This worksheet helps students practice multiplying and dividing decimal numbers by powers of 10, reinforcing place value concepts.
Math worksheet with multiplication and division problems using powers of 10 with decimal numbers and answer boxes
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Step-by-step solution for: Multiplication and Division by Powers of 10 - Math Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Multiplication and Division by Powers of 10 - Math Worksheets ...
You're working on a worksheet from SplashLearn titled “Multiplying and Dividing by Powers of 10”. The goal is to compute products (multiplication) and quotients (division) involving powers of 10.
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## 📌 Key Concept:
When you multiply a number by a power of 10 (like 10¹, 10², etc.), you move the decimal point to the right by the number of zeros in the power of 10.
When you divide a number by a power of 10, you move the decimal point to the left by the number of zeros in the power of 10.
Examples:
- `5.93 × 10¹ = 59.3` → move decimal 1 place right
- `482 ÷ 10¹ = 48.2` → move decimal 1 place left
---
# ✔ SECTION 1: Find the Product (Multiply by Powers of 10)
We'll go row by row.
---
1. 5.93 × 10¹
→ Move decimal 1 place right → 59.3
2. 0.83 × 10²
→ Move decimal 2 places right → 83
3. 44.2 × 10⁴
→ Move decimal 4 places right → 442,000
4. 6.101 × 10²
→ Move decimal 2 places right → 610.1
5. 0.0351 × 10³
→ Move decimal 3 places right → 35.1
6. 9.12 × 10³
→ Move decimal 3 places right → 9,120
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7. 1.372 × 10³
→ Move decimal 3 places right → 1,372
8. 9.2 × 10⁵
→ Move decimal 5 places right → 920,000
9. 0.06 × 10¹
→ Move decimal 1 place right → 0.6
10. 0.140 × 10²
→ Move decimal 2 places right → 14.0 (or just 14)
11. 13.13 × 10⁴
→ Move decimal 4 places right → 131,300
12. 80.93 × 10³
→ Move decimal 3 places right → 80,930
---
# ✔ SECTION 2: Find the Quotient (Divide by Powers of 10)
Now we divide — move decimal point left.
---
1. 482 ÷ 10¹
→ Move decimal 1 place left → 48.2
2. 77.49 ÷ 10²
→ Move decimal 2 places left → 0.7749
3. 45 ÷ 10⁴
→ Move decimal 4 places left → 0.0045
4. 502 ÷ 10²
→ Move decimal 2 places left → 5.02
5. 293.3 ÷ 10³
→ Move decimal 3 places left → 0.2933
6. 14.52 ÷ 10³
→ Move decimal 3 places left → 0.01452
---
7. 6,214.7 ÷ 10³
→ Move decimal 3 places left → 6.2147
8. 361.7 ÷ 10⁵
→ Move decimal 5 places left → 0.003617
9. 100.3 ÷ 10¹
→ Move decimal 1 place left → 10.03
10. 4.3 ÷ 10²
→ Move decimal 2 places left → 0.043
11. 22.09 ÷ 10⁴
→ Move decimal 4 places left → 0.002209
12. 0.42 ÷ 10³
→ Move decimal 3 places left → 0.00042
---
# 🧾 Final Answers Summary:
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## 🔢 Find the Product:
| Problem | Answer |
|-----------------------|------------|
| 5.93 × 10¹ | 59.3 |
| 0.83 × 10² | 83 |
| 44.2 × 10⁴ | 442,000|
| 6.101 × 10² | 610.1 |
| 0.0351 × 10³ | 35.1 |
| 9.12 × 10³ | 9,120 |
| 1.372 × 10³ | 1,372 |
| 9.2 × 10⁵ | 920,000|
| 0.06 × 10¹ | 0.6 |
| 0.140 × 10² | 14 |
| 13.13 × 10⁴ | 131,300|
| 80.93 × 10³ | 80,930 |
---
## ➗ Find the Quotient:
| Problem | Answer |
|-----------------------|--------------|
| 482 ÷ 10¹ | 48.2 |
| 77.49 ÷ 10² | 0.7749 |
| 45 ÷ 10⁴ | 0.0045 |
| 502 ÷ 10² | 5.02 |
| 293.3 ÷ 10³ | 0.2933 |
| 14.52 ÷ 10³ | 0.01452 |
| 6,214.7 ÷ 10³ | 6.2147 |
| 361.7 ÷ 10⁵ | 0.003617 |
| 100.3 ÷ 10¹ | 10.03 |
| 4.3 ÷ 10² | 0.043 |
| 22.09 ÷ 10⁴ | 0.002209 |
| 0.42 ÷ 10³ | 0.00042 |
---
✔ You’re all set! Just fill in the boxes with these answers. Let me know if you want this as a printable answer sheet or need help understanding any step!
