Fifth Grade Multiplying or Dividing by Powers of 10 Activity - Free Printable

Let's solve the problems on this worksheet step by step. The worksheet involves multiplying or dividing by powers of 10, which is a fundamental skill in working with decimals and scientific notation.

Key Concept:

When you multiply a number by a power of 10 (like $10^2$, $10^3$, etc.), you move the decimal point to the right by the number of zeros in the power of 10.

When you divide by a power of 10, you move the decimal point to the left by the number of zeros.

For example:
- $ 45 \times 10^3 = 45,000 $ → move decimal 3 places right
- $ 45 \div 10^3 = 0.045 $ → move decimal 3 places left

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Let’s go through each problem:

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Left Column: Multiplying or Dividing by Powers of 10

1. $ 45 \times 10^3 = ? $

- Move decimal 3 places right:
$ 45.0 \rightarrow 45000 $
- Answer: $ 45,000 $

2. $ 36,000 \div 10^2 = ? $

- Divide by 100 → move decimal 2 places left:
$ 36,000 \rightarrow 360 $
- Answer: $ 360 $

3. $ 7,000,000 \div 10^4 = ? $

- Divide by 10,000 → move decimal 4 places left:
$ 7,000,000 \rightarrow 700 $
- Answer: $ 700 $

4. $ 8 \times 10^2 = ? $

- Multiply by 100 → move decimal 2 places right:
$ 8.0 \rightarrow 800 $
- Answer: $ 800 $

5. $ 200,000 \times 10^1 = ? $

- Multiply by 10 → move decimal 1 place right:
$ 200,000 \rightarrow 2,000,000 $
- Answer: $ 2,000,000 $

6. $ 6.3 \times 10^4 = ? $

- Multiply by 10,000 → move decimal 4 places right:
$ 6.3 \rightarrow 63,000 $
- Answer: $ 63,000 $

7. $ 5.08 \times 10^3 = ? $

- Multiply by 1,000 → move decimal 3 places right:
$ 5.08 \rightarrow 5,080 $
- Answer: $ 5,080 $

8. $ 403 \times 10^1 = ? $

- Multiply by 10 → move decimal 1 place right:
$ 403 \rightarrow 4,030 $
- Answer: $ 4,030 $

9. $ 380 \div 10^2 = ? $

- Divide by 100 → move decimal 2 places left:
$ 380 \rightarrow 3.8 $
- Answer: $ 3.8 $

10. $ 80,000 \div 10^4 = ? $

- Divide by 10,000 → move decimal 4 places left:
$ 80,000 \rightarrow 8 $
- Answer: $ 8 $

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Right Column: Multiplying or Dividing by Powers of 10

1. $ 45 \times 10^2 = ? $

- Multiply by 100 → move decimal 2 places right:
$ 45 \rightarrow 4,500 $
- Answer: $ 4,500 $

2. $ 36,000 \div 10^3 = ? $

- Divide by 1,000 → move decimal 3 places left:
$ 36,000 \rightarrow 36 $
- Answer: $ 36 $

3. $ 7,000,000 \div 10^4 = ? $

- Already solved above: $ 7,000,000 \div 10,000 = 700 $
- Answer: $ 700 $

4. $ 8 \times 10^3 = ? $

- Multiply by 1,000 → move decimal 3 places right:
$ 8 \rightarrow 8,000 $
- Answer: $ 8,000 $

5. $ 200,000 \times 10^2 = ? $

- Multiply by 100 → move decimal 2 places right:
$ 200,000 \rightarrow 20,000,000 $
- Answer: $ 20,000,000 $

6. $ 6.3 \times 10^3 = ? $

- Multiply by 1,000 → move decimal 3 places right:
$ 6.3 \rightarrow 6,300 $
- Answer: $ 6,300 $

7. $ 5.08 \times 10^2 = ? $

- Multiply by 100 → move decimal 2 places right:
$ 5.08 \rightarrow 508 $
- Answer: $ 508 $

8. $ 403 \div 10^2 = ? $

- Divide by 100 → move decimal 2 places left:
$ 403 \rightarrow 4.03 $
- Answer: $ 4.03 $

9. $ 380 \div 10^1 = ? $

- Divide by 10 → move decimal 1 place left:
$ 380 \rightarrow 38 $
- Answer: $ 38 $

10. $ 80,000 \div 10^3 = ? $

- Divide by 1,000 → move decimal 3 places left:
$ 80,000 \rightarrow 80 $
- Answer: $ 80 $

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✔ Final Answers:

#### Left Column:
1. 45,000
2. 360
3. 700
4. 800
5. 2,000,000
6. 63,000
7. 5,080
8. 4,030
9. 3.8
10. 8

#### Right Column:
1. 4,500
2. 36
3. 700
4. 8,000
5. 20,000,000
6. 6,300
7. 508
8. 4.03
9. 38
10. 80

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📝 Summary Tip:

- Multiplying by $10^n$: Move decimal right $n$ times.
- Dividing by $10^n$: Move decimal left $n$ times.
- If there’s no visible decimal, it's at the end of the number (e.g., 45 = 45.0).

This method works quickly and efficiently for all such problems!