Fractions to Decimals — Complete Conversion Guide
From Grade 5 to GCSE
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1. The Division Method
The simplest way to convert a fraction to a decimal is to divide the numerator by the denominator. The fraction a/b means "a divided by b".
Examples:
- 1/4 = 1 ÷ 4 = 0.25
- 3/8 = 3 ÷ 8 = 0.375
- 5/6 = 5 ÷ 6 = 0.8333... (repeating)
- 7/4 = 7 ÷ 4 = 1.75
2. Terminating vs Repeating Decimals
When you convert a fraction to a decimal, the result will either terminate (end) or repeat (go on forever with a pattern).
Terminating decimals occur when the denominator's only prime factors are 2 and/or 5. Examples: 1/4 = 0.25 (denominator = 2²), 3/20 = 0.15 (denominator = 2² × 5).
Repeating decimals occur when the denominator has prime factors other than 2 or 5. Examples: 1/3 = 0.333..., 1/7 = 0.142857142857... (6-digit repeating cycle), 5/6 = 0.8333...
3. Quick Reference Conversion Table
Memorising these common fractions as decimals will dramatically speed up your mental math:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 6/7 | 0.857142... | 85.71% |
| 7/8 | 0.875 | 87.5% |
| 1/7 | 0.142857... | 14.29% |
4. Converting Decimals Back to Fractions
To convert a terminating decimal to a fraction: write the decimal over the appropriate power of 10, then simplify. 0.375 = 375/1000 = 3/8.
For repeating decimals: let x = 0.333... Multiply by 10: 10x = 3.333... Subtract: 10x − x = 3, so 9x = 3, x = 3/9 = 1/3.