---
## 📌 Key Concept:
When you multiply a number by a power of 10 (like 10¹, 10², etc.), you move the decimal point to the right by the number of zeros in the power of 10.
When you divide a number by a power of 10, you move the decimal point to the left by the number of zeros in the power of 10.
Examples:
- `5.93 × 10¹ = 59.3` → move decimal 1 place right
- `482 ÷ 10¹ = 48.2` → move decimal 1 place left
---
# ✔ SECTION 1: Find the Product (Multiply by Powers of 10)
We'll go row by row.
---
Left Column:
1. 5.93 × 10¹
→ Move decimal 1 place right → 59.3
2. 0.83 × 10²
→ Move decimal 2 places right → 83
3. 44.2 × 10⁴
→ Move decimal 4 places right → 442,000
4. 6.101 × 10²
→ Move decimal 2 places right → 610.1
5. 0.0351 × 10³
→ Move decimal 3 places right → 35.1
6. 9.12 × 10³
→ Move decimal 3 places right → 9,120
---
Right Column:
7. 1.372 × 10³
→ Move decimal 3 places right → 1,372
8. 9.2 × 10⁵
→ Move decimal 5 places right → 920,000
9. 0.06 × 10¹
→ Move decimal 1 place right → 0.6
10. 0.140 × 10²
→ Move decimal 2 places right → 14.0 (or just 14)
11. 13.13 × 10⁴
→ Move decimal 4 places right → 131,300
12. 80.93 × 10³
→ Move decimal 3 places right → 80,930
---
# ✔ SECTION 2: Find the Quotient (Divide by Powers of 10)
Now we divide — move decimal point left.
---
Left Column:
1. 482 ÷ 10¹
→ Move decimal 1 place left → 48.2
2. 77.49 ÷ 10²
→ Move decimal 2 places left → 0.7749
3. 45 ÷ 10⁴
→ Move decimal 4 places left → 0.0045
4. 502 ÷ 10²
→ Move decimal 2 places left → 5.02
5. 293.3 ÷ 10³
→ Move decimal 3 places left → 0.2933
6. 14.52 ÷ 10³
→ Move decimal 3 places left → 0.01452
---
Right Column:
7. 6,214.7 ÷ 10³
→ Move decimal 3 places left → 6.2147
8. 361.7 ÷ 10⁵
→ Move decimal 5 places left → 0.003617
9. 100.3 ÷ 10¹
→ Move decimal 1 place left → 10.03
10. 4.3 ÷ 10²
→ Move decimal 2 places left → 0.043
11. 22.09 ÷ 10⁴
→ Move decimal 4 places left → 0.002209
12. 0.42 ÷ 10³
→ Move decimal 3 places left → 0.00042
---
# 🧾 Final Answers Summary:
---
## 🔢 Find the Product:
| Problem | Answer |
|-----------------------|------------|
| 5.93 × 10¹ | 59.3 |
| 0.83 × 10² | 83 |
| 44.2 × 10⁴ | 442,000|
| 6.101 × 10² | 610.1 |
| 0.0351 × 10³ | 35.1 |
| 9.12 × 10³ | 9,120 |
| 1.372 × 10³ | 1,372 |
| 9.2 × 10⁵ | 920,000|
| 0.06 × 10¹ | 0.6 |
| 0.140 × 10² | 14 |
| 13.13 × 10⁴ | 131,300|
| 80.93 × 10³ | 80,930 |
---
## ➗ Find the Quotient:
| Problem | Answer |
|-----------------------|--------------|
| 482 ÷ 10¹ | 48.2 |
| 77.49 ÷ 10² | 0.7749 |
| 45 ÷ 10⁴ | 0.0045 |
| 502 ÷ 10² | 5.02 |
| 293.3 ÷ 10³ | 0.2933 |
| 14.52 ÷ 10³ | 0.01452 |
| 6,214.7 ÷ 10³ | 6.2147 |
| 361.7 ÷ 10⁵ | 0.003617 |
| 100.3 ÷ 10¹ | 10.03 |
| 4.3 ÷ 10² | 0.043 |
| 22.09 ÷ 10⁴ | 0.002209 |
| 0.42 ÷ 10³ | 0.00042 |
---
✔ You’re all set! Just fill in the boxes with these answers. Let me know if you want this as a printable answer sheet or need help understanding any step!
Parent Tip: Review the logic above to help your child master the concept of worksheet multiplying and dividing powers.
