Sure! Let’s solve the worksheet
“Convert fractions to repeating decimals” step by step. The instructions say: *Convert to decimals, round to 3 digits if necessary.*
This means we need to divide the numerator by the denominator for each fraction and write the decimal result. If the decimal repeats (like 0.333...), we can either show the repeating pattern or round it to 3 decimal places as instructed.
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🔢 Key Concept:
To convert a fraction to a decimal →
Divide numerator ÷ denominator.
If the decimal repeats infinitely (e.g., 1/3 = 0.333...), we can write it with a bar over the repeating digit(s) OR round it to 3 decimal places as the worksheet says.
Since the worksheet says “round to 3 digits if necessary,” we’ll
round all answers to 3 decimal places, unless otherwise specified. For repeating decimals, rounding is acceptable here.
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##
✔ Solutions:
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1. 7/10 = 0.700
> 7 ÷ 10 = 0.7 → Add trailing zeros to make 3 decimal places →
0.700
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2. 3/4 = 0.750
> 3 ÷ 4 = 0.75 →
0.750
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3. 4/9 = 0.444... → Round to 3 digits → 0.444
> 4 ÷ 9 = 0.4444... → Repeating →
0.444
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4. 7/10 = 0.700
> Same as #1 →
0.700
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5. 10/12 = 5/6 = 0.833... → Round to 3 digits → 0.833
> 10 ÷ 12 = 0.8333... →
0.833
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6. 2/7 = 0.285714... → Round to 3 digits → 0.286
> 2 ÷ 7 ≈ 0.2857 → Round up since 4th digit is 7 →
0.286
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7. 4/5 = 0.800
> 4 ÷ 5 = 0.8 →
0.800
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8. 2/14 = 1/7 ≈ 0.142857... → Round to 3 digits → 0.143
> 2 ÷ 14 = 0.142857... → 4th digit is 8 → round up →
0.143
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9. 4/9 = 0.444... → Same as #3 → 0.444
>
0.444
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10. 5/11 = 0.454545... → Round to 3 digits → 0.455
> 5 ÷ 11 = 0.4545... → 4th digit is 5 → round up →
0.455
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11. 1/3 = 0.333... → 0.333**
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12. 2/4 = 1/2 = 0.500
>
0.500
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13. 5/6 = 0.833... → 0.833**
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14. 8/13 ≈ 0.615384... → Round to 3 digits → 0.615
> 8 ÷ 13 ≈ 0.61538 → 4th digit is 3 → don’t round up →
0.615
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15. 7/11 = 0.636363... → Round to 3 digits → 0.636
> 7 ÷ 11 = 0.6363... → 4th digit is 3 →
0.636
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16. 4/6 = 2/3 ≈ 0.666... → 0.667**
> 4 ÷ 6 = 0.6666... → 4th digit is 6 → round up →
0.667
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17. 1/4 = 0.250
>
0.250
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18. 2/10 = 1/5 = 0.200
>
0.200
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## 📝 Final Answers (Rounded to 3 Decimal Places):
1.
0.700
2.
0.750
3.
0.444
4.
0.700
5.
0.833
6.
0.286
7.
0.800
8.
0.143
9.
0.444
10.
0.455
11.
0.333
12.
0.500
13.
0.833
14.
0.615
15.
0.636
16.
0.667
17.
0.250
18.
0.200
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✔ All done! These are the correct decimal conversions rounded to 3 decimal places as requested.
Let me know if you want to see long division steps or repeating decimal notation (with bars) instead!
Parent Tip: Review the logic above to help your child master the concept of converting repeating decimals to fractions worksheet with answers.
