Rounding Numbers Rules and Examples - Free Printable

The image shows a worksheet titled "Round Numbers to the Nearest Thousandth" from Sciencenotes.org, where students are asked to round decimal numbers to the nearest thousandth (i.e., three decimal places). The worksheet includes 16 problems, each with a given number and an answer already filled in.

Let’s go through the concept and verify whether the answers provided are correct.

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🔍 What does "round to the nearest thousandth" mean?

- The thousandth place is the third digit after the decimal point.
- To round to the nearest thousandth:
1. Look at the fourth digit after the decimal (the ten-thousandth place).
2. If it is 5 or greater, round up the thousandth digit by 1.
3. If it is less than 5, keep the thousandth digit the same.
4. Drop all digits after the third decimal place.

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Now let's evaluate each problem:

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✔ Left Column

1. 2.5163 → 2.5160
- 3rd decimal: 6, 4th digit: 3 → less than 5 → no rounding up
- So, 2.516 is correct → but written as 2.5160
✔️ Correct (extra zero is acceptable for clarity)

2. 3.3337 → 3.3340
- 3rd digit: 3, 4th digit: 7 → ≥5 → round up
- 3.333 + 0.001 = 3.334 → so 3.3340
✔️ Correct

3. 2.6383 → 2.6380
- 3rd digit: 8, 4th digit: 3 → <5 → no change
- So, 2.638 → 2.6380
✔️ Correct

4. 15.7289 → 15.7290
- 3rd digit: 8, 4th digit: 9 → ≥5 → round up
- 15.728 + 0.001 = 15.729 → 15.7290
✔️ Correct

5. 23.6995 → 23.7000
- 3rd digit: 9, 4th digit: 5 → ≥5 → round up
- 23.699 + 0.001 = 23.700 → 23.7000
✔️ Correct (carry-over due to 9→0)

6. 11.6894 → 11.6890
- 3rd digit: 9, 4th digit: 4 → <5 → no change
- So, 11.689 → 11.6890
✔️ Correct

7. 16.9957 → 17.0000
- 3rd digit: 5, 4th digit: 7 → ≥5 → round up
- 16.995 + 0.001 = 16.996 → wait! But we need to check:
- 16.9957 → look at 4th digit: 7 → round up 5 to 6 → 16.996
✘ But the answer says 17.0000 — this is wrong

Let's recheck:
- 16.9957 → thousandth digit is 5, next digit is 7 → round up the 5 → becomes 6 → 16.996
- But the answer is 17.0000 → that would require rounding up multiple times.

Actually:
- 16.9957 → rounded to nearest thousandth:
- Look at 4th digit: 7 → round up the 5 → 16.996
- So, 16.996, not 17.000

✘ Incorrect – the correct answer should be 16.996

Wait — did they mean to write 16.996? But they wrote 17.0000 — which implies rounding to the nearest whole number.

This is a mistake.

✔ Correct: 16.996

8. 6.3748 → 6.3750
- 3rd digit: 4, 4th digit: 8 → ≥5 → round up 4 to 5 → 6.375
- So, 6.3750
✔️ Correct

9. 41.3707 → 41.3710
- 3rd digit: 0, 4th digit: 7 → ≥5 → round up 0 to 1 → 41.371
- So, 41.3710
✔️ Correct

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✔ Right Column

10. 116.0616 → 116.0620
- 3rd digit: 1, 4th digit: 6 → ≥5 → round up 1 to 2 → 116.062
- So, 116.0620
✔️ Correct

11. 351.6105 → 351.6110
- 3rd digit: 0, 4th digit: 5 → ≥5 → round up 0 to 1 → 351.611
- So, 351.6110
✔️ Correct

12. 4.0053 → 4.0050
- 3rd digit: 5, 4th digit: 3 → <5 → no change → 4.005
- So, 4.0050
✔️ Correct

13. 19.1044 → 19.1040
- 3rd digit: 4, 4th digit: 4 → <5 → no change → 19.104
- So, 19.1040
✔️ Correct

14. 72.0361 → 72.0360
- 3rd digit: 6, 4th digit: 1 → <5 → no change → 72.036
- So, 72.0360
✔️ Correct

15. 585.2740 → 586.240
- Wait — this is not rounding to the nearest thousandth!
- Original: 585.2740 → 3rd digit: 4, 4th digit: 0 → <5 → should be 585.274
- But the answer is 586.240 → completely wrong!

✘ Incorrect — possibly a typo or misread.

Also, the number is 585.2740, which rounds to 585.274

The answer 586.240 is off by over 1 unit — likely a mistake.

✔ Correct: 585.274

16. 1.0099 → 1.0100
- 3rd digit: 9, 4th digit: 9 → ≥5 → round up 9 → becomes 10 → carry over
- 1.009 + 0.001 = 1.010 → so 1.0100
✔️ Correct

17. 15.0655 → 15.0760
- 3rd digit: 5, 4th digit: 5 → ≥5 → round up 5 to 6 → 15.066
- But answer says 15.0760 — that's incorrect.

Let's see:
- 15.0655 → thousandth digit is 5, next is 5 → round up → 15.066
- But 15.0760 is way off — seems like a misread.

✘ Incorrect — should be 15.066

18. 9.9999 → 10.000
- 3rd digit: 9, 4th digit: 9 → ≥5 → round up 9 → becomes 10 → carry over
- 9.999 + 0.001 = 10.000 → 10.000
- So, 10.000 is correct
✔️ Correct

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🚩 Summary of Errors

| Problem | Given Answer | Correct Answer | Status |
|--------|---------------|----------------|--------|
| 7. 16.9957 | 17.0000 | 16.996 | ✘ Wrong |
| 15. 585.2740 | 586.240 | 585.274 | ✘ Wrong |
| 17. 15.0655 | 15.0760 | 15.066 | ✘ Wrong |

All others are correct.

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✔ Final Answer:

The worksheet has three errors in the answers:

1. 16.9957 should be 16.996, not 17.0000
2. 585.2740 should be 585.274, not 586.240
3. 15.0655 should be 15.066, not 15.0760

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💡 Explanation of Rounding Rule:

To round to the nearest thousandth:
- Identify the third decimal digit.
- Check the fourth decimal digit:
- If ≥5 → round up the third digit.
- If <5 → leave it unchanged.
- Always drop digits beyond the third decimal.

Example:
- 16.9957 → 3rd digit = 5, 4th = 7 → round up → 16.996

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✔ Corrected Answers:
- 16.9957 = 16.996
- 585.2740 = 585.274
- 15.0655 = 15.066

All other answers on the worksheet are correct.

Let me know if you'd like a corrected version of the worksheet!