Irrational Numbers Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of these problems step by step. The task is to convert each rational number (given as a fraction) into its decimal form.

We’ll simplify the fractions first if possible, then divide the numerator by the denominator to get the decimal.

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1) $-\frac{20}{50}$

- Simplify: $ \frac{20}{50} = \frac{2}{5} $
- $ \frac{2}{5} = 0.4 $
- So, $-\frac{20}{50} = -0.4$

✔ Answer: -0.4

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2) $\frac{18}{-24}$

- This is the same as $-\frac{18}{24}$
- Simplify: $ \frac{18}{24} = \frac{3}{4} $
- $ \frac{3}{4} = 0.75 $
- So, $-\frac{18}{24} = -0.75$

✔ Answer: -0.75

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3) $-\frac{36}{80}$

- Simplify: $ \frac{36}{80} = \frac{9}{20} $
- $ \frac{9}{20} = 0.45 $
- So, $-\frac{36}{80} = -0.45$

✔ Answer: -0.45

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4) $\frac{22}{40}$

- Simplify: $ \frac{22}{40} = \frac{11}{20} $
- $ \frac{11}{20} = 0.55 $

✔ Answer: 0.55

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5) $-\frac{70}{160}$

- Simplify: $ \frac{70}{160} = \frac{7}{16} $
- $ \frac{7}{16} = 0.4375 $
- So, $-\frac{70}{160} = -0.4375$

✔ Answer: -0.4375

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6) $\frac{48}{64}$

- Simplify: $ \frac{48}{64} = \frac{3}{4} $
- $ \frac{3}{4} = 0.75 $

✔ Answer: 0.75

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7) $-\frac{25}{50}$

- Simplify: $ \frac{25}{50} = \frac{1}{2} $
- $ \frac{1}{2} = 0.5 $
- So, $-\frac{25}{50} = -0.5$

✔ Answer: -0.5

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8) $\frac{11}{25}$

- $ \frac{11}{25} = 0.44 $
(Because $ \frac{1}{25} = 0.04 $, so $ 11 \times 0.04 = 0.44 $)

✔ Answer: 0.44

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9) $\frac{52}{64}$

- Simplify: $ \frac{52}{64} = \frac{13}{16} $
- $ \frac{13}{16} = 0.8125 $

✔ Answer: 0.8125

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10) $\frac{48}{80}$

- Simplify: $ \frac{48}{80} = \frac{3}{5} $
- $ \frac{3}{5} = 0.6 $

✔ Answer: 0.6

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11) $\frac{32}{50}$

- Simplify: $ \frac{32}{50} = \frac{16}{25} $
- $ \frac{16}{25} = 0.64 $

✔ Answer: 0.64

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12) $\frac{9}{24}$

- Simplify: $ \frac{9}{24} = \frac{3}{8} $
- $ \frac{3}{8} = 0.375 $

✔ Answer: 0.375

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13) $\frac{55}{80}$

- Simplify: $ \frac{55}{80} = \frac{11}{16} $
- $ \frac{11}{16} = 0.6875 $

✔ Answer: 0.6875

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14) $\frac{12}{64}$

- Simplify: $ \frac{12}{64} = \frac{3}{16} $
- $ \frac{3}{16} = 0.1875 $

✔ Answer: 0.1875

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15) $\frac{98}{160}$

- Simplify: $ \frac{98}{160} = \frac{49}{80} $
- Now divide: $ 49 \div 80 = 0.6125 $

✔ Answer: 0.6125

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16) $\frac{12}{50}$

- Simplify: $ \frac{12}{50} = \frac{6}{25} $
- $ \frac{6}{25} = 0.24 $

✔ Answer: 0.24

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✔ Final Answers:

| Problem | Answer |
|--------|------------|
| 1) | -0.4 |
| 2) | -0.75 |
| 3) | -0.45 |
| 4) | 0.55 |
| 5) | -0.4375 |
| 6) | 0.75 |
| 7) | -0.5 |
| 8) | 0.44 |
| 9) | 0.8125 |
| 10) | 0.6 |
| 11) | 0.64 |
| 12) | 0.375 |
| 13) | 0.6875 |
| 14) | 0.1875 |
| 15) | 0.6125 |
| 16) | 0.24 |

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🔍 Explanation:

All these are rational numbers, meaning they can be expressed as fractions and have terminating or repeating decimals. In this case, all the decimals terminate because the denominators (after simplifying) only have prime factors of 2 and/or 5 — which guarantees terminating decimals.

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