Given rational number is 7/80
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
7 = 7 × 1
80 = 2 × 2 × 2 × 2 × 5
7 and 80 have no common factors
Therefore, 7 and 80 are co-prime.
Now, we have to check that q is in the form of 2n5m
80 = 24 × 5
So, denominator is of the form 2n5m where n = 4 and m = 1
Thus, 7/80 is a terminating decimal.