Question

Look at several examples of rational numbers in the form p
q
(q ≠ 0), where p and q are
integers with no common factors other than 1 and having terminating decimal
representations (expansions). Can you guess what property q must satisfy?

Answer 1

Answer:

p/q( q ≠ 0) if q=0 then the division is not defined

Answer 2

$\sf \underline\red{Solution:}$

The decimal representation will be terminating, if the denominators have factors 2 or 5 or both.

Therefore, p/q is a terminating decimal, when prime factorization of q must have only powers of 2 or 5 or both.