Friday, December 14, 2012

Q2/126) When does a/b repeat when it terminates



Reduce a/b to the lowest form p/q such that p and q are co-primes.
Now q is of the form 2^m5^nc
We can convert  power of 2 and 5 to power of 10 by multiplying properly so the denominator can be converted to 10^r c
If c is 1  then it terminates.
If c is not 1 then c is coprime to 10 and the remainder and hence the quotient repeats. 

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