Question

Without actually performing the long division state whether 17/3125 will have a
terminating decimal expansion or a non- terminating repeating decimal expansion.

Answer 1

17/3125 is a terminating decimal.
reason: for a fraction to have terminating decimal the prime factorisation of denominator should contain factor 2 or factor 5 or both factors 2 & 5.
For a fraction to have non-terminating repeating decimal the prime factorisation of denominator should contain factor 2 & any other number or factor 5 & any other number or factors 2,5.& any other number.
The prime factorisation of 3125 contain only factor 5 i.e., 3125=5X5X5X5X5
so the fraction 17/3125 is terminating decimal

Answer 2

Hope it helps

In the pic below there is step by step explanation