Math worksheet for practicing multiplying and dividing by powers of ten.

Let's solve this worksheet step by step. The task is to multiply and divide decimals by powers of ten (10, 100, 1000, etc.). The key rule is:

> When multiplying by a power of 10, move the decimal point to the right by the number of zeros in the power of 10.
> When dividing by a power of 10, move the decimal point to the left by the number of zeros.

We'll go through each problem.

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Problems 1–9 & 18–26: Direct Multiplication/Division

#### 1) $ 0.245 \times 10 = $
Move decimal 1 place right → 2.45

#### 2) $ 29.467 \div 100 = $
Move decimal 2 places left → 0.29467

#### 3) $ 9.3 \times 1000 = $
Move decimal 3 places right → 9300

#### 4) $ 3891.1 \times 100 = $
Move decimal 2 places right → 389110

#### 5) $ 0.0987 \div 10 = $
Move decimal 1 place left → 0.00987

#### 6) $ 0.39 \div 100 = $
Move decimal 2 places left → 0.0039

#### 7) $ 1562 \times 1000 = $
Move decimal 3 places right → 1,562,000

#### 8) $ 798.62 \div 1000 = $
Move decimal 3 places left → 0.79862

#### 9) $ 10.04 \times 10000 = $
Move decimal 4 places right → 100,400

#### 18) $ 0.505 \times 100 = $
Move decimal 2 places right → 50.5

#### 19) $ 1.334 \div 10 = $
Move decimal 1 place left → 0.1334

#### 20) $ 248.6 \div 1000 = $
Move decimal 3 places left → 0.2486

#### 21) $ 662.1 \div 100 = $
Move decimal 2 places left → 6.621

#### 22) $ 0.0042 \times 10 = $
Move decimal 1 place right → 0.042

#### 23) $ 53.1 \times 100 = $
Move decimal 2 places right → 5310

#### 24) $ 2028 \div 1000 = $
Move decimal 3 places left → 2.028

#### 25) $ 95.13 \times 1000 = $
Move decimal 3 places right → 95,130

#### 26) $ 4 \div 1000 = $
Move decimal 3 places left → 0.004

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Problems 10–17 & 27–34: Find the Missing Number

These require working backwards using inverse operations.

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#### 10) $ 3.88 \times \boxed{?} = 38.8 $

We see that 3.88 becomes 38.8 → decimal moved 1 place right → multiplied by 10

→ Answer: 10

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#### 11) $ 91.2 \div \boxed{?} = 0.912 $

91.2 → 0.912 → decimal moved 2 places left → divided by 100

→ Answer: 100

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#### 12) $ 1.34 \times \boxed{?} = 1340 $

1.34 → 1340 → decimal moved 3 places right → ×1000

→ Answer: 1000

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#### 13) $ 0.011 \div \boxed{?} = 0.0011 $

0.011 → 0.0011 → decimal moved 1 place left → ÷10

→ Answer: 10

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#### 14) $ 100 \times \boxed{?} = 200.56 $

100 × ? = 200.56 → ? = 200.56 ÷ 100 = 2.0056

→ Answer: 2.0056

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#### 15) $ 1000 \times \boxed{?} = 3 $

? = 3 ÷ 1000 = 0.003

→ Answer: 0.003

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#### 16) $ 10 \times \boxed{?} = 589.99 $

? = 589.99 ÷ 10 = 58.999

→ Answer: 58.999

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#### 17) $ \boxed{?} \times 10 = 0.2 $

? = 0.2 ÷ 10 = 0.02

→ Answer: 0.02

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#### 27) $ 6.01 \div \boxed{?} = 0.601 $

6.01 → 0.601 → decimal moved 1 place left → ÷10

→ Answer: 10

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#### 28) $ 0.042 \times \boxed{?} = 4.2 $

0.042 → 4.2 → decimal moved 2 places right → ×100

→ Answer: 100

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#### 29) $ 75.002 \times \boxed{?} = 7500.2 $

75.002 → 7500.2 → decimal moved 2 places right → ×100

→ Answer: 100

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#### 30) $ 45 \div \boxed{?} = 0.0045 $

45 → 0.0045 → decimal moved 4 places left → ÷10,000

→ Answer: 10,000

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#### 31) $ \boxed{?} \div 10 = 474.99 $

? = 474.99 × 10 = 4749.9

→ Answer: 4749.9

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#### 32) $ \boxed{?} \div 100 = 5 $

? = 5 × 100 = 500

→ Answer: 500

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#### 33) $ \boxed{?} \div 1000 = 10.81 $

? = 10.81 × 1000 = 10,810

→ Answer: 10,810

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#### 34) $ \boxed{?} \div 10 = 0.007 $

? = 0.007 × 10 = 0.07

→ Answer: 0.07

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 2.45 |
| 2 | 0.29467 |
| 3 | 9300 |
| 4 | 389110 |
| 5 | 0.00987 |
| 6 | 0.0039 |
| 7 | 1,562,000 |
| 8 | 0.79862 |
| 9 | 100,400 |
| 10 | 10 |
| 11 | 100 |
| 12 | 1000 |
| 13 | 10 |
| 14 | 2.0056 |
| 15 | 0.003 |
| 16 | 58.999 |
| 17 | 0.02 |
| 18 | 50.5 |
| 19 | 0.1334 |
| 20 | 0.2486 |
| 21 | 6.621 |
| 22 | 0.042 |
| 23 | 5310 |
| 24 | 2.028 |
| 25 | 95,130 |
| 26 | 0.004 |
| 27 | 10 |
| 28 | 100 |
| 29 | 100 |
| 30 | 10,000 |
| 31 | 4749.9 |
| 32 | 500 |
| 33 | 10,810 |
| 34 | 0.07 |

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📝 Summary Tips:

- When multiplying by 10, 100, 1000... → move decimal right
- When dividing by 10, 100, 1000... → move decimal left
- For missing numbers: use inverse operations (division for multiplication, multiplication for division)

This helps build fluency with decimals and powers of ten — essential for real-world math! 😊