# Lesson 4

Dividing Powers of 10

### Problem 1

Evaluate:

1. $$10^0$$
2. $$\frac{10^3}{10^3}$$
3. $$10^2 + 10^1 + 10^0$$

### Solution

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### Problem 2

Write each expression as a single power of 10.

1. $$\frac{10^3 \boldcdot 10^4}{10^5}$$
2. $$(10^4) \boldcdot \frac{10^{12}}{10^7}$$
3. $$\left(\frac{10^5}{10^3}\right)^4$$
4. $$\frac{10^4 \boldcdot 10^5 \boldcdot 10^6}{10^3 \boldcdot 10^7}$$
5. $$\frac{(10^5)^2}{(10^2)^3}$$

### 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.

1. Write an equation relating the two variables.
2. Rearrange the equation so $$b$$ is the independent variable.
3. 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.