Decimals - Grade 4 Math Worksheets - Free Printable

Let's solve the problem of converting decimals to fractions step by step.

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🔢 How to Convert a Decimal to a Fraction:

1. Write the decimal as a fraction with the denominator as a power of 10, based on the number of decimal places.
- 1 decimal place → denominator = 10
- 2 decimal places → denominator = 100
- 3 decimal places → denominator = 1000, etc.

2. Simplify the fraction (if possible).

3. If the decimal has a whole number part, write it as a mixed number or an improper fraction.

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Now, let’s go through each problem:

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1. $ 3.4 $

- 1 decimal place → denominator = 10
- $ 3.4 = \frac{34}{10} $
- Simplify: $ \frac{34 ÷ 2}{10 ÷ 2} = \frac{17}{5} $
- Or as mixed number: $ 3\frac{2}{5} $

✔ Answer: $ \boxed{\frac{17}{5}} $ or $ \boxed{3\frac{2}{5}} $

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2. $ 8.5 $

- $ 8.5 = \frac{85}{10} $
- Simplify: $ \frac{85 ÷ 5}{10 ÷ 5} = \frac{17}{2} $
- Or $ 8\frac{1}{2} $

✔ Answer: $ \boxed{\frac{17}{2}} $ or $ \boxed{8\frac{1}{2}} $

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3. $ 52.4 $

- $ 52.4 = \frac{524}{10} $
- Simplify: $ \frac{524 ÷ 2}{10 ÷ 2} = \frac{262}{5} $
- Or $ 52\frac{2}{5} $

✔ Answer: $ \boxed{\frac{262}{5}} $ or $ \boxed{52\frac{2}{5}} $

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4. $ 62.82 $

- 2 decimal places → denominator = 100
- $ 62.82 = \frac{6282}{100} $
- Simplify: divide numerator and denominator by 2:
- $ \frac{6282 ÷ 2}{100 ÷ 2} = \frac{3141}{50} $
- $ 3141 ÷ 50 = 62\frac{41}{50} $

✔ Answer: $ \boxed{\frac{3141}{50}} $ or $ \boxed{62\frac{41}{50}} $

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5. $ 70.84 $

- $ 70.84 = \frac{7084}{100} $
- Divide numerator and denominator by 4:
- $ \frac{7084 ÷ 4}{100 ÷ 4} = \frac{1771}{25} $
- $ 1771 ÷ 25 = 70\frac{21}{25} $

✔ Answer: $ \boxed{\frac{1771}{25}} $ or $ \boxed{70\frac{21}{25}} $

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6. $ 51.73 $

- $ 51.73 = \frac{5173}{100} $
- Check if reducible: 5173 and 100 have no common factors (since 5173 is not divisible by 2, 5, or 10).
- So, it's already simplified.

✔ Answer: $ \boxed{\frac{5173}{100}} $ or $ \boxed{51\frac{73}{100}} $

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7. $ 66.64 $

- $ 66.64 = \frac{6664}{100} $
- Divide by 4: $ \frac{6664 ÷ 4}{100 ÷ 4} = \frac{1666}{25} $
- $ 1666 ÷ 25 = 66\frac{16}{25} $

✔ Answer: $ \boxed{\frac{1666}{25}} $ or $ \boxed{66\frac{16}{25}} $

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8. $ 43.6 $

- $ 43.6 = \frac{436}{10} $
- Simplify: $ \frac{436 ÷ 2}{10 ÷ 2} = \frac{218}{5} $
- $ 218 ÷ 5 = 43\frac{3}{5} $

✔ Answer: $ \boxed{\frac{218}{5}} $ or $ \boxed{43\frac{3}{5}} $

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9. $ 55.6 $

- $ 55.6 = \frac{556}{10} $
- Simplify: $ \frac{556 ÷ 2}{10 ÷ 2} = \frac{278}{5} $
- $ 278 ÷ 5 = 55\frac{3}{5} $

✔ Answer: $ \boxed{\frac{278}{5}} $ or $ \boxed{55\frac{3}{5}} $

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10. $ 14.5 $

- $ 14.5 = \frac{145}{10} $
- Simplify: $ \frac{145 ÷ 5}{10 ÷ 5} = \frac{29}{2} $
- $ 14\frac{1}{2} $

