\begin{definition}[Definition:Most Significant Digit]
Let $b \in \Z: b \ge 2$ be a number base
Let $n$ be a number which is reported to $r$ significant figures, to base $b$, that is:
:$n = d_1 \times b^k + d_2 \times b^{k - 1} + \dotsb + d_{r - 1} \times b^{k - r + 2} + d_r \times b^{k - r + 1}$
where:
:$d_1, d_2, \dotsc, d_r$ are the significant figures of $n$
:$b^k$ is the largest power of $b$ less than or equal to $n$.
Then the digit $d_1$ is known as the '''most significant digit''' of $n$.
Note that the usual situation is when $b = 10$, but in the field of computer science, binary is usual.
\end{definition}