Question

Without actual division decide which of following rational numbers have terminating decimal representation :- 33/375

Answer 1

375=5×5×5×3 one of the factor is other than 2 or 5 but the rational no. is not in its lowest format so 33÷375 have a terminating decimal representation

Answer 2

HI there !

Without actual division we can check whether 33/375 has  terminating decimal expansion

for this , the prime factorization of 375 [ q ] must consist of 2 and 5

375 = 3 × 5³

Here , we can see that the q does not have prime factorization of the form 2ⁿ × 5ˣ

So , the rational no: does not have terminating decimal expansion