Given rational number is 13/125
p/q 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
13 = 13 × 1
125 = 5 × 5 × 5
13 and 125 have no common factors
Therefore, 13 and 125 are co-prime.
Now, we have to check that q is in the form of 2n5m
125 = 53
= 1 × 23
= 20 × 53
So, denominator is of the form 2n5m where n = 0 and m = 3
Thus, 13/125 is a terminating decimal.