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Concept
Percentage
Summary
In mathematics, a percentage () is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number (pure number), primarily used for expressing proportions, but percent is nonetheless a unit of measurement in its orthography and usage.
For example, 45% (read as "forty-five per cent") is equal to the fraction 45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45.
Percentages are often used to express a proportionate part of a total.
(Similarly, one can also express a number as a fraction of 1,000, using the term "per mille" or the symbol "".)
If 50% of the total number of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male.
An increase of 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is a 6% increase.
While many percentage values are between 0 and 100, there is no mathematical restriction and percentages may take on other values. For example, it is common to refer to 111% or −35%, especially for percent changes and comparisons.
In Ancient Rome, long before the existence of the decimal system, computations were often made in fractions in the multiples of 1/100. For example, Augustus levied a tax of 1/100 on goods sold at auction known as centesima rerum venalium. Computation with these fractions was equivalent to computing percentages.
As denominations of money grew in the Middle Ages, computations with a denominator of 100 became increasingly standard, such that from the late 15th century to the early 16th century, it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three. By the 17th century, it was standard to quote interest rates in hundredths.
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