Fractions to Decimals - Worksheet Digital - Free Printable

Let's solve each of the fractions on the worksheet by converting them into decimals. The method shown in the examples is to divide the numerator by the denominator.

We'll go through each fraction one by one and compute its decimal value using division (you can use a calculator or long division).

---

1. $ \frac{4}{11} $

$ 4 \div 11 = 0.\overline{36} $ → 0.3636...

> This repeats: 0.363636..., so we write it as $ 0.\overline{36} $

---

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

$ 8 \div 15 = 0.5333... $ → 0.5333...

> Repeats: 0.5333..., so $ 0.5\overline{3} $

---

3. $ \frac{12}{37} $

$ 12 \div 37 = 0.324324... $ → 0.324324...

> Repeats: $ 0.\overline{324} $

---

4. $ \frac{4}{7} $

$ 4 \div 7 = 0.\overline{571428} $ → 0.571428571428...

> Repeating cycle: $ 0.\overline{571428} $

---

5. $ \frac{7}{19} $

$ 7 \div 19 = 0.368421052631578947... $

> Long repeating decimal: 0.368421052631578947...

> It repeats every 18 digits: $ 0.\overline{368421052631578947} $

---

6. $ \frac{5}{8} $

$ 5 \div 8 = 0.625 $

> Terminating decimal: 0.625

---

7. $ \frac{2}{7} $

$ 2 \div 7 = 0.\overline{285714} $

> Repeats: $ 0.\overline{285714} $

---

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

$ 5 \div 11 = 0.\overline{45} $

> Alternates: 0.454545...

---

9. $ \frac{8}{9} $

$ 8 \div 9 = 0.\overline{8} $

> Repeats: 0.8888...

---

10. $ \frac{3}{15} $

Simplify first: $ \frac{3}{15} = \frac{1}{5} $

$ 1 \div 5 = 0.2 $

> So, 0.2

---

11. $ \frac{5}{13} $

$ 5 \div 13 = 0.\overline{384615} $

> Repeats every 6 digits: 0.384615384615...

---

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

$ 4 \div 9 = 0.\overline{4} $

> Repeats: 0.4444...

---

13. $ \frac{11}{15} $

$ 11 \div 15 = 0.7333... $ → 0.7\overline{3}

> Repeats: 0.7333...

---

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

$ 9 \div 11 = 0.\overline{81} $

> Repeats: 0.818181...

---

15. $ \frac{12}{13} $

$ 12 \div 13 = 0.\overline{923076} $

> Repeats every 6 digits: 0.923076923076...

---

✔ Final Answers:

| Fraction | Decimal |
|--------|--------|
| $ \frac{4}{11} $ | $ 0.\overline{36} $ |
| $ \frac{8}{15} $ | $ 0.5\overline{3} $ |
| $ \frac{12}{37} $ | $ 0.\overline{324} $ |
| $ \frac{4}{7} $ | $ 0.\overline{571428} $ |
| $ \frac{7}{19} $ | $ 0.\overline{368421052631578947} $ |
| $ \frac{5}{8} $ | $ 0.625 $ |
| $ \frac{2}{7} $ | $ 0.\overline{285714} $ |
| $ \frac{5}{11} $ | $ 0.\overline{45} $ |
| $ \frac{8}{9} $ | $ 0.\overline{8} $ |
| $ \frac{3}{15} $ | $ 0.2 $ |
| $ \frac{5}{13} $ | $ 0.\overline{384615} $ |
| $ \frac{4}{9} $ | $ 0.\overline{4} $ |
| $ \frac{11}{15} $ | $ 0.7\overline{3} $ |
| $ \frac{9}{11} $ | $ 0.\overline{81} $ |
| $ \frac{12}{13} $ | $ 0.\overline{923076} $ |

---

🔍 Explanation:

To convert any fraction to a decimal:
- Divide the numerator by the denominator.
- If the result repeats, use a bar over the repeating digits (e.g., $ 0.\overline{3} $).
- If it terminates, just write the decimal.

Some fractions terminate (like $ \frac{5}{8} = 0.625 $), while others repeat infinitely (like $ \frac{1}{3} = 0.\overline{3} $). This depends on the denominator’s prime factors.

> ✔️ All answers are correct based on standard division.

Let me know if you'd like these rounded to a certain number of decimal places!