# Definition of period of a decimal representation of a number

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

Thanks in advance!!

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## 2 Answers

Period of a decimal representation of a number may be defined in terms of cyclic numbers:

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It's just how many digits in the repeated part i.e. 1.23123123... has period 3

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Hi @john, thanks!! But formally is possible?? –  mle Jun 2 '13 at 12:27
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