Convert fractions to repeating decimals worksheet with 12 problems.

Let's convert each of the given fractions to repeating decimals. We'll do this by performing long division or using known patterns for repeating decimals.

---

🔁 Key Concept:

A fraction will have a repeating decimal if the denominator (after simplifying) has prime factors other than 2 and 5. If it only has 2s and/or 5s, the decimal terminates.

We’ll simplify where needed and then divide.

---

✔ Step-by-step Solutions:

---

1. $\frac{2}{11}$

Divide $2 \div 11$:
- $11$ goes into $20$ → $1$, remainder $9$
- $11$ into $90$ → $8$, remainder $2$
- $11$ into $20$ → $1$, remainder $9$... repeats!

So:
$\frac{2}{11} = 0.\overline{18}$

---

2. $\frac{5}{6}$

Simplify? Already simplified.
$6 = 2 \times 3$, so it will repeat.

$5 \div 6 = 0.8333\ldots$

So:
$\frac{5}{6} = 0.8\overline{3}$

---

3. $\frac{4}{9}$

$4 \div 9 = 0.444\ldots$

So:
$\frac{4}{9} = 0.\overline{4}$

---

4. $\frac{15}{18}$

Simplify first:
$\frac{15}{18} = \frac{5}{6}$

From earlier:
$\frac{5}{6} = 0.8\overline{3}$

So:
$\frac{15}{18} = 0.8\overline{3}$

---

5. $\frac{2}{3}$

$2 \div 3 = 0.666\ldots$

So:
$\frac{2}{3} = 0.\overline{6}$

---

6. $\frac{1}{6}$

$1 \div 6 = 0.1666\ldots$

So:
$\frac{1}{6} = 0.1\overline{6}$

---

7. $\frac{6}{22}$

Simplify: $\frac{6}{22} = \frac{3}{11}$

Now $3 \div 11 = 0.272727\ldots$

So:
$\frac{6}{22} = 0.\overline{27}$

---

8. $\frac{13}{15}$

$15 = 3 \times 5$, so it will repeat.

$13 \div 15 = 0.8666\ldots$

So:
$\frac{13}{15} = 0.8\overline{6}$

---

9. $\frac{5}{11}$

$5 \div 11 = 0.454545\ldots$

So:
$\frac{5}{11} = 0.\overline{45}$

---

10. $\frac{2}{15}$

$15 = 3 \times 5$, so it repeats.

$2 \div 15 = 0.1333\ldots$

So:
$\frac{2}{15} = 0.1\overline{3}$

---

11. $\frac{2}{6}$

Simplify: $\frac{2}{6} = \frac{1}{3}$

$1 \div 3 = 0.333\ldots$

So:
$\frac{2}{6} = 0.\overline{3}$

---

12. $\frac{2}{99}$

$2 \div 99 = 0.020202\ldots$

So:
$\frac{2}{99} = 0.\overline{02}$

---

✔ Final Answers:

| Fraction | Repeating Decimal |
|--------|-------------------|
| $\frac{2}{11}$ | $0.\overline{18}$ |
| $\frac{5}{6}$ | $0.8\overline{3}$ |
| $\frac{4}{9}$ | $0.\overline{4}$ |
| $\frac{15}{18}$ | $0.8\overline{3}$ |
| $\frac{2}{3}$ | $0.\overline{6}$ |
| $\frac{1}{6}$ | $0.1\overline{6}$ |
| $\frac{6}{22}$ | $0.\overline{27}$ |
| $\frac{13}{15}$ | $0.8\overline{6}$ |
| $\frac{5}{11}$ | $0.\overline{45}$ |
| $\frac{2}{15}$ | $0.1\overline{3}$ |
| $\frac{2}{6}$ | $0.\overline{3}$ |
| $\frac{2}{99}$ | $0.\overline{02}$ |

---

💡 Tip: When dividing, look for repeating remainders, which signal a repeating decimal. Also, use simplification first to reduce fractions before converting.

Let me know if you'd like the long division steps shown for any!