Worksheet for estimating multiplication with decimals, including problems and answer choices.

Let's solve each problem by estimating the product using decimal placement. The key idea is to round the numbers to simpler values, multiply them, and then use decimal placement to estimate the correct answer.

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1) 2.894 × 0.2

- Round:
- 2.894 ≈ 3
- 0.2 = 0.2 (already simple)
- Estimate: 3 × 0.2 = 0.6
- Now look at options:
- A. 0.5788 → Closest to 0.6
- B. 0.0058 → Too small
- C. 5.7880 → Too big
- D. 0.0579 → Too small

✔ Answer: A. 0.5788

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2) 1.81 × 0.8

- Round:
- 1.81 ≈ 2
- 0.8 = 0.8
- Estimate: 2 × 0.8 = 1.6
- Options:
- A. 0.014 → too small
- B. 0.145 → too small
- C. 1.448 → close to 1.6
- D. 144.800 → way too big

✔ Answer: C. 1.448

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3) 3.9 × 0.47

- Round:
- 3.9 ≈ 4
- 0.47 ≈ 0.5
- Estimate: 4 × 0.5 = 2.0
- Options:
- A. 0.183 → too small
- B. 18.330 → too big
- C. 1.833 → close to 2.0
- D. 0.018 → too small

✔ Answer: C. 1.833

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4) 4.2 × 0.717

- Round:
- 4.2 ≈ 4
- 0.717 ≈ 0.7
- Estimate: 4 × 0.7 = 2.8
- Options:
- A. 30.1140 → too big
- B. 0.0301 → too small
- C. 0.3011 → too small
- D. 3.0114 → close to 2.8? Wait — 3.0114 is a bit higher, but let’s check actual value.

Wait — 4.2 × 0.717:

→ Let's do quick multiplication:
- 4.2 × 0.717 = ?

But we're estimating. But note: 4.2 × 0.7 = 2.94 → about 2.94

Now check options:
- A. 30.1140 → 30 → too big
- B. 0.0301 → no
- C. 0.3011 → no
- D. 3.0114 → very close to 2.94?

Wait — actually, none of these seem right?

Wait — let's calculate more carefully:

4.2 × 0.717:

Break it down:
- 4 × 0.717 = 2.868
- 0.2 × 0.717 = 0.1434
- Total = 2.868 + 0.1434 = 3.0114

So exact answer is 3.0114

So option D. 3.0114 is correct.

✔ Answer: D. 3.0114

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5) 6.7 × 0.94

- Round:
- 6.7 ≈ 7
- 0.94 ≈ 1
- Estimate: 7 × 1 = 7
- But 0.94 is less than 1 → so product should be less than 7
- Look at options:
- A. 0.630 → too small
- B. 62.980 → too big
- C. 0.063 → too small
- D. 6.298 → close to 7

Yes! 6.7 × 0.94 ≈ 6.3

Actual: 6.7 × 0.94 = ?
- 6.7 × 0.9 = 6.03
- 6.7 × 0.04 = 0.268
- Total = 6.03 + 0.268 = 6.298

✔ Answer: D. 6.298

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6) 9.63 × 0.6

- Round:
- 9.63 ≈ 10
- 0.6 = 0.6
- Estimate: 10 × 0.6 = 6.0
- Options:
- A. 0.578 → too small
- B. 577.800 → too big
- C. 5.778 → close to 6.0
- D. 0.058 → too small

So C. 5.778 is closest.

Check actual:
9.63 × 0.6 = ?

9.63 × 0.6 = (9.63 × 6)/10 = 57.78 / 10 = 5.778

✔ Answer: C. 5.778

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7) 0.47 × 5.1

- Round:
- 0.47 ≈ 0.5
- 5.1 ≈ 5
- Estimate: 0.5 × 5 = 2.5
- Options:
- A. 23.970 → too big
- B. 0.024 → too small
- C. 2.397 → close to 2.5
- D. 0.240 → too small

Yes, 0.47 × 5.1 ≈ 2.4

Actual:
0.47 × 5.1 = ?

