Definition:Basis Expansion/Recurrence/Period
< Definition:Basis Expansion | Recurrence(Redirected from Definition:Period of Recurrence)
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Definition
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.