Percentage, Decimals and Fractions

## Percentage, Decimals and Fractions

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%

## Example 1

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

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