= 0.47 × (5 + 0.1) = 0.47×5 = 2.35; 0.47×0.1 = 0.047 → total = 2.397

✔ Answer: C. 2.397

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8) 0.4 × 9.75

- Round:
- 0.4 = 0.4
- 9.75 ≈ 10
- Estimate: 0.4 × 10 = 4.0
- Options:
- A. 3.900 → close
- B. 0.039 → too small
- C. 390.000 → too big
- D. 0.390 → too small

So A. 3.900 is best.

Actual: 0.4 × 9.75 = ?

0.4 × 9.75 = (4/10) × 9.75 = (4 × 9.75)/10 = 39 / 10 = 3.9

✔ Answer: A. 3.900

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9) 5.3 × 7.456

- Round:
- 5.3 ≈ 5
- 7.456 ≈ 7.5
- Estimate: 5 × 7.5 = 37.5
- Options:
- A. 395.1680 → too big
- B. 39.5168 → close
- C. 3,951.6800 → way too big
- D. 3.9517 → too small

So B. 39.5168 is closest.

Actual:
5.3 × 7.456 = ?

Let’s compute:
- 5 × 7.456 = 37.28
- 0.3 × 7.456 = 2.2368
- Total = 37.28 + 2.2368 = 39.5168

✔ Answer: B. 39.5168

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10) 2.6 × 2.735

- Round:
- 2.6 ≈ 3
- 2.735 ≈ 3
- Estimate: 3 × 3 = 9
- But both are under 3 → so product < 9
- Try: 2.6 × 2.7 ≈ ?

Estimate:
2.6 × 2.7 = ?

(2.6 × 2) = 5.2
(2.6 × 0.7) = 1.82 → total = 7.02

But actual number is 2.735 → slightly more than 2.7

Try actual:
2.6 × 2.735

= 2.6 × (2 + 0.7 + 0.035)
= 2.6×2 = 5.2
2.6×0.7 = 1.82
2.6×0.035 = 0.091
Total = 5.2 + 1.82 = 7.02 + 0.091 = 7.111

Options:
- A. 7.1110 → matches!
- B. 0.0711 → too small
- C. 711.1000 → too big
- D. 71.1100 → too big

✔ Answer: A. 7.1110

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11) 5.583 × 0.9

- Round:
- 5.583 ≈ 5.6
- 0.9 = 0.9
- Estimate: 5.6 × 0.9 = 5.04
- So around 5.04
- Options:
- A. 5.0247 → very close
- B. 0.5025 → too small
- C. 50.2470 → too big
- D. 0.0502 → too small

So A. 5.0247

Actual:
5.583 × 0.9 = ?

= 5.583 × 9 / 10 = 50.247 / 10 = 5.0247

✔ Answer: A. 5.0247

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12) 0.434 × 8.12

- Round:
- 0.434 ≈ 0.4
- 8.12 ≈ 8
- Estimate: 0.4 × 8 = 3.2
- Options:
- A. 352.40800 → too big
- B. 0.35241 → too small
- C. 35.24080 → too big
- D. 3.52408 → close to 3.2

So D. 3.52408 is best.

Check actual:
0.434 × 8.12

Break it down:
- 0.434 × 8 = 3.472
- 0.434 × 0.12 = ?
- 0.434 × 0.1 = 0.0434
- 0.434 × 0.02 = 0.00868
- Total = 0.0434 + 0.00868 = 0.05208
- Add: 3.472 + 0.05208 = 3.52408

✔ Answer: D. 3.52408

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✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | A. 0.5788 |
| 2 | C. 1.448 |
| 3 | C. 1.833 |
| 4 | D. 3.0114 |
| 5 | D. 6.298 |
| 6 | C. 5.778 |
| 7 | C. 2.397 |
| 8 | A. 3.900 |
| 9 | B. 39.5168 |
|10 | A. 7.1110 |
|11 | A. 5.0247 |
|12 | D. 3.52408 |

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✔ Summary of Estimation Strategy:

For each problem:
1. Round decimals to simpler numbers.
2. Multiply the rounded numbers.
3. Use that to estimate the magnitude.
4. Choose the option that matches in size and decimal place.
5. Verify with actual multiplication if needed.

This method helps avoid calculation errors and builds number sense.

Let me know if you want a printable version or explanation for any specific one!