Multiplication and Division by Powers of 10 - Math Worksheets ... - Free Printable

Let's solve each problem step by step, using the rules of multiplying and dividing by powers of 10.

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🔹 Rule Reminder:

- When multiplying by $10^n$, move the decimal point n places to the right.
- When dividing by $10^n$, move the decimal point n places to the left.
- If there are not enough digits, add zeros as placeholders.

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## ✔ Part 1: Find the Product

We multiply each number by a power of 10.

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1. $5.93 \times 10^1 = 5.93 \times 10 = 59.3$
→ Move decimal 1 place right

2. $1.372 \times 10^3 = 1.372 \times 1000 = 1372$
→ Move decimal 3 places right

3. $0.83 \times 10^2 = 0.83 \times 100 = 83$
→ Move decimal 2 places right

4. $9.2 \times 10^5 = 9.2 \times 100000 = 920000$
→ Move decimal 5 places right

5. $44.2 \times 10^4 = 44.2 \times 10000 = 442000$
→ Move decimal 4 places right

6. $0.06 \times 10^1 = 0.06 \times 10 = 0.6$
→ Move decimal 1 place right

7. $6.101 \times 10^2 = 6.101 \times 100 = 610.1$
→ Move decimal 2 places right

8. $0.140 \times 10^2 = 0.140 \times 100 = 14.0$
→ Move decimal 2 places right

9. $0.0351 \times 10^3 = 0.0351 \times 1000 = 35.1$
→ Move decimal 3 places right

10. $13.13 \times 10^4 = 13.13 \times 10000 = 131300$
→ Move decimal 4 places right

11. $9.12 \times 10^3 = 9.12 \times 1000 = 9120$
→ Move decimal 3 places right

12. $80.93 \times 10^3 = 80.93 \times 1000 = 80930$
→ Move decimal 3 places right

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## ✔ Part 2: Find the Quotient

Now divide each number by a power of 10.

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1. $482 \div 10^1 = 482 \div 10 = 48.2$
→ Move decimal 1 place left

2. $6,214.7 \div 10^3 = 6,214.7 \div 1000 = 6.2147$
→ Move decimal 3 places left

3. $77.49 \div 10^2 = 77.49 \div 100 = 0.7749$
→ Move decimal 2 places left

4. $361.7 \div 10^5 = 361.7 \div 100000 = 0.003617$
→ Move decimal 5 places left (add zeros)

5. $45 \div 10^4 = 45 \div 10000 = 0.0045$
→ Move decimal 4 places left

6. $100.3 \div 10^1 = 100.3 \div 10 = 10.03$
→ Move decimal 1 place left

7. $502 \div 10^2 = 502 \div 100 = 5.02$
→ Move decimal 2 places left

8. $4.3 \div 10^2 = 4.3 \div 100 = 0.043$
→ Move decimal 2 places left

9. $293.3 \div 10^3 = 293.3 \div 1000 = 0.2933$
→ Move decimal 3 places left

10. $22.09 \div 10^4 = 22.09 \div 10000 = 0.002209$
→ Move decimal 4 places left

11. $14.52 \div 10^3 = 14.52 \div 1000 = 0.01452$
→ Move decimal 3 places left

12. $0.42 \div 10^3 = 0.42 \div 1000 = 0.00042$
→ Move decimal 3 places left

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✔ Final Answers:

#### Find the product:

| Expression | Answer |
|----------|--------|
| $5.93 \times 10^1$ | 59.3 |
| $1.372 \times 10^3$ | 1372 |
| $0.83 \times 10^2$ | 83 |
| $9.2 \times 10^5$ | 920000 |
| $44.2 \times 10^4$ | 442000 |
| $0.06 \times 10^1$ | 0.6 |
| $6.101 \times 10^2$ | 610.1 |
| $0.140 \times 10^2$ | 14.0 |
| $0.0351 \times 10^3$ | 35.1 |
| $13.13 \times 10^4$ | 131300 |
| $9.12 \times 10^3$ | 9120 |
| $80.93 \times 10^3$ | 80930 |

#### Find the quotient:

| Expression | Answer |
|----------|--------|
| $482 \div 10^1$ | 48.2 |
| $6,214.7 \div 10^3$ | 6.2147 |
| $77.49 \div 10^2$ | 0.7749 |
| $361.7 \div 10^5$ | 0.003617 |
| $45 \div 10^4$ | 0.0045 |
| $100.3 \div 10^1$ | 10.03 |
| $502 \div 10^2$ | 5.02 |
| $4.3 \div 10^2$ | 0.043 |
| $293.3 \div 10^3$ | 0.2933 |
| $22.09 \div 10^4$ | 0.002209 |
| $14.52 \div 10^3$ | 0.01452 |
| $0.42 \div 10^3$ | 0.00042 |

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Let me know if you'd like this in a printable format or need explanations for any specific one!