Converting Decimals to Fractions Worksheet - Free Printable

Let's solve each problem step by step.

We are converting decimals to fractions, first as a decimal fraction (with denominator based on the number of decimal places), then simplifying it to its simplest form.

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🔹 General Rule:

- A decimal like `0.abc` has 3 decimal places → write as `abc/1000`
- Then simplify the fraction by dividing numerator and denominator by their Greatest Common Divisor (GCD)

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Now, let’s go through each one:

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#### 1) 0.34
Already done:
Decimal fraction = $ \frac{34}{100} $
Simplify: $ \frac{34 \div 2}{100 \div 2} = \frac{17}{50} $

✔ Done

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#### 2) 0.05
Decimal fraction = $ \frac{5}{100} $
Simplify: $ \frac{5 \div 5}{100 \div 5} = \frac{1}{20} $

✔ $ \frac{5}{100} = \frac{1}{20} $

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#### 3) 0.14
Decimal fraction = $ \frac{14}{100} $
Simplify: $ \frac{14 \div 2}{100 \div 2} = \frac{7}{50} $

✔ $ \frac{14}{100} = \frac{7}{50} $

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#### 4) 0.125
Decimal fraction = $ \frac{125}{1000} $
Simplify: Divide numerator and denominator by 125:
$ \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} $

✔ $ \frac{125}{1000} = \frac{1}{8} $

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#### 5) 0.64
Decimal fraction = $ \frac{64}{100} $
Simplify: $ \frac{64 \div 4}{100 \div 4} = \frac{16}{25} $

✔ $ \frac{64}{100} = \frac{16}{25} $

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#### 6) 0.27
Decimal fraction = $ \frac{27}{100} $
Check GCD of 27 and 100: only common factor is 1 → already simplified

✔ $ \frac{27}{100} $ (already simplest)

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#### 7) 0.216
Decimal fraction = $ \frac{216}{1000} $
Simplify: Find GCD of 216 and 1000
- 216 = $ 2^3 \times 3^3 $
- 1000 = $ 2^3 \times 5^3 $
- GCD = $ 2^3 = 8 $

So:
$ \frac{216 \div 8}{1000 \div 8} = \frac{27}{125} $

✔ $ \frac{216}{1000} = \frac{27}{125} $

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#### 8) 0.89
Decimal fraction = $ \frac{89}{100} $
89 is prime, doesn’t divide 100 → already in simplest form

✔ $ \frac{89}{100} $

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#### 9) 0.625
Decimal fraction = $ \frac{625}{1000} $
Simplify:
Divide numerator and denominator by 125:
$ \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} $

✔ $ \frac{625}{1000} = \frac{5}{8} $

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#### 10) 0.428
Decimal fraction = $ \frac{428}{1000} $
Simplify:
Find GCD of 428 and 1000
- 428 ÷ 4 = 107
- 1000 ÷ 4 = 250
→ $ \frac{428 \div 4}{1000 \div 4} = \frac{107}{250} $

Check: 107 is prime? Yes → no further simplification

✔ $ \frac{428}{1000} = \frac{107}{250} $

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#### 11) 0.08
Decimal fraction = $ \frac{8}{100} $
Simplify: $ \frac{8 \div 4}{100 \div 4} = \frac{2}{25} $

✔ $ \frac{8}{100} = \frac{2}{25} $

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#### 12) 0.546
Decimal fraction = $ \frac{546}{1000} $
Simplify:
Find GCD of 546 and 1000
- 546 = 2 × 3 × 7 × 13
- 1000 = 2³ × 5³
→ GCD = 2

So: $ \frac{546 \div 2}{1000 \div 2} = \frac{273}{500} $

Check if 273 and 500 have common factors:
273 = 3 × 7 × 13 → none with 500 → simplified

✔ $ \frac{546}{1000} = \frac{273}{500} $

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#### 13) 0.35
Decimal fraction = $ \frac{35}{100} $
Simplify: $ \frac{35 \div 5}{100 \div 5} = \frac{7}{20} $

✔ $ \frac{35}{100} = \frac{7}{20} $

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#### 14) 0.864
Decimal fraction = $ \frac{864}{1000} $
Simplify:
Find GCD of 864 and 1000
- 864 = 2⁵ × 3³
- 1000 = 2³ × 5³
→ GCD = 2³ = 8

So:
$ \frac{864 \div 8}{1000 \div 8} = \frac{108}{125} $

Check: 108 and 125 → no common factors (125 = 5³, 108 = 2²×3³) → simplified

✔ $ \frac{864}{1000} = \frac{108}{125} $

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✔ Final Answer Table:

| Decimal | Decimal Fraction | Simplest Form |
|--------|------------------|----------------|
| 1) 0.34 | $ \frac{34}{100} $ | $ \frac{17}{50} $ |
| 2) 0.05 | $ \frac{5}{100} $ | $ \frac{1}{20} $ |
| 3) 0.14 | $ \frac{14}{100} $ | $ \frac{7}{50} $ |
| 4) 0.125 | $ \frac{125}{1000} $ | $ \frac{1}{8} $ |
| 5) 0.64 | $ \frac{64}{100} $ | $ \frac{16}{25} $ |
| 6) 0.27 | $ \frac{27}{100} $ | $ \frac{27}{100} $ |
| 7) 0.216 | $ \frac{216}{1000} $ | $ \frac{27}{125} $ |
| 8) 0.89 | $ \frac{89}{100} $ | $ \frac{89}{100} $ |
| 9) 0.625 | $ \frac{625}{1000} $ | $ \frac{5}{8} $ |
| 10) 0.428 | $ \frac{428}{1000} $ | $ \frac{107}{250} $ |
| 11) 0.08 | $ \frac{8}{100} $ | $ \frac{2}{25} $ |
| 12) 0.546 | $ \frac{546}{1000} $ | $ \frac{273}{500} $ |
| 13) 0.35 | $ \frac{35}{100} $ | $ \frac{7}{20} $ |
| 14) 0.864 | $ \frac{864}{1000} $ | $ \frac{108}{125} $ |

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📌 Summary Tips:

- Always write decimal as fraction over power of 10 (based on decimal places)
- Simplify by finding GCD of numerator and denominator
- Use prime factorization or trial division for simplifying

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