Multiplying and Dividing by Powers of Ten Worksheet (15 Minute ... - Free Printable
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Step-by-step solution for: Multiplying and Dividing by Powers of Ten Worksheet (15 Minute ...
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Show Answer Key & Explanations
Step-by-step solution for: Multiplying and Dividing by Powers of Ten Worksheet (15 Minute ...
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.
---
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#### Problems 1–9: Multiply or Divide by Powers of Ten
1) $ 0.245 \times 10 = 2.45 $
→ Move decimal 1 place right.
2) $ 29.467 \div 100 = 0.29467 $
→ Move decimal 2 places left.
3) $ 9.3 \times 1000 = 9300 $
→ Move decimal 3 places right → 9.3 → 9300
4) $ 3891.1 \times 100 = 389110 $
→ Move decimal 2 places right.
5) $ 0.0987 \div 10 = 0.00987 $
→ Move decimal 1 place left.
6) $ 0.39 \div 100 = 0.0039 $
→ Move decimal 2 places left.
7) $ 1562 \times 1000 = 1,562,000 $
→ Move decimal 3 places right → 1562 → 1,562,000
8) $ 798.62 \div 1000 = 0.79862 $
→ Move decimal 3 places left.
9) $ 10.04 \times 10000 = 100,400 $
→ Move decimal 4 places right.
---
#### Problems 10–17: Find Missing Factor/Divisor
10) $ 3.88 \times ? = 38.8 $
→ 3.88 → 38.8 → moved 1 place right → ×10
✔ Answer: 10
11) $ 91.2 \div ? = 0.912 $
→ 91.2 → 0.912 → moved 2 places left → ÷100
✔ Answer: 100
12) $ 1.34 \times ? = 1340 $
→ 1.34 → 1340 → moved 3 places right → ×1000
✔ Answer: 1000
13) $ 0.011 \div ? = 0.0011 $
→ 0.011 → 0.0011 → moved 1 place left → ÷10
✔ Answer: 10
14) $ 100 \times ? = 200.56 $
→ 100 → 200.56 → need to find what multiplied by 100 gives 200.56
→ $ ? = 200.56 \div 100 = 2.0056 $
✔ Answer: 2.0056
15) $ 1000 \times ? = 3 $
→ $ ? = 3 \div 1000 = 0.003 $
✔ Answer: 0.003
16) $ 10 \times ? = 589.99 $
→ $ ? = 589.99 \div 10 = 58.999 $
✔ Answer: 58.999
17) $ ? \times 10 = 0.2 $
→ $ ? = 0.2 \div 10 = 0.02 $
✔ Answer: 0.02
---
#### Problems 18–26: More Multiplication/Division
18) $ 0.505 \times 100 = 50.5 $
→ Move decimal 2 places right.
19) $ 1.334 \div 10 = 0.1334 $
→ Move decimal 1 place left.
20) $ 248.6 \div 1000 = 0.2486 $
→ Move decimal 3 places left.
21) $ 662.1 \div 100 = 6.621 $
→ Move decimal 2 places left.
22) $ 0.0042 \times 10 = 0.042 $
→ Move decimal 1 place right.
23) $ 53.1 \times 100 = 5310 $
→ Move decimal 2 places right.
24) $ 2028 \div 1000 = 2.028 $
→ Move decimal 3 places left.
25) $ 95.13 \times 1000 = 95130 $
→ Move decimal 3 places right.
26) $ 4 \div 1000 = 0.004 $
→ Move decimal 3 places left.
---
#### Problems 27–30: Find Missing Divisor/Multiplier
27) $ 6.01 \div ? = 0.601 $
→ 6.01 → 0.601 → moved 1 place left → ÷10
✔ Answer: 10
28) $ 0.042 \times ? = 4.2 $
→ 0.042 → 4.2 → moved 2 places right → ×100
✔ Answer: 100
29) $ 75.002 \times ? = 7500.2 $
→ 75.002 → 7500.2 → moved 2 places right → ×100
✔ Answer: 100
30) $ 45 \div ? = 0.0045 $
→ 45 → 0.0045 → moved 4 places left → ÷10000
✔ Answer: 10000
---
#### Problems 31–34: Find Missing Number
31) $ ? \div 10 = 474.99 $
→ $ ? = 474.99 \times 10 = 4749.9 $
✔ Answer: 4749.9
32) $ ? \div 100 = 5 $
→ $ ? = 5 \times 100 = 500 $
✔ Answer: 500
33) $ ? \div 1000 = 10.81 $
→ $ ? = 10.81 \times 1000 = 10810 $
✔ Answer: 10810
34) $ ? \div 10 = 0.007 $
→ $ ? = 0.007 \times 10 = 0.07 $
✔ Answer: 0.07
---
| # | 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 | 95130 |
| 26 | 0.004 |
| 27 | 10 |
| 28 | 100 |
| 29 | 100 |
| 30 | 10000 |
| 31 | 4749.9 |
| 32 | 500 |
| 33 | 10810 |
| 34 | 0.07 |
---
- ×10: Move decimal 1 right
- ×100: Move decimal 2 right
- ×1000: Move decimal 3 right
- ÷10: Move decimal 1 left
- ÷100: Move decimal 2 left
- ÷1000: Move decimal 3 left
This skill helps with understanding place value and simplifying calculations involving decimals.
