Given rational number is 6/15
6/15 = 2/5
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
2 and 5 have no common factor
Therefore, 2 and 5 are co-prime.
Now, we have to check that q is in the form of 2n5m
5 = 51 × 1
= 51 × 20
So, denominator is of the form 2n5m where n = 0 and m = 1
Thus, 6/15 is a terminating decimal.