All real numbers can be written in the form n + r where n is an integer (the integer part) and the remaining fractional part r is a nonnegative real number less than one. For a positive number written in decimal notation, the fractional part corresponds to the digits appearing after the decimal point.
The fractional part of a real number x is, where is the floor function. It is sometimes denoted or .
If x is rational, then the fractional part of x can be expressed in the form, where p and q are integers and . For example, if, then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.
Famous quotes containing the words fractional and/or part:
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“Nihilism as a symptom that the losers have no more consolation: that they destroy in order to be destroyed, that without morality they no longer have any reason to “resign themselves”Mthat they put themselves on the level of the opposite principle and for their part also want power in that they compel the mighty to be their hangmen. This is the European form of Buddhism, renunciation, once all existence has lost its “meaning.””
—Friedrich Nietzsche (1844–1900)