The period of decimal fraction

To search for a period of a rational number, there is a separate algorithm. We sort one after a different degree of the number 10: 10, 100, 1000, 10000, etc. We look at the remainder from dividing this number into denominator. If the rest of the division is 1, then the degree of number 10, this is the length of the period. For example, if the denominator costs 13, then:

   10  %  13  =  10    100  %  13  =  9    1000  13  13  =  12    10000  %  13  =  3    100000  %  13  =  4    1000000  %  13  =  1      
 it tus out, the period is 6. This period does not depend on what is in the numerator (if the fraction is reduced). 
  
 the method does not work if the denominator is divided by 5 or 2. In this case, it needs to be divided by 2, or 5, until the number that is not divided by 2, 2, 2, 5. 
  
 In the general case (as for your example 1/117), you will have to use long arithmetic. 
  
 the algorithm is looking for only the length of the period to get the period itself, you need to divide it yourself.