Definition:Number Base/Integer 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:

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

the part $r_m r_{m-1} \ldots r_2 r_1 r_0$ is known as the integer part.


Also known as

The integer part of a real number can also be seen as integral part, but this can be confused by unwary readers with the concept of integration.


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 $16$: