# Lesson 5

Decimal Points in Products

### Problem 1

1. Find the product of each number and $$\frac{1}{100}$$.

122.1

11.8

1350.1

1.704

2. 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.

A:

$$6 \boldcdot \frac{1}{100} \boldcdot 154 \boldcdot \frac{1}{1,000}$$

B:

$$6 \boldsymbol \boldcdot 154 \boldcdot \frac{1}{100,000}$$

C:

$$6 \boldcdot (0.1) \boldcdot 154 \boldcdot (0.01)$$

D:

$$6 \boldsymbol \boldcdot 154 \boldcdot (0.00001)$$

E:

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.

1. $$(0.01)\boldcdot (0.02)$$
2. $$(0.3) \boldcdot (0.2)$$
3. $$(1.2) \boldcdot 5$$
4. $$(0.9) \boldcdot (1.1)$$
5. $$(1.5)\boldcdot 2$$

### 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.

1. $$33.1+ 1.95$$
1. $$1.075 + 27.105$$
1. $$0.401+9.28$$

### Solution

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(From Unit 5, Lesson 3.)

### Problem 6

Calculate each difference. Show your reasoning.

1. $$13.2 - 1.78$$
1. $$23.11 - 0.376$$
1. $$0.9 - 0.245$$

### 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.