3 places to the left. **Explanation:** When you multiply a number by 10, you effectively increase its place value by one digit as each digit shifts one place to the left. This is because multiplying by 10 increases the value of each digit tenfold. For example, multiplying 25 by 10 results in 250. Similarly, multiplying a number by 1000 involves increasing its place value by three digits as each digit shifts three places to the left. This is because multiplying by 1000 increases the value of each digit a thousandfold. For example, multiplying 25 by 1000 results in 25000. Thus, moving digits 3 places to the left when multiplying by 1000 is analogous to moving digits 1 place to the left when multiplying by 10.
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