\begin{definition}[Definition:Basis Expansion/Recurrence/Period]
Let $b \in \N: b \ge 2$.
Let $x$ be a rational number.
Let the basis expansion of $x$ in base $b$ be:
:$\sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_b$
From Basis Expansion of Rational Number, $x$ either terminates or recurs.
The '''period of recurrence''' is the number of digits in the recurring part after which it repeats itself.
Category:Definitions/Basis Expansions
\end{definition}