Multiplying Decimals by Powers of Ten Worksheets - Free Printable

Problem Description:

The task involves multiplying decimals by powers of ten (10, 100, 1000). The worksheet is divided into sections, each containing a decimal number to be multiplied by different powers of ten. The goal is to solve these multiplications and fill in the blanks.

Solution Approach:

When multiplying a decimal by a power of ten:
1. Identify the power of ten: Powers of ten are represented as 10, 100, 1000, etc.
2. Move the decimal point:
- For each zero in the power of ten, move the decimal point one place to the right.
- For example:
- Multiplying by 10 moves the decimal point 1 place to the right.
- Multiplying by 100 moves the decimal point 2 places to the right.
- Multiplying by 1000 moves the decimal point 3 places to the right.

Step-by-Step Solution:

#### Section I:
1. 12.5 × 10
- Move the decimal point 1 place to the right: \( 12.5 \rightarrow 125 \)
- Answer: 125

2. 12.5 × 100
- Move the decimal point 2 places to the right: \( 12.5 \rightarrow 1250 \)
- Answer: 1250

3. 12.5 × 1000
- Move the decimal point 3 places to the right: \( 12.5 \rightarrow 12500 \)
- Answer: 12500

#### Section II:
4. 0.02 × 10
- Move the decimal point 1 place to the right: \( 0.02 \rightarrow 0.2 \)
- Answer: 0.2

5. 0.02 × 100
- Move the decimal point 2 places to the right: \( 0.02 \rightarrow 2 \)
- Answer: 2

6. 0.02 × 1000
- Move the decimal point 3 places to the right: \( 0.02 \rightarrow 20 \)
- Answer: 20

#### Section III:
7. 1.17 × 10
- Move the decimal point 1 place to the right: \( 1.17 \rightarrow 11.7 \)
- Answer: 11.7

8. 1.17 × 100
- Move the decimal point 2 places to the right: \( 1.17 \rightarrow 117 \)
- Answer: 117

9. 1.17 × 1000
- Move the decimal point 3 places to the right: \( 1.17 \rightarrow 1170 \)
- Answer: 1170

#### Section IV:
10. 6.6 × 10
- Move the decimal point 1 place to the right: \( 6.6 \rightarrow 66 \)
- Answer: 66

11. 6.6 × 100
- Move the decimal point 2 places to the right: \( 6.6 \rightarrow 660 \)
- Answer: 660

12. 6.6 × 1000
- Move the decimal point 3 places to the right: \( 6.6 \rightarrow 6600 \)
- Answer: 6600

#### Section V:
13. 4.5932 × 10
- Move the decimal point 1 place to the right: \( 4.5932 \rightarrow 45.932 \)
- Answer: 45.932

14. 4.5932 × 100
- Move the decimal point 2 places to the right: \( 4.5932 \rightarrow 459.32 \)
- Answer: 459.32

15. 4.5932 × 1000
- Move the decimal point 3 places to the right: \( 4.5932 \rightarrow 4593.2 \)
- Answer: 4593.2

#### Section VI:
16. 86.89 × 10
- Move the decimal point 1 place to the right: \( 86.89 \rightarrow 868.9 \)
- Answer: 868.9

17. 86.89 × 100
- Move the decimal point 2 places to the right: \( 86.89 \rightarrow 8689 \)
- Answer: 8689

18. 86.89 × 1000
- Move the decimal point 3 places to the right: \( 86.89 \rightarrow 86890 \)
- Answer: 86890

#### Section VII:
19. 3.85 × 10
- Move the decimal point 1 place to the right: \( 3.85 \rightarrow 38.5 \)
- Answer: 38.5

20. 3.85 × 100
- Move the decimal point 2 places to the right: \( 3.85 \rightarrow 385 \)
- Answer: 385

21. 3.85 × 1000
- Move the decimal point 3 places to the right: \( 3.85 \rightarrow 3850 \)
- Answer: 3850

#### Section VIII:
22. 0.74 × 10
- Move the decimal point 1 place to the right: \( 0.74 \rightarrow 7.4 \)
- Answer: 7.4

23. 0.74 × 100
- Move the decimal point 2 places to the right: \( 0.74 \rightarrow 74 \)
- Answer: 74

24. 0.74 × 1000
- Move the decimal point 3 places to the right: \( 0.74 \rightarrow 740 \)
- Answer: 740

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{I} & 125, 1250, 12500 \\
\text{II} & 0.2, 2, 20 \\
\text{III} & 11.7, 117, 1170 \\
\text{IV} & 66, 660, 6600 \\
\text{V} & 45.932, 459.32, 4593.2 \\
\text{VI} & 868.9, 8689, 86890 \\
\text{VII} & 38.5, 385, 3850 \\
\text{VIII} & 7.4, 74, 740 \\
\end{array}
}
\]