Math worksheet featuring practice problems for multiplying and dividing decimals by powers of 10.

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 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:
1. $5.93 \times 10^1 = \boxed{59.3}$
2. $0.83 \times 10^2 = \boxed{83}$
3. $44.2 \times 10^4 = \boxed{442000}$
4. $6.101 \times 10^2 = \boxed{610.1}$
5. $0.0351 \times 10^3 = \boxed{35.1}$
6. $9.12 \times 10^3 = \boxed{9120}$

7. $1.372 \times 10^3 = \boxed{1372}$
8. $9.2 \times 10^5 = \boxed{920000}$
9. $0.06 \times 10^1 = \boxed{0.6}$
10. $0.140 \times 10^2 = \boxed{14.0}$
11. $13.13 \times 10^4 = \boxed{131300}$
12. $80.93 \times 10^3 = \boxed{80930}$

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#### Find the quotient:
1. $482 \div 10^1 = \boxed{48.2}$
2. $77.49 \div 10^2 = \boxed{0.7749}$
3. $45 \div 10^4 = \boxed{0.0045}$
4. $502 \div 10^2 = \boxed{5.02}$
5. $293.3 \div 10^3 = \boxed{0.2933}$
6. $14.52 \div 10^3 = \boxed{0.01452}$

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

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📝 Summary:

- Multiplying by $10^n$: Move decimal right $n$ places.
- Dividing by $10^n$: Move decimal left $n$ places.

This method works for any power of 10, and helps simplify scientific notation problems efficiently!