Fractions to Decimals Worksheet for converting fractions into decimal numbers.

Let's solve each of the fractions on the "Fractions to Decimals Worksheet" step by step and convert them into decimal numbers.

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🔢 How to Convert Fractions to Decimals:

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). You can use long division or a calculator.

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Now let’s go through each one:

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

$$
3 ÷ 10 = 0.3
$$

✔ Answer: 0.3

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2. $ \frac{16}{40} $

Simplify first:
$ \frac{16}{40} = \frac{2}{5} $ (divide numerator and denominator by 8)

Now:
$ 2 ÷ 5 = 0.4 $

✔ Answer: 0.4

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3. $ \frac{58}{100} $

This is already over 100, so:
$$
\frac{58}{100} = 0.58
$$

✔ Answer: 0.58

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4. $ \frac{6}{20} $

Simplify: $ \frac{6}{20} = \frac{3}{10} $
$ 3 ÷ 10 = 0.3 $

✔ Answer: 0.3

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

Divide: $ 4 ÷ 9 = 0.\overline{4} $ (repeating decimal)

$$
= 0.4444\ldots
$$

✔ Answer: 0.4̅ or 0.444...

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6. $ \frac{1}{3} $

$ 1 ÷ 3 = 0.\overline{3} $

✔ Answer: 0.3̅ or 0.333...

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

$ 11 ÷ 4 = 2.75 $

✔ Answer: 2.75

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8. $ \frac{20}{3} $

$ 20 ÷ 3 = 6.\overline{6} $ → $ 6.666... $

✔ Answer: 6.6̅ or 6.666...

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9. $ \frac{50}{3} $

$ 50 ÷ 3 = 16.\overline{6} $ → $ 16.666... $

✔ Answer: 16.6̅ or 16.666...

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10. $ \frac{100}{22} $

Simplify: $ \frac{100}{22} = \frac{50}{11} $

Now divide: $ 50 ÷ 11 = 4.\overline{54} $ → $ 4.545454... $

✔ Answer: 4.5̅4̅ or 4.5454...

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11. $ \frac{1000}{170} $

Simplify: Divide numerator and denominator by 10 → $ \frac{100}{17} $

Now: $ 100 ÷ 17 ≈ 5.88235294... $

It's a repeating decimal but not simple. Let's compute:

$$
100 ÷ 17 ≈ 5.88235294117647...
$$

Rounded to 4 decimal places: 5.8824

But since it's exact, we can write:

✔ Answer: ≈ 5.8824 (or leave as repeating if needed)

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12. $ \frac{1}{28} $

$ 1 ÷ 28 ≈ 0.0357142857... $

Repeats every 6 digits: $ 0.\overline{035714} $

✔ Answer: ≈ 0.0357 (rounded to 4 decimals)

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

$ 9 ÷ 14 ≈ 0.6428571428... $

Repeats: $ 0.\overline{642857} $

✔ Answer: ≈ 0.6429 (rounded)

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

$ 7 ÷ 22 = 0.\overline{31818} $ → $ 0.3181818... $

✔ Answer: 0.3̅1̅8̅ or ≈ 0.3182

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15. $ \frac{8}{34} $

Simplify: $ \frac{8}{34} = \frac{4}{17} $

Now: $ 4 ÷ 17 ≈ 0.235294117... $

Repeats: $ 0.\overline{235294117647} $

✔ Answer: ≈ 0.2353

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16. $ \frac{18}{16} $

Simplify: $ \frac{18}{16} = \frac{9}{8} $

$ 9 ÷ 8 = 1.125 $

✔ Answer: 1.125

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17. $ \frac{22}{13} $

$ 22 ÷ 13 ≈ 1.692307692... $

Repeats: $ 1.\overline{692307} $

✔ Answer: ≈ 1.6923

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18. $ \frac{52}{14} $

Simplify: $ \frac{52}{14} = \frac{26}{7} $

Now: $ 26 ÷ 7 ≈ 3.714285714... $

Repeats: $ 3.\overline{714285} $

✔ Answer: ≈ 3.7143

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✔ Final Answers (Summary):

| Problem | Answer |
|--------|--------|
| 1 | 0.3 |
| 2 | 0.4 |
| 3 | 0.58 |
| 4 | 0.3 |
| 5 | 0.4̅ |
| 6 | 0.3̅ |
| 7 | 2.75 |
| 8 | 6.6̅ |
| 9 | 16.6̅ |
| 10 | 4.5̅4̅ |
| 11 | ≈ 5.8824 |
| 12 | ≈ 0.0357 |
| 13 | ≈ 0.6429 |
| 14 | ≈ 0.3182 |
| 15 | ≈ 0.2353 |
| 16 | 1.125 |
| 17 | ≈ 1.6923 |
| 18 | ≈ 3.7143 |

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💡 Tips:

- Always simplify fractions before dividing.
- Use long division for non-repeating or repeating decimals.
- For repeating decimals, use the bar notation (e.g., $ 0.\overline{3} $).
- Round to 4 decimal places if needed unless specified otherwise.

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