Multiplying with Powers of Ten math worksheet with 15 multiplication problems.

Problem: Multiplying with Powers of Ten

The task involves solving multiplication problems, many of which involve multiplying by powers of ten (e.g., 10, 100, 1,000). Let's solve each problem step by step.

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#### Row 1:
1. 684 × 10 =
- When multiplying by 10, simply add one zero to the end of the number.
- Answer: \( 684 \times 10 = 6,840 \)

2. 569 × 1,000 =
- When multiplying by 1,000, add three zeros to the end of the number.
- Answer: \( 569 \times 1,000 = 569,000 \)

3. 333 × 4,000 =
- First, multiply 333 by 4: \( 333 \times 4 = 1,332 \).
- Then, multiply by 1,000 (add three zeros): \( 1,332 \times 1,000 = 1,332,000 \).
- Answer: \( 333 \times 4,000 = 1,332,000 \)

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#### Row 2:
4. 145 × 50 =
- Break it down: \( 145 \times 50 = 145 \times (5 \times 10) \).
- First, multiply 145 by 5: \( 145 \times 5 = 725 \).
- Then, multiply by 10: \( 725 \times 10 = 7,250 \).
- Answer: \( 145 \times 50 = 7,250 \)

5. 525 × 30 =
- Break it down: \( 525 \times 30 = 525 \times (3 \times 10) \).
- First, multiply 525 by 3: \( 525 \times 3 = 1,575 \).
- Then, multiply by 10: \( 1,575 \times 10 = 15,750 \).
- Answer: \( 525 \times 30 = 15,750 \)

6. 876 × 300 =
- Break it down: \( 876 \times 300 = 876 \times (3 \times 100) \).
- First, multiply 876 by 3: \( 876 \times 3 = 2,628 \).
- Then, multiply by 100: \( 2,628 \times 100 = 262,800 \).
- Answer: \( 876 \times 300 = 262,800 \)

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#### Row 3:
7. 510 × 600 =
- Break it down: \( 510 \times 600 = 510 \times (6 \times 100) \).
- First, multiply 510 by 6: \( 510 \times 6 = 3,060 \).
- Then, multiply by 100: \( 3,060 \times 100 = 306,000 \).
- Answer: \( 510 \times 600 = 306,000 \)

8. 172 × 100 =
- When multiplying by 100, add two zeros to the end of the number.
- Answer: \( 172 \times 100 = 17,200 \)

9. 486 × 2,000 =
- Break it down: \( 486 \times 2,000 = 486 \times (2 \times 1,000) \).
- First, multiply 486 by 2: \( 486 \times 2 = 972 \).
- Then, multiply by 1,000: \( 972 \times 1,000 = 972,000 \).
- Answer: \( 486 \times 2,000 = 972,000 \)

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#### Row 4:
10. 277 × 8,000 =
- Break it down: \( 277 \times 8,000 = 277 \times (8 \times 1,000) \).
- First, multiply 277 by 8: \( 277 \times 8 = 2,216 \).
- Then, multiply by 1,000: \( 2,216 \times 1,000 = 2,216,000 \).
- Answer: \( 277 \times 8,000 = 2,216,000 \)

11. 631 × 40 =
- Break it down: \( 631 \times 40 = 631 \times (4 \times 10) \).
- First, multiply 631 by 4: \( 631 \times 4 = 2,524 \).
- Then, multiply by 10: \( 2,524 \times 10 = 25,240 \).
- Answer: \( 631 \times 40 = 25,240 \)

12. 923 × 500 =
- Break it down: \( 923 \times 500 = 923 \times (5 \times 100) \).
- First, multiply 923 by 5: \( 923 \times 5 = 4,615 \).
- Then, multiply by 100: \( 4,615 \times 100 = 461,500 \).
- Answer: \( 923 \times 500 = 461,500 \)

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#### Row 5:
13. 658 × 3,000 =
- Break it down: \( 658 \times 3,000 = 658 \times (3 \times 1,000) \).
- First, multiply 658 by 3: \( 658 \times 3 = 1,974 \).
- Then, multiply by 1,000: \( 1,974 \times 1,000 = 1,974,000 \).
- Answer: \( 658 \times 3,000 = 1,974,000 \)

14. 652 × 400 =
- Break it down: \( 652 \times 400 = 652 \times (4 \times 100) \).
- First, multiply 652 by 4: \( 652 \times 4 = 2,608 \).
- Then, multiply by 100: \( 2,608 \times 100 = 260,800 \).
- Answer: \( 652 \times 400 = 260,800 \)

15. 367 × 700 =
- Break it down: \( 367 \times 700 = 367 \times (7 \times 100) \).
- First, multiply 367 by 7: \( 367 \times 7 = 2,569 \).
- Then, multiply by 100: \( 2,569 \times 100 = 256,900 \).
- Answer: \( 367 \times 700 = 256,900 \)

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Final Answers:

\[
\boxed{
\begin{array}{ccc}
684 \times 10 = 6,840 & 569 \times 1,000 = 569,000 & 333 \times 4,000 = 1,332,000 \\
145 \times 50 = 7,250 & 525 \times 30 = 15,750 & 876 \times 300 = 262,800 \\
510 \times 600 = 306,000 & 172 \times 100 = 17,200 & 486 \times 2,000 = 972,000 \\
277 \times 8,000 = 2,216,000 & 631 \times 40 = 25,240 & 923 \times 500 = 461,500 \\
658 \times 3,000 = 1,974,000 & 652 \times 400 = 260,800 & 367 \times 700 = 256,900 \\
\end{array}
}
\]