# Definition:Digit

## Definition

Let $n$ be a number expressed in a particular number base, $b$ for example.

Then $n$ can be expressed as:

$\left[{r_m r_{m-1} \ldots r_2 r_1 r_0 . r_{-1} r_{-2} \ldots}\right]_b$

where:

$m$ is such that $b^m \le n < b^{m+1}$;
all the $r_i$ are such that $0 \le r_i < b$.

Each of the $r_i$ are known as the digits of $n$ (base $b$).