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

Thanks in advance!!

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3 Answers 3

up vote 1 down vote accepted

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

See https://en.wikipedia.org/wiki/Cyclic_number#Relation_to_repeating_decimals for fun details

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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
1  
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.

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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 yesterday

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