percentage

Way of representing a number as a fraction of 100. For example, 45 percent (45%) equals 45/100, and 45% of 20 is 45/100 × 20 = 9.

Percentage increase/decrease
In general, if a quantity changes from one value to another then

percentage = 100 × (difference in the values)/old value

For example, in a sale the price of a bicycle is reduced from £120 to £90, that is there is a discount of £30. The percentage decrease is 100 × 30/120 = 25%.

Fractions as percentages
To express a fraction as a percentage, its denominator must first be converted to 100. For example, value-added tax (VAT) as a fraction is 7/40:

7/40 = 17.5/100 = 17.5%

The use of percentages often makes it easier to compare fractions that do not have a common denominator (a number divisible by both the bottom numbers), for instance when comparing rates of inflation or rates of simple interest.

To convert a fraction to a percentage on a calculator, divide the numerator by the denominator and then multiply by 100. The percentage will correspond to the first two figures of the decimal; for example, 7/12 = 0.5833333 = 58.3% (correct to 1 decimal place), and 7/32 = 0.21875 = 21.9% (correct to 1 decimal place).

The percentage sign is thought to have been derived as an economy measure when recording in old counting houses; writing in the numeric symbol for 25/100 would take two lines of parchment, and hence the ‘100’ denominator was put alongside the 25 and rearranged to ‘%’.