Percentage, Decimals and Fractions

Percentage, Decimals and Fractions

GCSE(F),

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:

FractionDecimalPercentage
000
`frac(1)(10)`0.110%
`frac(1)(8)`0.12512.5%
`frac(1)(5)`0.220%
`frac(1)(4)`0.2525%
`frac(1)(3)`0.33 (rounded)33% (rounded)
`frac(1)(2)`0.550%
`frac(3)(4)`0.7575%
`frac(1)(1)` = 11.0100%

Examples

1. Write `frac(3)(8)` as a percentage.

Answer: 37.5%

`frac(1)(8)` is 12.5%. Three times that is 3 x 12.5 = 37.5%

2. 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.

Answer: 0.45

`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.