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)
“A real man doesn’t have to run from his mother, and may even have to face the reality that no great deed is going to be great enough for him to ransom himself completely, and he may always be in his mother’s debt. If he understands that . . . he won’t have to feel guilty, and he won’t have to please her completely. He can go ahead and be nice to her and let her be part of his life.”
—Frank Pittman (20th century)