The per cent symbol is used in mathematics, engineering, and science to indicate parts per hundred. The symbol resembles a fraction with zero in both the numerator and the denominator ( or %).

Suppose *m* and *n* are integer s. The ratio or quotient *m* / *n* is converted to a percentage by multiplying by 100, and then reducing the result to decimal form. Thus, for example, to convert 3/5 to a percentage, we first multiply by 100, getting (300/5)%, and then reduce this to its simplest form, obtaining 60%. If we have 30/5 and want to convert it to a percentage, we follow the same procedure, obtaining (3000/5)% which reduces to 600%.

If we have a decimal number and want to convert it to a percentage, we simply multiply it by 100. Therefore, 0.6 is 60%, while 6.0 is 600%.

Percentages are sometimes used to indicate the extent to which a quantity increases or decreases. Such percentages can be greater than 100, indicating an increase to more than twice the original value, or negative, indicating a decrease in a value. For example, suppose a light aircraft is traveling at 50 meters per second (m/s). If its speed changes to 125 m/s, it is an increase of 75 m/s which is 1.5 times the original speed, so the speed is said to change by +150%. If the speed changes from 50 m/s to only 10 m/s, it decreases by 4/5, or 80%, of the original speed, so the speed is said to change by -80%.

Compare per mil symbol . Also see Mathematical Symbols .

*This was last updated in*March 2011

*Posted by:*Margaret Rouse

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