# Definition of period of a decimal representation of a number

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

-

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

-

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

-
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

PERIOD IN DECIMAL NUMBERS- Period means that in recurring or in terminating decimal the repeating decimal is known as period Example- 7.9999........ continuously goes So, Here 9 is period because only 9 repeat continuously.

-
This is not right; the period is the number of digits that repeat, not the repeating sequence of digits. Also, your example is misleading: $7.999\!\ldots$ is in fact equal to $8$. – Pierre-Guy Plamondon Jun 29 '15 at 15:49