fractional part

The fractional part of a nonnegative real number is the part of the number that appears after the decimal . For example, the fractional part of $\frac{7}{3}$ is $\frac{1}{3}$.

To be more precise, for $x\in ℝ$ 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.