Decimals to Fractions Worksheets - Free Printable

Let's solve each decimal-to-fraction conversion step by step.

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1. 0.2

- This is 2 tenths → $ \frac{2}{10} $
- Simplify: $ \frac{2}{10} = \frac{1}{5} $

✔ Answer: $ \frac{1}{5} $

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2. 0.875

- This is 875 thousandths → $ \frac{875}{1000} $
- Simplify: Divide numerator and denominator by 125:
- $ 875 ÷ 125 = 7 $
- $ 1000 ÷ 125 = 8 $
- So, $ \frac{875}{1000} = \frac{7}{8} $

✔ Answer: $ \frac{7}{8} $

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3. 0.833

- This is approximately 833 thousandths → $ \frac{833}{1000} $
- But this is a repeating decimal (likely $ 0.\overline{833} $), but since it’s written as 0.833, we assume it's terminating.
- However, $ 0.833 $ is close to $ \frac{5}{6} = 0.8333... $, but not exactly.
- Let's keep it as $ \frac{833}{1000} $
- Check if reducible: GCF of 833 and 1000?
- 833 ÷ 7 = 119 → 7×119 = 833
- 1000 ÷ 7 ≠ integer → Not divisible
- So $ \frac{833}{1000} $ is already simplified.

But wait — if it's meant to be repeating, like $ 0.\overline{833} $, that's tricky. But in standard worksheets, 0.833 usually means terminating.

So unless specified, treat it as $ \frac{833}{1000} $

✔ Answer: $ \frac{833}{1000} $ (or possibly $ \frac{5}{6} $ if it's repeating — but based on notation, likely $ \frac{833}{1000} $)

Wait — actually, let’s check:
$ \frac{5}{6} = 0.8333... $, so 0.833 is not exactly $ \frac{5}{6} $

So best to leave as $ \frac{833}{1000} $

✔ Answer: $ \frac{833}{1000} $

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4. 0.667

- This is 667 thousandths → $ \frac{667}{1000} $
- Is it reducible? Check GCF of 667 and 1000.
- 667 ÷ 23 = 29 → 23 × 29 = 667
- 1000 not divisible by 23 or 29 → irreducible

But note: $ \frac{2}{3} = 0.666... $, so 0.667 is a rounded version.

So if exact, $ \frac{667}{1000} $; if approximate, $ \frac{2}{3} $

But since the problem says "convert", and it's given as 0.667, we use $ \frac{667}{1000} $

✔ Answer: $ \frac{667}{1000} $

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5. 0.75

- 75 hundredths → $ \frac{75}{100} $
- Simplify: divide numerator and denominator by 25 → $ \frac{3}{4} $

✔ Answer: $ \frac{3}{4} $

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6. 0.5

- 5 tenths → $ \frac{5}{10} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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7. 0.25

- 25 hundredths → $ \frac{25}{100} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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8. 0.333

- This is likely meant to be $ 0.\overline{3} $, which is $ \frac{1}{3} $
- But written as 0.333, so it might be terminating.
- $ \frac{333}{1000} $, but $ \frac{1}{3} = 0.333... $, so often in such problems, 0.333 represents $ \frac{1}{3} $

So likely expected answer is $ \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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9. 0.5

- Same as #6 → $ \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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10. 0.5

- Again → $ \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. 0.2 | $ \frac{1}{5} $ |
| 2. 0.875 | $ \frac{7}{8} $ |
| 3. 0.833 | $ \frac{833}{1000} $ |
| 4. 0.667 | $ \frac{667}{1000} $ |
| 5. 0.75 | $ \frac{3}{4} $ |
| 6. 0.5 | $ \frac{1}{2} $ |
| 7. 0.25 | $ \frac{1}{4} $ |
| 8. 0.333 | $ \frac{1}{3} $ |
| 9. 0.5 | $ \frac{1}{2} $ |
| 10. 0.5 | $ \frac{1}{2} $ |

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📝 Notes:

- For repeating decimals, like 0.333..., the fraction is $ \frac{1}{3} $. Even though it's written as 0.333, in math worksheets, this often implies $ \frac{1}{3} $
- Similarly, 0.833 might be intended as $ \frac{5}{6} $, but since it's written without a bar, we take it literally as $ \frac{833}{1000} $
- But if you're following common practice, sometimes these are approximations.

However, to be precise, we’ll go with exact conversions based on the decimal given.

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✔ Recommended Answers (Most Accurate):

1. $ \frac{1}{5} $
2. $ \frac{7}{8} $
3. $ \frac{833}{1000} $
4. $ \frac{667}{1000} $
5. $ \frac{3}{4} $
6. $ \frac{1}{2} $
7. $ \frac{1}{4} $
8. $ \frac{1}{3} $ (assuming 0.333 means $ \frac{1}{3} $)
9. $ \frac{1}{2} $
10. $ \frac{1}{2} $

> If the worksheet expects simplified fractions for recurring decimals, then 8 should be $ \frac{1}{3} $, even if written as 0.333.

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✔ Final Answer Sheet:

```
1. 0.2 = 1/5
2. 0.875 = 7/8
3. 0.833 = 833/1000
4. 0.667 = 667/1000
5. 0.75 = 3/4
6. 0.5 = 1/2
7. 0.25 = 1/4
8. 0.333 = 1/3
9. 0.5 = 1/2
10. 0.5 = 1/2
```

Let me know if you want explanations for any specific one!