Dividing Powers of 10: IM 8.7.4
[url=https://im.kendallhunt.com/MS/teachers/3/7/4/preparation.html]“Dividing Powers of 10”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.7.4
- IM 8.7.4 Lesson: Dividing Powers of 10
- Practice 8.7.4
- IM 8.7.4 Practice: Dividing Powers of 10
IM 8.7.4 Lesson: Dividing Powers of 10
What is the value of the expression?
[math]\frac{2^{^5}\cdot3^4\cdot3^2}{2\cdot3^6\cdot2^4}[/math]
Complete the table to explore patterns in the exponents when dividing powers of 10. Use the “expanded” column to show why the given expression is equal to the single power of 10. You may skip a single box in the table, but if you do, explain below.
If you chose to skip one entry in the table, which entry did you skip? Why?
It is predicted that by 2050, there will be [math]10^{10}[/math] people living on Earth. At that time, it is predicted there will be approximately [math]10^{^{12}}[/math] trees. How many trees will there be for each person?[br][br]
So far we have looked at powers of 10 with exponents greater than 0. What would happen to our patterns if we included 0 as a possible exponent?
Write [math]10^{^{12}}\cdot10^0[/math] with a power of 10 with a single exponent using the appropriate exponent rule.[br]Explain or show your reasoning.
Explain or show your reasoning.
What number could you multiply [math]10^{12}[/math] by to get this same answer?
Explain or show your reasoning.
Write [math]\frac{10^8}{10^0}[/math] with a single power of 10 using the appropriate exponent rule. [br]Explain or show your reasoning.
What number could you divide [math]10^8[/math] by to get this same answer?
If we want the exponent rules we found to work even when the exponent is 0, then what does the value of [math]10^0[/math] have to be?
Noah says, “If I try to write [math]10^0[/math] expanded, it should have zero factors that are 10, so it must be equal to 0.” Do you agree? Discuss with your partner.
Write as many expressions as you can that have the same value as [math]10^6[/math]. Focus on using exponents, multiplication, and division. What patterns do you notice with the exponents?
IM 8.7.4 Practice: Dividing Powers of 10
Evaluate:
[math]10^0[/math]
[math]\frac{10^3}{10^3}[/math]
[math]10^2+10^1+10^0[/math]
Write each expression as a single power of 10.
[size=150]The Sun is roughly [math]10^2[/math] times as wide as Earth. The star KW Sagittarii is roughly [math]10^5[/math] times as wide as Earth.[/size] [br][br]About how many times as wide as the Sun is KW Sagittarii? Explain how you know.
[size=150]Bananas cost $1.50 per pound, and guavas cost $3.00 per pound. Kiran spends $12 on fruit for a breakfast his family is hosting. Let [math]b[/math] be the number of pounds of bananas Kiran buys and [math]g[/math] be the number of pounds of guavas he buys.[br][/size][br]Write an equation relating the two variables.
Rearrange the equation so [math]b[/math] is the independent variable.
Rearrange the equation so [math]g[/math] is the independent variable.
[size=150]Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed [math]\frac{1}{3}[/math] of the speed her mom bikes. [/size]