Section B Section B Checkpoint

Problem 1

A rectangular wall is 7.2 meters long and is 3.8 meters in height. What is its area in square meters? Show your reasoning.

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Solution

27.36 square meters. Sample reasoning:

  •  

  • (7.2)⋅(3.8)=7210⋅3810=2,736100=27.36(7.2) \boldcdot (3.8) = \frac{72}{10} \boldcdot \frac{38}{10} = \frac{2,736}{100} = 27.36

Show Sample Response
Sample Response

27.36 square meters. Sample reasoning:

  •  

  • (7.2)⋅(3.8)=7210⋅3810=2,736100=27.36(7.2) \boldcdot (3.8) = \frac{72}{10} \boldcdot \frac{38}{10} = \frac{2,736}{100} = 27.36

Problem 2

  1. Find the product of 64 and 9.

  2. Explain how you can use the value of 64⋅964 \boldcdot 9 to find the value of (6.4)⋅(0.009)(6.4) \boldcdot (0.009).
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Solution

  1. 576

  2. Sample responses:
    • There is 1 decimal place in 6.4 and 3 decimal places in 0.009, so the product will have 4 decimal places. I can move the digits in 576 to the right 4 places to get 0.0576.
    • 64 is 10⋅(6.4)10 \boldcdot (6.4), and 9 is 1,000⋅(0.009)1,000 \boldcdot (0.009), so the product of 64 and 9 is 10,000 times the product of 6.4 and 0.009. Dividing 576 by 10,000 gives 0.0576.
       
Show Sample Response
Sample Response

  1. 576

  2. Sample responses:
    • There is 1 decimal place in 6.4 and 3 decimal places in 0.009, so the product will have 4 decimal places. I can move the digits in 576 to the right 4 places to get 0.0576.
    • 64 is 10⋅(6.4)10 \boldcdot (6.4), and 9 is 1,000⋅(0.009)1,000 \boldcdot (0.009), so the product of 64 and 9 is 10,000 times the product of 6.4 and 0.009. Dividing 576 by 10,000 gives 0.0576.