Percentages, fractions and decimals can be freely interchanged. A percentage can be written as a fraction (38% is `frac(38)(100)` which simplifies to `frac(19)(50)`). The fraction can also be converted to a decimal number by a division.
To turn a percentage into a:
• fraction: make the percentage the numerator and 100 the denominator;
• decimal: divide by 100.
To turn a decimal into a:
• fraction: multiply numerator and denominator by 10s until the decimal point has been removed;
• percentage: multiply by 100.
To turn a fraction into a:
• decimal: divide the numerator by the denominator;
• percentage: divide the numerator by the denominator and multiply by 100.
Common fractions, percentages and decimals should be known:
| Fraction | Decimal | Percentage |
| 0 | 0 | 0 |
| `frac(1)(10)` | 0.1 | 10% |
| `frac(1)(8)` | 0.125 | 12.5% |
| `frac(1)(5)` | 0.2 | 20% |
| `frac(1)(4)` | 0.25 | 25% |
| `frac(1)(3)` | 0.33 (rounded) | 33% (rounded) |
| `frac(1)(2)` | 0.5 | 50% |
| `frac(3)(4)` | 0.75 | 75% |
| `frac(1)(1)` = 1 | 1.0 | 100% |
Write `frac(3)(8)` as a percentage.
`frac(1)(8)` is 12.5%. Three times that is 3 x 12.5 = 37.5%
Answer: 37.5%
Jon eats `frac(1)(4)` of a bar of chocolate. Sally eats 30% of the same bar. How much of the bar is left? Write the answer as a decimal.
`frac(1)(4)` is 0.25. 30% is equivalent to 0.3. Added together this totals to 0.55. The question asked for the remainder: 1 - 0.55 = 0.45.
Answer: 0.45