Let me know if you'd like this as a printable PDF or want explanations for any specific problem!
> 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.
---
✔ Let's go through each problem:
---
#### Problems 1–9: Multiply or Divide by Powers of Ten
1) $ 0.245 \times 10 = 2.45 $
→ Move decimal 1 place right.
2) $ 29.467 \div 100 = 0.29467 $
→ Move decimal 2 places left.
3) $ 9.3 \times 1000 = 9300 $
→ Move decimal 3 places right → 9.3 → 9300
4) $ 3891.1 \times 100 = 389110 $
→ Move decimal 2 places right.
5) $ 0.0987 \div 10 = 0.00987 $
→ Move decimal 1 place left.
6) $ 0.39 \div 100 = 0.0039 $
→ Move decimal 2 places left.
7) $ 1562 \times 1000 = 1,562,000 $
→ Move decimal 3 places right → 1562 → 1,562,000
8) $ 798.62 \div 1000 = 0.79862 $
→ Move decimal 3 places left.
9) $ 10.04 \times 10000 = 100,400 $
→ Move decimal 4 places right.
---
#### Problems 10–17: Find Missing Factor/Divisor
10) $ 3.88 \times ? = 38.8 $
→ 3.88 → 38.8 → moved 1 place right → ×10
✔ Answer: 10
11) $ 91.2 \div ? = 0.912 $
→ 91.2 → 0.912 → moved 2 places left → ÷100
✔ Answer: 100
12) $ 1.34 \times ? = 1340 $
→ 1.34 → 1340 → moved 3 places right → ×1000
✔ Answer: 1000
13) $ 0.011 \div ? = 0.0011 $
→ 0.011 → 0.0011 → moved 1 place left → ÷10
✔ Answer: 10
14) $ 100 \times ? = 200.56 $
→ 100 → 200.56 → need to find what multiplied by 100 gives 200.56
→ $ ? = 200.56 \div 100 = 2.0056 $
✔ Answer: 2.0056
15) $ 1000 \times ? = 3 $
→ $ ? = 3 \div 1000 = 0.003 $
✔ Answer: 0.003
16) $ 10 \times ? = 589.99 $
→ $ ? = 589.99 \div 10 = 58.999 $
✔ Answer: 58.999
17) $ ? \times 10 = 0.2 $
→ $ ? = 0.2 \div 10 = 0.02 $
✔ Answer: 0.02
---
#### Problems 18–26: More Multiplication/Division
18) $ 0.505 \times 100 = 50.5 $
→ Move decimal 2 places right.
19) $ 1.334 \div 10 = 0.1334 $
→ Move decimal 1 place left.
20) $ 248.6 \div 1000 = 0.2486 $
→ Move decimal 3 places left.
21) $ 662.1 \div 100 = 6.621 $
→ Move decimal 2 places left.
22) $ 0.0042 \times 10 = 0.042 $
→ Move decimal 1 place right.
23) $ 53.1 \times 100 = 5310 $
→ Move decimal 2 places right.
24) $ 2028 \div 1000 = 2.028 $
→ Move decimal 3 places left.
25) $ 95.13 \times 1000 = 95130 $
→ Move decimal 3 places right.
26) $ 4 \div 1000 = 0.004 $
→ Move decimal 3 places left.
---
#### Problems 27–30: Find Missing Divisor/Multiplier
27) $ 6.01 \div ? = 0.601 $
→ 6.01 → 0.601 → moved 1 place left → ÷10
✔ Answer: 10
28) $ 0.042 \times ? = 4.2 $
→ 0.042 → 4.2 → moved 2 places right → ×100
✔ Answer: 100
29) $ 75.002 \times ? = 7500.2 $
→ 75.002 → 7500.2 → moved 2 places right → ×100
✔ Answer: 100
30) $ 45 \div ? = 0.0045 $
→ 45 → 0.0045 → moved 4 places left → ÷10000
✔ Answer: 10000
---
#### Problems 31–34: Find Missing Number
31) $ ? \div 10 = 474.99 $
→ $ ? = 474.99 \times 10 = 4749.9 $
✔ Answer: 4749.9
32) $ ? \div 100 = 5 $
→ $ ? = 5 \times 100 = 500 $
✔ Answer: 500
33) $ ? \div 1000 = 10.81 $
→ $ ? = 10.81 \times 1000 = 10810 $
✔ Answer: 10810
34) $ ? \div 10 = 0.007 $
→ $ ? = 0.007 \times 10 = 0.07 $
✔ Answer: 0.07
---
✔ Final Answers:
| # | 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 | 95130 |
| 26 | 0.004 |
| 27 | 10 |
| 28 | 100 |
| 29 | 100 |
| 30 | 10000 |
| 31 | 4749.9 |
| 32 | 500 |
| 33 | 10810 |
| 34 | 0.07 |
---
📌 Summary of Rules Used:
- ×10: Move decimal 1 right
- ×100: Move decimal 2 right
- ×1000: Move decimal 3 right
- ÷10: Move decimal 1 left
- ÷100: Move decimal 2 left
- ÷1000: Move decimal 3 left
This skill helps with understanding place value and simplifying calculations involving decimals.
Let me know if you'd like this as a printable PDF or want explanations for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of multiplying and dividing by powers of 10 worksheet.
