Question

without actually performing the long division the rational number will have a reanimating decimal expansion or a non terminating repeating decimal expansion

Answer 1

We have to do prime factorization of the denominator if its factors include only 2 and 5 then it is either terminating decimal or non terminating reoccurring decimal.

And if it has factors other than 2 and 5 then it is non terminating non reoccurring decimal i.e. it is irrational number.

Hope this will help you....