✔ Answer: $ \boxed{\frac{29}{2}} $ or $ \boxed{14\frac{1}{2}} $

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11. $ 96.24 $

- $ 96.24 = \frac{9624}{100} $
- Divide by 4: $ \frac{9624 ÷ 4}{100 ÷ 4} = \frac{2406}{25} $
- $ 2406 ÷ 25 = 96\frac{6}{25} $

✔ Answer: $ \boxed{\frac{2406}{25}} $ or $ \boxed{96\frac{6}{25}} $

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12. $ 46.5 $

- $ 46.5 = \frac{465}{10} $
- Simplify: $ \frac{465 ÷ 5}{10 ÷ 5} = \frac{93}{2} $
- $ 46\frac{1}{2} $

✔ Answer: $ \boxed{\frac{93}{2}} $ or $ \boxed{46\frac{1}{2}} $

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13. $ 16.4 $

- $ 16.4 = \frac{164}{10} $
- Simplify: $ \frac{164 ÷ 2}{10 ÷ 2} = \frac{82}{5} $
- $ 16\frac{2}{5} $

✔ Answer: $ \boxed{\frac{82}{5}} $ or $ \boxed{16\frac{2}{5}} $

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14. $ 97.5 $

- $ 97.5 = \frac{975}{10} $
- Simplify: $ \frac{975 ÷ 5}{10 ÷ 5} = \frac{195}{2} $
- $ 97\frac{1}{2} $

✔ Answer: $ \boxed{\frac{195}{2}} $ or $ \boxed{97\frac{1}{2}} $

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15. $ 23.89 $

- $ 23.89 = \frac{2389}{100} $
- Check: 2389 and 100 have no common factors (2389 is not divisible by 2, 5, or other small primes)
- Already simplified.

✔ Answer: $ \boxed{\frac{2389}{100}} $ or $ \boxed{23\frac{89}{100}} $

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16. $ 14.3 $

- $ 14.3 = \frac{143}{10} $
- Check: 143 and 10 — 143 = 11 × 13, no common factors with 10
- So, already simplified.

✔ Answer: $ \boxed{\frac{143}{10}} $ or $ \boxed{14\frac{3}{10}} $

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✔ Final Answers:

| Problem | Answer (as improper fraction) | Answer (as mixed number) |
|--------|-------------------------------|--------------------------|
| 1. 3.4 | $ \frac{17}{5} $ | $ 3\frac{2}{5} $ |
| 2. 8.5 | $ \frac{17}{2} $ | $ 8\frac{1}{2} $ |
| 3. 52.4 | $ \frac{262}{5} $ | $ 52\frac{2}{5} $ |
| 4. 62.82 | $ \frac{3141}{50} $ | $ 62\frac{41}{50} $ |
| 5. 70.84 | $ \frac{1771}{25} $ | $ 70\frac{21}{25} $ |
| 6. 51.73 | $ \frac{5173}{100} $ | $ 51\frac{73}{100} $ |
| 7. 66.64 | $ \frac{1666}{25} $ | $ 66\frac{16}{25} $ |
| 8. 43.6 | $ \frac{218}{5} $ | $ 43\frac{3}{5} $ |
| 9. 55.6 | $ \frac{278}{5} $ | $ 55\frac{3}{5} $ |
| 10. 14.5 | $ \frac{29}{2} $ | $ 14\frac{1}{2} $ |
| 11. 96.24 | $ \frac{2406}{25} $ | $ 96\frac{6}{25} $ |
| 12. 46.5 | $ \frac{93}{2} $ | $ 46\frac{1}{2} $ |
| 13. 16.4 | $ \frac{82}{5} $ | $ 16\frac{2}{5} $ |
| 14. 97.5 | $ \frac{195}{2} $ | $ 97\frac{1}{2} $ |
| 15. 23.89 | $ \frac{2389}{100} $ | $ 23\frac{89}{100} $ |
| 16. 14.3 | $ \frac{143}{10} $ | $ 14\frac{3}{10} $ |

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🎯 Tip: Always check for simplification by finding the Greatest Common Divisor (GCD) of numerator and denominator.

Let me know if you'd like these in a printable format! 😊