Question

without actual division how can we state whether the following numbers have the terminating decimal representation

Answer 1

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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 decimal.

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