Definition of period of a decimal representation of a number

I need to define the period of a decimal representation of a number!!

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well I suppose I could define a sequence by $a_1=N$ and $a_{n+1}=10(a_n-Floor[a_n])$ and then the period is the minimum value of $k$ such that $a_{m+k}=a_m$ for some $m$ –  john Jun 2 '13 at 12:31