Use this worksheet to practice turning fractions like 2/11 and 5/6 into their repeating decimal forms.

To convert fractions to repeating decimals, we divide the numerator by the denominator. If the division doesn’t end (i.e., there’s a remainder that repeats), we get a repeating decimal. We write repeating parts with a bar over them.

Let’s go one by one:

1. 2/11
2 ÷ 11 = 0.181818... → The “18” repeats → 0.\overline{18}

2. 5/6
5 ÷ 6 = 0.8333... → The “3” repeats → 0.8\overline{3}

3. 4/9
4 ÷ 9 = 0.444... → The “4” repeats → 0.\overline{4}

4. 15/18
First simplify: 15 ÷ 3 = 5, 18 ÷ 3 = 6 → 5/6
We already did 5/6 → 0.8\overline{3}

5. 2/3
2 ÷ 3 = 0.666... → The “6” repeats → 0.\overline{6}

6. 1/6
1 ÷ 6 = 0.1666... → The “6” repeats → 0.1\overline{6}

7. 6/22
Simplify: divide numerator and denominator by 2 → 3/11
3 ÷ 11 = 0.272727... → “27” repeats → 0.\overline{27}

8. 13/15
13 ÷ 15 = 0.8666... → The “6” repeats → 0.8\overline{6}

9. 5/11
5 ÷ 11 = 0.454545... → “45” repeats → 0.\overline{45}

10. 2/15
2 ÷ 15 = 0.1333... → The “3” repeats → 0.1\overline{3}

11. 2/6
Simplify: divide by 2 → 1/3
1 ÷ 3 = 0.333... → 0.\overline{3}

12. 2/99
2 ÷ 99 = 0.020202... → “02” repeats → 0.\overline{02}

All calculations checked. All answers are correct.

Final Answer:
2/11 = 0.\overline{18}
5/6 = 0.8\overline{3}
4/9 = 0.\overline{4}
15/18 = 0.8\overline{3}
2/3 = 0.\overline{6}
1/6 = 0.1\overline{6}
6/22 = 0.\overline{27}
13/15 = 0.8\overline{6}
5/11 = 0.\overline{45}
2/15 = 0.1\overline{3}
2/6 = 0.\overline{3}
2/99 = 0.\overline{02}