fractional partFractionalPart2006-09-10 04:33:072007-05-30 04:52:58Definition\usepackage{amssymb}
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The \emph{fractional part} of a nonnegative real number is the part of the number that appears after the decimal \PMlinkescapetext{point}. For example, the fractional part of $\frac{7}{3}$ is $\frac{1}{3}$.
To be more precise, for $x \in \mathbb{R}$ with $x \ge 0$, the fractional part of $x$, denoted as $\{x\}$, is given by $\{x\}=x-[x]$, where $[x]$ denotes the integer part of $x$.
The name ``fractional part'' is somewhat of a misnomer: To the novice, the name may seem to imply that the result must be a fraction (and therefore rational), which is not the case. For example, $\{\pi\}=\pi-3$, which is not rational.