Lesson 4
Dividing Powers of 10
Problem 1
Evaluate:
- \(10^0\)
- \(\frac{10^3}{10^3}\)
- \(10^2 + 10^1 + 10^0\)
Solution
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Problem 2
Write each expression as a single power of 10.
- \(\frac{10^3 \boldcdot 10^4}{10^5}\)
- \((10^4) \boldcdot \frac{10^{12}}{10^7}\)
- \(\left(\frac{10^5}{10^3}\right)^4\)
- \(\frac{10^4 \boldcdot 10^5 \boldcdot 10^6}{10^3 \boldcdot 10^7}\)
- \(\frac{(10^5)^2}{(10^2)^3}\)
Solution
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Problem 3
The Sun is roughly \(10^2\) times as wide as Earth. The star KW Sagittarii is roughly \(10^5\) times as wide as Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.
Solution
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Problem 4
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 \(b\) be the number of pounds of bananas Kiran buys and \(g\) be the number of pounds of guavas he buys.
- Write an equation relating the two variables.
- Rearrange the equation so \(b\) is the independent variable.
- Rearrange the equation so \(g\) is the independent variable.
Solution
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(From Unit 5, Lesson 3.)Problem 5
Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed \(\frac13\) of the speed her mom bikes. Sketch a graph of both of these relationships.
![Blank coordinate plane, x, time, hours, 0 to 1 point 2 by point 1, y, distance, miles, 0 to 8 by 2.](https://cms-im.s3.amazonaws.com/YN7iNCVJGaYnRQc5e5WbExhB?response-content-disposition=inline%3B%20filename%3D%228-8.3.A1.PP.LinsMomAxes.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A1.PP.LinsMomAxes.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171240Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d15bf76b0fd24794509781f3820382777cd94edad80791cf38c2e8cf5a5fa2ff)
Solution
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(From Unit 3, Lesson 1.)