To convert fractions to repeating decimals, we divide the numerator by the denominator. If the division doesn’t end (i.e., it repeats), we write the repeating part with a bar over it.
Let’s go one by one:
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1. 2/11
Divide 2 by 11:
2 ÷ 11 = 0.181818... → The digits “18” repeat.
So,
0.18̅
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2. 5/6
5 ÷ 6 = 0.8333... → The digit “3” repeats.
So,
0.83̅
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3. 4/9
4 ÷ 9 = 0.4444... → The digit “4” repeats.
So,
0.4̅
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4. 15/18
First simplify: 15 ÷ 3 = 5, 18 ÷ 3 = 6 → 5/6
We already did 5/6 above →
0.83̅
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5. 2/3
2 ÷ 3 = 0.6666... → The digit “6” repeats.
So,
0.6̅
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6. 1/6
1 ÷ 6 = 0.1666... → The digit “6” repeats after the first decimal.
So,
0.16̅
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7. 6/22
Simplify: divide numerator and denominator by 2 → 3/11
3 ÷ 11 = 0.272727... → “27” repeats.
So,
0.27̅
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8. 13/15
13 ÷ 15 = 0.8666... → “6” repeats after the first decimal.
So,
0.86̅
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9. 5/11
5 ÷ 11 = 0.454545... → “45” repeats.
So,
0.45̅
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10. 2/15
2 ÷ 15 = 0.1333... → “3” repeats after the first decimal.
So,
0.13̅
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11. 2/6
Simplify: divide by 2 → 1/3
1 ÷ 3 = 0.333... → “3” repeats.
So,
0.3̅
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12. 2/99
2 ÷ 99 = 0.020202... → “02” repeats.
So,
0.02̅
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All answers verified by long division or simplification.
Final Answer:
2/11 = 0.18̅
5/6 = 0.83̅
4/9 = 0.4̅
15/18 = 0.83̅
2/3 = 0.6̅
1/6 = 0.16̅
6/22 = 0.27̅
13/15 = 0.86̅
5/11 = 0.45̅
2/15 = 0.13̅
2/6 = 0.3̅
2/99 = 0.02̅
Parent Tip: Review the logic above to help your child master the concept of converting repeating decimals to fractions worksheet.
