Negative Exponents with Powers of 10: IM 8.7.5
[url=https://im.kendallhunt.com/MS/teachers/3/7/5/preparation.html]“Negative Exponents with 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 8.7.5
- IM 8.7.5 Lesson: Negative Exponents with Powers of 10
- Practice 8.7.5
- IM 8.7.5 Practice: Negative Exponents with Powers of 10
IM 8.7.5 Lesson: Negative Exponents with Powers of 10
Solve each equation mentally.
[math]\frac{100}{1}=10^x[/math]
[math]\frac{100}{x}=10^1[/math]
[math]\frac{x}{100}=10^0[/math]
[math]\frac{100}{1,000}=10^x[/math]
Complete the table to explore what negative exponents mean.
Match each exponential expression with an equivalent multiplication expression:
Write [math](10^2)^{-3}[/math]as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Match each exponential expression with an equivalent multiplication expression:
Write [math]\frac{10^{-2}}{10^{-5}}[/math] as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Match each exponential expression with an equivalent multiplication expression:
Write [math]10^{-4}\cdot10^3[/math] as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Priya, Jada, Han, and Diego stand in a circle and take turns playing a game.
[size=150]Priya says, SAFE. Jada, standing to Priya's left, says, OUT and leaves the circle. Han is next: he says, SAFE. Then Diego says, OUT and leaves the circle. At this point, only Priya and Han are left. They continue to alternate. Priya says, SAFE. Han says, OUT and leaves the circle. Priya is the only person left, so she is the winner.[br]Priya says, “I knew I’d be the only one left, since I went first.”[/size][br][br]Record this game on paper a few times with different numbers of players. Does the person who starts always win?
Try to find as many numbers as you can where the person who starts always wins. What patterns do you notice?
IM 8.7.5 Practice: Negative Exponents with Powers of 10
Write with a single exponent:
Write each expression as a single power of 10.
Select [b]all[/b] of the following that are equivalent to [math]\frac{1}{10,000}[/math]:
Match each equation to the situation it describes. Explain what the constant of proportionality means in each equation.
Explain why triangle [math]ABC[/math] is similar to [math]EDC[/math].
Find the missing side lengths.