5TH GRADE MATH - MULTIPLY AND DIVIDE BY 10, 100 and 1000 ... - Free Printable

Let's solve each problem step by step and provide explanations.

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1. Solve the following problems

We are multiplying or dividing by powers of 10 (10, 100, 1000). When multiplying by 10, 100, or 1000, we move the decimal point to the right. When dividing, we move it to the left.

#### a. $ 33,000 \times 10 = $
- Multiply by 10 → move decimal one place to the right.
- $ 33,000 \times 10 = 330,000 $

#### b. $ 85,000 \div 10 = $
- Divide by 10 → move decimal one place to the left.
- $ 85,000 \div 10 = 8,500 $

#### c. $ 3.6 \times 10 = $
- Move decimal one place to the right.
- $ 3.6 \times 10 = 36 $

#### d. $ 3.6 \div 10 = $
- Move decimal one place to the left.
- $ 3.6 \div 10 = 0.36 $

#### e. $ 0.37 \times 100 = $
- Multiply by 100 → move decimal two places to the right.
- $ 0.37 \times 100 = 37 $

#### f. $ 37 \div 1,000 = $
- Divide by 1,000 → move decimal three places to the left.
- $ 37 \div 1,000 = 0.037 $

#### g. $ 5.21 \times 1,000 = $
- Multiply by 1,000 → move decimal three places to the right.
- $ 5.21 \times 1,000 = 5,210 $

#### h. $ 6,042.1 \div 100 = $
- Divide by 100 → move decimal two places to the left.
- $ 6,042.1 \div 100 = 60.421 $

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2. Find the products

#### a. $ 42,260 \times 10 = $
- Move decimal one place right → $ 422,600 $

#### b. $ 42,260 \times 100 = $
- Move decimal two places right → $ 4,226,000 $

#### c. $ 42,260 \times 1,000 = $
- Move decimal three places right → $ 42,260,000 $

#### d. Explain how you decided on the number of zeros in the products for (a), (b), and (c) above.

> When multiplying a whole number by a power of 10:
>
> - Multiply by 10: add one zero
> - Multiply by 100: add two zeros
> - Multiply by 1,000: add three zeros
>
> This is because multiplying by 10 shifts all digits one place to the left (adding a zero at the end), and so on.
>
> So:
> - $ 42,260 \times 10 = 422,600 $ → added one zero
> - $ 42,260 \times 100 = 4,226,000 $ → added two zeros
> - $ 42,260 \times 1,000 = 42,260,000 $ → added three zeros

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3. Find the quotients

#### a. $ 283 \div 10 = $
- Move decimal one place to the left → $ 28.3 $

#### b. $ 283 \div 100 = $
- Move decimal two places to the left → $ 2.83 $

#### c. $ 283 \div 1,000 = $
- Move decimal three places to the left → $ 0.283 $

#### d. Explain how you decided where to place the decimal in the quotients for (a), (b), and (c) above.

> When dividing by a power of 10, we move the decimal point to the left by the number of zeros in the divisor:
>
> - Dividing by 10 → move decimal 1 place left
> - Dividing by 100 → move decimal 2 places left
> - Dividing by 1,000 → move decimal 3 places left
>
> Since 283 has no visible decimal point, we can imagine it as $ 283.0 $. Then:
> - $ 283.0 \div 10 = 28.3 $
> - $ 283.0 \div 100 = 2.83 $
> - $ 283.0 \div 1,000 = 0.283 $

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✔ Final Answers:

#### 1.
a. 330,000
b. 8,500
c. 36
d. 0.36
e. 37
f. 0.037
g. 5,210
h. 60.421

#### 2.
a. 422,600
b. 4,226,000
c. 42,260,000
d. I added the same number of zeros as the number of zeros in the multiplier (10, 100, 1000), which corresponds to moving the decimal point right by that many places.

#### 3.
a. 28.3
b. 2.83
c. 0.283
d. I moved the decimal point to the left by the number of zeros in the divisor: 1 place for 10, 2 for 100, 3 for 1,000.

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