Converting decimals to fractions worksheet - Free Printable

Let's solve each problem by converting decimals to fractions. We'll simplify each fraction where possible.

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General Method:

To convert a decimal to a fraction:
1. Write the decimal as a fraction with denominator 1.
2. Multiply numerator and denominator by 10 for each decimal place to eliminate the decimal.
3. Simplify the fraction.

For repeating decimals (like 0.333...), we use special techniques.

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Now, let’s go through each one:

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1) 0.167 = ?

- This is likely 0.167 (not repeating).
- $ \frac{167}{1000} $
- Already simplified → $ \boxed{\frac{167}{1000}} $

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2) 0.083 = ?

- $ \frac{83}{1000} $
- Cannot be simplified → $ \boxed{\frac{83}{1000}} $

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3) 0.2 = ?

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

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4) 0.75 = ?

- $ \frac{75}{100} = \frac{3}{4} $ → $ \boxed{\frac{3}{4}} $

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5) 0.2 = ?

- Same as #3 → $ \boxed{\frac{1}{5}} $

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6) 0.833 = ?

- Likely 0.833, not repeating.
- $ \frac{833}{1000} $
- Check if simplifiable: GCF of 833 and 1000 is 1 → $ \boxed{\frac{833}{1000}} $

*(Note: If it were 0.83̅, it would be different, but here it's written as 0.833)*

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7) 0.25 = ?

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

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8) 0.75 = ?

- Same as #4 → $ \boxed{\frac{3}{4}} $

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9) 0.25 = ?

- Same as #7 → $ \boxed{\frac{1}{4}} $

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10) 0.833 = ?

- Same as #6 → $ \boxed{\frac{833}{1000}} $

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11) 0.7 = ?

- $ \frac{7}{10} $ → $ \boxed{\frac{7}{10}} $

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12) 0.6 = ?

- $ \frac{6}{10} = \frac{3}{5} $ → $ \boxed{\frac{3}{5}} $

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13) 0.625 = ?

- $ \frac{625}{1000} = \frac{5}{8} $ (divide numerator and denominator by 125)
- $ \boxed{\frac{5}{8}} $

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14) 0.333 = ?

- This is approximately $ \frac{1}{3} $
- But 0.333 is finite, so $ \frac{333}{1000} $
- However, since 0.333 is close to $ \frac{1}{3} $, but not exactly, unless specified as repeating.
- Since it's written as 0.333, assume finite → $ \frac{333}{1000} $
- Simplify: GCF of 333 and 1000 is 1 → $ \boxed{\frac{333}{1000}} $

*(But often in such problems, 0.333 means $ \frac{1}{3} $. Let’s check context.)*

Wait — note that #19 also says 0.333 → same issue.

But if it's meant to be repeating, then $ 0.\overline{3} = \frac{1}{3} $

Since both #14 and #19 are 0.333, and they’re likely testing repetition, perhaps it's intended to be $ \frac{1}{3} $

But notation matters: if it's 0.333, it's three digits, so finite.

So safest answer: $ \boxed{\frac{333}{1000}} $

But many educators treat 0.333 as approximation of $ \frac{1}{3} $

We’ll go with exact value unless stated otherwise.

So: $ \boxed{\frac{333}{1000}} $

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15) 0.4 = ?

- $ \frac{4}{10} = \frac{2}{5} $ → $ \boxed{\frac{2}{5}} $

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16) 0.375 = ?

- $ \frac{375}{1000} = \frac{3}{8} $ (divide by 125)
- $ \boxed{\frac{3}{8}} $

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17) 0.6 = ?

- Same as #12 → $ \boxed{\frac{3}{5}} $

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18) 0.917 = ?

- $ \frac{917}{1000} $
- Check GCF: 917 ÷ 7 = 131, 1000 ÷ 7 ≠ integer
- 917 is prime? Let’s check: 917 ÷ 7 = 131 → 7×131=917 → yes!
- So $ \frac{917}{1000} = \frac{7 \times 131}{1000} $
- No common factors → $ \boxed{\frac{917}{1000}} $

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19) 0.333 = ?

- Same as #14 → $ \boxed{\frac{333}{1000}} $

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20) 0.125 = ?

- $ \frac{125}{1000} = \frac{1}{8} $ → $ \boxed{\frac{1}{8}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) 0.167 | $ \frac{167}{1000} $ |
| 2) 0.083 | $ \frac{83}{1000} $ |
| 3) 0.2 | $ \frac{1}{5} $ |
| 4) 0.75 | $ \frac{3}{4} $ |
| 5) 0.2 | $ \frac{1}{5} $ |
| 6) 0.833 | $ \frac{833}{1000} $ |
| 7) 0.25 | $ \frac{1}{4} $ |
| 8) 0.75 | $ \frac{3}{4} $ |
| 9) 0.25 | $ \frac{1}{4} $ |
| 10) 0.833 | $ \frac{833}{1000} $ |
| 11) 0.7 | $ \frac{7}{10} $ |
| 12) 0.6 | $ \frac{3}{5} $ |
| 13) 0.625 | $ \frac{5}{8} $ |
| 14) 0.333 | $ \frac{333}{1000} $ |
| 15) 0.4 | $ \frac{2}{5} $ |
| 16) 0.375 | $ \frac{3}{8} $ |
| 17) 0.6 | $ \frac{3}{5} $ |
| 18) 0.917 | $ \frac{917}{1000} $ |
| 19) 0.333 | $ \frac{333}{1000} $ |
| 20) 0.125 | $ \frac{1}{8} $ |

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🔍 Notes:

- For repeating decimals, like $ 0.\overline{3} $, the answer is $ \frac{1}{3} $
- But here, 0.333 has three decimal places, so it's treated as finite, not repeating.
- If the problem had shown $ 0.\overline{3} $ or “0.333…” then it would be $ \frac{1}{3} $

If you believe some decimals are meant to be repeating (e.g., 0.333…), please clarify — but based on the notation, we used exact values.

Let me know if you'd like the reverse (fraction to decimal)!