Question

without actually performing the division state if 15/18 will have terminating decimal expansion or not​

Answer 1

For terminating decimal the prime factorisation of denominator should only contain the factor 2 or factor 5 or both factors 2 and 5. prime factorisation of denominator containing factors 2 & any other number or factors 5 & any other number or faciors 2,5 & any other number are non terminating decimals.