(from , "broken") are numbers
expressed as the ratio
of two numbers, and are used primarily to express a comparison between parts and a whole.
The earliest fractions were reciprocals
: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator
and a denominator
, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole.An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.
A still later development was the decimal fraction, now called simply a decimal
, in which the denominator is a power of ten
, determined by the number of digit
to the right of a decimal separator
, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale (for examples, see decimal separator
). Thus for 0.75 the numerator is 75
and the denominator is 10 to the second power, viz. 100
, because there are two digits to the right of the decimal separator.
A third kind of fraction still in common use is the percentage
, in which the denominator is always 100. Thus 75% means 75/100.
Other uses for fractions are to represent ratios
, and to represent division
. Thus the... Read More