Lesson 5
Decimal Points in Products
Problem 1
-
Find the product of each number and \(\frac{1}{100}\).
122.1
11.8
1350.1
1.704
- What happens to the decimal point of the original number when you multiply it by \(\frac{1}{100}\)? Why do you think that is? Explain your reasoning.
Solution
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Problem 2
Which expression has the same value as \((0.06) \boldcdot (0.154)\)? Select all that apply.
\(6 \boldcdot \frac{1}{100} \boldcdot 154 \boldcdot \frac{1}{1,000}\)
\(6 \boldsymbol \boldcdot 154 \boldcdot \frac{1}{100,000}\)
\(6 \boldcdot (0.1) \boldcdot 154 \boldcdot (0.01)\)
\(6 \boldsymbol \boldcdot 154 \boldcdot (0.00001)\)
0.00924
Solution
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Problem 3
Calculate the value of each expression by writing the decimal factors as fractions, then writing their product as a decimal. Show your reasoning.
- \((0.01)\boldcdot (0.02)\)
- \((0.3) \boldcdot (0.2)\)
- \((1.2) \boldcdot 5\)
- \((0.9) \boldcdot (1.1)\)
- \((1.5)\boldcdot 2\)
Solution
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Problem 4
Write three numerical expressions that are equivalent to \((0.0004) \boldcdot (0.005)\).
Solution
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Problem 5
Calculate each sum.
- \(33.1+ 1.95\)
- \(1.075 + 27.105\)
- \(0.401+9.28\)
Solution
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(From Unit 5, Lesson 3.)Problem 6
Calculate each difference. Show your reasoning.
- \(13.2 - 1.78\)
- \(23.11 - 0.376\)
- \(0.9 - 0.245\)
Solution
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(From Unit 5, Lesson 4.)Problem 7
On the grid, draw a quadrilateral that is not a rectangle that has an area of 18 square units. Show how you know the area is 18 square units.
![A blank coordinate plane with 16 evenly spaced horizontal units and 12 evenly spaced vertical units.](https://cms-im.s3.amazonaws.com/Mtje8WXsjQDE9fQ8VtAvNX1D?response-content-disposition=inline%3B%20filename%3D%226-6.7.C.PP.Image.00.Blank-Grid.png%22%3B%20filename%2A%3DUTF-8%27%276-6.7.C.PP.Image.00.Blank-Grid.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T074958Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c81780360011f0868b352c2d90873a30400cc346468c389b71e340330ebb2191)
Solution
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(From Unit 1, Lesson 3.)