# 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 $16$: