Fractions, decimals, and percentages are three different ways of expressing the same value. Being able to move between them fluently is an essential skill.
Fraction → Decimal: divide the numerator by the denominator. $$\frac{3}{8} = 3 \div 8 = 0.375$$
Decimal → Percentage: multiply by 100. $$0.375 \times 100 = 37.5%$$
Percentage → Fraction: write over 100 and simplify. $$45% = \frac{45}{100} = \frac{9}{20}$$
Common values worth memorising:
| Fraction | Decimal | Percentage |
|---|---|---|
| $\frac{1}{2}$ | 0.5 | 50% |
| $\frac{1}{4}$ | 0.25 | 25% |
| $\frac{1}{5}$ | 0.2 | 20% |
| $\frac{1}{3}$ | $0.\dot{3}$ | $33.\dot{3}%$ |
| $\frac{1}{8}$ | 0.125 | 12.5% |
Common error: converting 5% as 0.5 rather than 0.05 — divide by 100, not 10.