Length of recurring pattern when q is less than p in q/p. Help fully question in addditonal info.

When the fraction 2/11 is written as a decimal the answer is 0.1818 recurring. The length of the recurring pattern is 2. What can you say about the length of the recurring pattern for q/p when q is less than p.  Help help help
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The length of the recurring pattern depends on p, the denominator. For example 5/37=0.135135... and 17/37=0.459459... both of which have a recurring pattern of 3 digits.

7/13=0.538461 and 11/13=0.846153 (both 6 digits long with the digits in the same cyclic order).

So q does not affect the number of digits in the recurring decimal.

 

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