Multiplying and Dividing by Powers of 10 worksheet with exercises for calculating products and quotients.

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

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🔹 Multiplying by Powers of 10

When you multiply a number by $10^n$, move the decimal point n places to the right.

- If $n$ is positive → move right.
- If $n$ is negative → move left.

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#### ✔ Find the product:

1. $5.93 \times 10^1 = 5.93 \times 10 = 59.3$
2. $0.83 \times 10^2 = 0.83 \times 100 = 83$
3. $44.2 \times 10^4 = 44.2 \times 10,000 = 442,000$
4. $6.101 \times 10^2 = 6.101 \times 100 = 610.1$
5. $0.0351 \times 10^3 = 0.0351 \times 1,000 = 35.1$
6. $9.12 \times 10^3 = 9.12 \times 1,000 = 9,120$

7. $1.372 \times 10^3 = 1.372 \times 1,000 = 1,372$
8. $9.2 \times 10^5 = 9.2 \times 100,000 = 920,000$
9. $0.06 \times 10^1 = 0.06 \times 10 = 0.6$
10. $0.140 \times 10^2 = 0.140 \times 100 = 14.0$
11. $13.13 \times 10^4 = 13.13 \times 10,000 = 131,300$
12. $80.93 \times 10^3 = 80.93 \times 1,000 = 80,930$

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🔹 Dividing by Powers of 10

When you divide a number by $10^n$, move the decimal point n places to the left.

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#### ✔ Find the quotient:

1. $482 \div 10^1 = 482 \div 10 = 48.2$
2. $77.49 \div 10^2 = 77.49 \div 100 = 0.7749$
3. $45 \div 10^4 = 45 \div 10,000 = 0.0045$
4. $502 \div 10^2 = 502 \div 100 = 5.02$
5. $293.3 \div 10^3 = 293.3 \div 1,000 = 0.2933$
6. $14.52 \div 10^3 = 14.52 \div 1,000 = 0.01452$

7. $6,214.7 \div 10^3 = 6,214.7 \div 1,000 = 6.2147$
8. $361.7 \div 10^5 = 361.7 \div 100,000 = 0.003617$
9. $100.3 \div 10^1 = 100.3 \div 10 = 10.03$
10. $4.3 \div 10^2 = 4.3 \div 100 = 0.043$
11. $22.09 \div 10^4 = 22.09 \div 10,000 = 0.002209$
12. $0.42 \div 10^3 = 0.42 \div 1,000 = 0.00042$

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✔ Final Answers:

#### Find the product:
| Problem | Answer |
|--------|--------|
| $5.93 \times 10^1$ | 59.3 |
| $0.83 \times 10^2$ | 83 |
| $44.2 \times 10^4$ | 442,000 |
| $6.101 \times 10^2$ | 610.1 |
| $0.0351 \times 10^3$ | 35.1 |
| $9.12 \times 10^3$ | 9,120 |
| $1.372 \times 10^3$ | 1,372 |
| $9.2 \times 10^5$ | 920,000 |
| $0.06 \times 10^1$ | 0.6 |
| $0.140 \times 10^2$ | 14.0 |
| $13.13 \times 10^4$ | 131,300 |
| $80.93 \times 10^3$ | 80,930 |

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

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📌 Key Rule Recap:

- Multiply by $10^n$: Move decimal right $n$ places.
- Divide by $10^n$: Move decimal left $n$ places.

Let me know if you'd like this in a printable format!