Question

without actual division state which of the following decimal expansion have a terminating decimal or non terminating recuring 7/80

Answer 1

80 = 2*2*2*2*5
    =2^4 * 5^1

bcoz denominator i.e. 80 can be expressed as 2^n *5^m , 7/80 is terminating decimal .

Answer 2

Let y be a rational number whose decimal expansion terminates.Then y can be expressed in the form p/q where p and q are co-prime,and the prime factorization of q is of the form 2^n x 5^m ,where n and m are non-negative integers.Here,in this case, q i.e. 80 can be expressed in the form 2^n x 5^m where n and m are 4 and 1 respectively.