For questions related to the fractional part of a number.
If $r$ is a real number, we can define the floor function $$\lfloor r \rfloor = \max \{n \in \mathbb{Z} : n \le r\}$$
to be the greatest integer which is not larger than $r$. The fractional part of $r$, frequently written $\{r\}$ or $r \bmod 1$, is then defined to be $$\{r\} = r - \lfloor r \rfloor$$
The fractional part of any number is thus a non-negative real number which is strictly less than $1$. The fractional part of a number is rational if and only if the number itself is rational.
Fractional parts satisfy the inequality $$\{x+y\}\leq\{x\}+\{y\},$$ with equality iff the RHS is less than $1$. Another useful fact is that, for $x\in\mathbb R\setminus\mathbb Q$, the sequence $$a_n=\{nx\}$$ is equidistributed (and in particular, dense) in $[0,1]$.
Questions involving fractional parts can often be tagged with ceiling-and-floor-functions as well.
Reference: Fractional part.
