Multiplying and Dividing Powers of Ten Worksheet Download - Free Printable

Let's solve each problem in the worksheet "Multiplying and Dividing Powers of Ten" step by step, using the rules for multiplying and dividing by powers of 10.

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🔷 Key Concepts:

- When you multiply a number by $10^n$, move the decimal point n places to the right.
- When you divide a number by $10^n$, move the decimal point n places to the left.
- For negative exponents: $10^{-n} = \frac{1}{10^n}$, so dividing by $10^n$ is the same as multiplying by $10^{-n}$.

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Now, let’s go through each problem:

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1) $489.22 \div 10^4$

- $10^4 = 10,000$
- Move decimal 4 places left:
- $489.22 \to 0.048922$

✔ Answer: $0.048922$

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2) $18.995 \times 10^1$

- Multiply by 10 → move decimal 1 place right
- $18.995 \to 189.95$

✔ Answer: $189.95$

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3) $294.32 \div 10^1$

- Divide by 10 → move decimal 1 place left
- $294.32 \to 29.432$

✔ Answer: $29.432$

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4) $327.498 \times 10^1$

- Multiply by 10 → move decimal 1 place right
- $327.498 \to 3,274.98$

✔ Answer: $3,274.98$

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5) $8.72 \div 10^1$

- Divide by 10 → move decimal 1 place left
- $8.72 \to 0.872$

✔ Answer: $0.872$

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6) $163.761 \times 10^4$

- Multiply by $10^4 = 10,000$ → move decimal 4 places right
- $163.761 \to 1,637,610$

✔ Answer: $1,637,610$

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7) $6.41 \div 10^1$

- Divide by 10 → move decimal 1 place left
- $6.41 \to 0.641$

✔ Answer: $0.641$

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8) $847.5 \times 10^2$

- Multiply by $10^2 = 100$ → move decimal 2 places right
- $847.5 \to 84,750$

✔ Answer: $84,750$

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9) $4.56 \div 10^1$

- Divide by 10 → move decimal 1 place left
- $4.56 \to 0.456$

✔ Answer: $0.456$

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10) $747.3 \times 10^1$

- Multiply by 10 → move decimal 1 place right
- $747.3 \to 7,473$

✔ Answer: $7,473$

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11) $56.99 \div 10^2$

- Divide by $10^2 = 100$ → move decimal 2 places left
- $56.99 \to 0.5699$

Wait — the answer key says 0.5699, but the provided answer is written as 0.5699? Let's check.

Actually, the answer key says: 0.5699 → but wait, it shows 0.5699? No, the answer key says 0.5699, but the printed answer is 0.5699?

Wait — the image shows:
> 11. 0.5699

But our calculation:
$56.99 \div 100 = 0.5699$

✔ Answer: $0.5699$

Wait — but the answer key says 0.5699? Yes, that matches.

But the original image has:

> 11. 0.5699

Yes — correct.

✔ Answer: $0.5699$

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12) $843.12 \times 10^1$

- Multiply by 10 → move decimal 1 place right
- $843.12 \to 8,431.2$

✔ Answer: $8,431.2$

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13) $7.15 \div 10^4$

- Divide by $10^4 = 10,000$ → move decimal 4 places left
- $7.15 \to 0.000715$

✔ Answer: $0.000715$

But the answer key says 0.000715? Wait — it shows:

> 13. 0.000715

Yes — matches.

✔ Answer: $0.000715$

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14) $23.745 \times 10^4$

- Multiply by $10^4 = 10,000$ → move decimal 4 places right
- $23.745 \to 237,450$

✔ Answer: $237,450$

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15) $335.668 \div 10^1$

- Divide by 10 → move decimal 1 place left
- $335.668 \to 33.5668$

✔ Answer: $33.5668$

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16) $95.81 \times 10^4$

- Multiply by $10^4 = 10,000$ → move decimal 4 places right
- $95.81 \to 958,100$

✔ Answer: $958,100$

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17) $1.7 \div 10^2$

- Divide by $10^2 = 100$ → move decimal 2 places left
- $1.7 \to 0.017$

✔ Answer: $0.017$

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18) $67.296 \times 10^2$

- Multiply by $10^2 = 100$ → move decimal 2 places right
- $67.296 \to 6,729.6$

✔ Answer: $6,729.6$

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19) $837.892 \div 10^2$

- Divide by $10^2 = 100$ → move decimal 2 places left
- $837.892 \to 8.37892$

✔ Answer: $8.37892$

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20) $22.411 \times 10^3$

- Multiply by $10^3 = 1,000$ → move decimal 3 places right
- $22.411 \to 22,411$

✔ Answer: $22,411$

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✔ Final Answers (Matched with Answer Key):

| Problem | Answer |
|--------|--------|
| 1 | 0.048922 |
| 2 | 189.95 |
| 3 | 29.432 |
| 4 | 3,274.98 |
| 5 | 0.872 |
| 6 | 1,637,610 |
| 7 | 0.641 |
| 8 | 84,750 |
| 9 | 0.456 |
| 10 | 7,473 |
| 11 | 0.5699 |
| 12 | 8,431.2 |
| 13 | 0.000715 |
| 14 | 237,450 |
| 15 | 33.5668 |
| 16 | 958,100 |
| 17 | 0.017 |
| 18 | 6,729.6 |
| 19 | 8.37892 |
| 20 | 22,411 |

All answers match the provided Answer Key.

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📌 Summary of Rules Used:

- Multiplication by $10^n$: Move decimal right n times.
- Division by $10^n$: Move decimal left n times.
- Always add zeros if needed to maintain place value.

This skill is essential in scientific notation and real-world applications like measuring very large or small quantities.

Let me know if you'd like this explained in video format or with visual examples!