Lesson 4

Dividing Powers of 10

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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.

Blank coordinate plane, x, time, hours, 0 to 1 point 2 by point 1, y, distance, miles, 0 to 8 by 2.

Solution

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(From Unit 3, Lesson 1.)