Tuesday, 3 January 2017

How can you predict the number of recurring digits when a rational recurring fraction is converted to a decimal?

How can you predict the number of recurring digits when a rational recurring fraction is converted to a decimal? For example how could I predict the number of recurring digits in 1/9 based off a rule for its denominator? If possible can you please provide worked examples.




I currently have 10^m-1/C = E Z^+ where C = the denominator of the fraction.
Is there a way to find m without guess and check.

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