Fractions, Decimals and Percentages Compared
How the three forms relate, how to convert between them, and how to compare values.
Fractions, decimals and percentages are three ways to write the same kind of quantity: part of a whole.
Converting between forms
| From | To | Method | Example |
|---|---|---|---|
| Fraction | Decimal | Divide numerator by denominator | 3/4 = 3 ÷ 4 = 0.75 |
| Decimal | Percentage | Multiply by 100 | 0.75 → 75% |
| Percentage | Decimal | Divide by 100 | 40% → 0.40 |
| Percentage | Fraction | Write over 100, then simplify | 40% = 40/100 = 2/5 |
| Decimal | Fraction | Use place value, then simplify | 0.6 = 6/10 = 3/5 |
Useful equivalents to know
- 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... (repeating) ≈ 33.3%
Finding a percentage of an amount
To find 15% of 60: 10% of 60 is 6, 5% is 3, so 15% is 9. Or multiply: 0.15 × 60 = 9.
Percentage change
Percentage change = (new − old) ÷ old × 100.
Example. A price rises from 80 to 92.
- Change: 92 − 80 = 12.
- 12 ÷ 80 = 0.15.
- Increase of 15%.
Comparing values
To compare 3/8, 0.4 and 35%, convert all to decimals: 3/8 = 0.375, 0.4, and 35% = 0.35. In order from smallest: 35%, 3/8, 0.4.
Common mistakes
- Dividing the wrong way round when converting a fraction (use numerator ÷ denominator).
- Using the new value instead of the original in percentage change.
- Adding percentages from different bases. A 10% rise followed by a 10% fall does not return to the start: 100 → 110 → 99.
Quick recap
Think of the three forms as interchangeable. Memorise common equivalents, and for percentage change always divide by the original value.