Equivalent fractions, decimals and percentages
The conversion triangle
| FROM → TO | Method |
|---|---|
| Fraction → Decimal | Divide numerator by denominator |
| Decimal → Fraction | Use place value, then simplify |
| Decimal → Percentage | Multiply by 100 |
| Percentage → Decimal | Divide by 100 |
| Fraction → Percentage | Convert to decimal × 100 (or scale denominator to 100) |
| Percentage → Fraction | Write over 100, then simplify |
Common values to memorise
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333… | 33.3% (recurring) |
| 2/3 | 0.666… | 66.7% (recurring) |
| 1/8 | 0.125 | 12.5% |
Recurring decimals
Some fractions give recurring decimals: 1/3 = 0.333… written 0.3̇. 1/7 = 0.142857142857… written 0.1̇42857̇ (overdots on first and last digits of the repeating block).
To convert a recurring decimal back to a fraction (Higher tier): Let x = 0.4̇5̇ = 0.454545… 100x = 45.454545… 99x = 45 → x = 45/99 = 5/11.
Ordering mixed forms
Convert all values to the same form (usually decimals) before comparing.
Example: order 3/8, 0.4, 35%, 7/20. 3/8 = 0.375; 0.4 = 0.4; 35% = 0.35; 7/20 = 0.35. Ascending: 0.35, 0.35, 0.375, 0.4 → 35% / 7/20, 3/8, 0.4. Note: 35% and 7/20 are equal.
Common CCEA exam tip
When asked to compare or order, always convert to the same form first and write that as a working line. The M1 mark depends on it; just writing the answer rarely scores all available marks.
AI-generated · claude-opus-4-7 · v3-ccea-maths-leaves