Fractional part

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The fractional part of a real number $x$, usually denoted $\{x\}$, is equvalent to removing the integer part of $x$. Thus $\{x\} = x - [x]$, where $[x]$ denotes the floor function. For positive numbers, this is equivalent to taking "everything after the decimal point," but this is not true in general for negative numbers. For example,

$\{3.14\} = 0.14$

$\{5\} = 0$

$\{-3.2\} = 0.8$

The fractional part function has the real numbers as its domain and the interval $[0, 1)$ as its range.

See Also