Answer :

Given rational number is


is terminating if


a) p and q are co-prime &


b) q is of the form of 2n 5m where n and m are non-negative integers.


Firstly, we check co-prime


129 = 3 × 43


Denominator = 22 ×57 ×75


129 and 22 ×57 ×75 have no common factors


Therefore, 129 and 22 ×57 ×75 are co-prime.


Now, we have to check that q is in the form of 2n5m


Denominator = 22 ×57 ×75


So, denominator is not of the form 2n5m


Thus, is a non-terminating repeating decimal.


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