Percentage is a number or ratio that is expressed as a fraction of 100. It is often marked in with percentages sign “%” or “pct”. The word “percentages” means “out of 100” or “per 100”.  Also number can be expressed as a fraction of 1,000, that system uses terms “per mil” and “millage”.

Percentages are used to express how large or small one quantity is relative to another quantity. The first quantity usually represents a part of, or a change in the second quantity. For example: an increase of $ 0.15 on a price of $ 3.00 is an increase by a fraction of 0.15/3.00 = 0.05. Expressed as a percentage this increase is in amount of 6%.

Percentages are usually used to express values between zero and one, but they can be used to express any ratio as a percentage.

For example: 125% is 1.25 and -45% is -0.45.
The percentage value is computed by multiplying the numeric value of the ratio by 100.

For example: to find 40 apples as a percentage of 1250 apples. First of all we need to compute the ratio 40/1250 = 0.032 and then we need to multiply with 100 and the result is 3.2%.

It is also possible to calculate a percentage of a percentage. First of all we need to convert both percentages to fractions of 100, or to decimals and then we need to multiply them.

In our example we will calculate 50% of 60%:
(50/100) * (60/100) = 0.50 * 0.60 = 0.30 = 30/100 = 30%

Related units
Per mil (‰)    1 part in 1,000
Basic point     1 part in 10,000
Per cent mille (pcm) 1 part in 100,000
Parts-per notation
Grade (slope)

A long before the existence of the decimal system computations were made in fractions which were multiplied with of 1/100. In ancient Rome Augustus levied a tax of 1/100 on goods sold at auction known as “ centesima rerum venalium”. Computations with these fractions were similar to computing of percentages. The word “percent” is derived from the Latin word “per centrum” that is meaning “by the hundred”.

The percentages are not used only in math. They are also used in daily life, in economics and other sciences. The percentages are also vital part of modern sport statistics.