Lesson 4: Practice Problems

Problem 1

Evaluate:

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

Problem 2

Write each expression as a single power of 10.

$\frac{10^{3} \cdot 10^{4}}{10^{5}}$
$(10^{4}) \cdot \frac{10^{12}}{10^{7}}$
${(\frac{10^{5}}{10^{3}})}^{4}$
$\frac{10^{4} \cdot 10^{5} \cdot 10^{6}}{10^{3} \cdot 10^{7}}$
$\frac{{(10^{5})}^{2}}{{(10^{2})}^{3}}$

Problem 3

The Sun is roughly $10^{2}$ times as wide as the Earth. The star KW Sagittarii is roughly $10^{5}$ times as wide as the Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.

Problem 4 From Unit 5 Lesson 3

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.

Problem 5 From Unit 3 Lesson 1

Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed $\frac{1}{3}$ of the speed her mom bikes. Sketch a graph of both of these relationships.

A graph of time (hours) on the x from 0 to 1.2 in 0.1 increments and distance on the y from 0 to 8 in increments of 1.