Definition:Number Base/Fractional Part

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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:

$x = \sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0 . d_1 d_2 d_3 \ldots}_b$

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

Also see

The most common number base is of course base $10$.

So common is it, that numbers written in base $10$ are written merely by concatenating the digits:

$r_m r_{m-1} \ldots r_2 r_1 r_0$

$2$ is a fundamentally important number base in computer science, as is $16$:

• Definition:Binary Notation
• Definition:Hexadecimal Notation