Definition:Number Base/Fractional Part

Definition
Let $x \in \R$ be a real number such that $x \ge 0$.

Let $b \in \N: b \ge 2$.

In the basis expansion:
 * $x = \sqrt {r_m r_{m - 1} \ldots r_2 r_1 r_0 . d_1 d_2 d_3 \ldots}_b$

the part $.d_1 d_2 d_3 \ldots$ is known as the fractional part.