The per mil symbol is used in mathematics, and especially in economics, to indicate parts per thousand. The symbol resembles a fraction with zero in the numerator and a double zero in the denominator ( ).

Suppose m and n are two integer s. The ratio or quotient m / n is converted to a per mil value by multiplying by 1000, and then reducing the result to decimal form. Thus, for example, to convert 3/50 to a per mil value, we first multiply by 1000, getting (3000/50) , and then reduce this to its simplest form, obtaining 60 . If we have 3/5 and want to convert it to a per mil value, 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 per mil value, we multiply it by 1000. Therefore, 0.06 is 60 , while 0.6 is 600 .

Per mil values are sometimes used to indicate the extent to which a quantity increases or decreases. Such values can be greater than 1000, indicating an increase to more than twice the original value, or negative, indicating a decrease in a value. For example, suppose an 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 +1500 . If the speed changes from 50 m/s to only 10 m/s, it decreases by 4/5, or 800 , of the original speed, so the speed is said to change by -800 .

Per mil values are sometimes used to express the extent of an annual tax levy on a property, particularly real estate. For example, if the levy is 15 in a particular area, that means $15 per $1000 of assessed value. A $300,000 house would thus be assessed an annual tax of $300,000 x 15 , or $4500.

Compare per cent symbol . Also see Mathematical Symbols .