Question

a rational number in its decimal expansion is 327.7081. what can you say about the prime factor of q, when this number is expressed in the form p/q?

Answer 1

327.7081 in p/q =3277081/10000
                         =q in p/q is equals to 10000
                         = prime factor of 10000 = 2*5*2*5*2*5*2*5

Answer 2

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Since, 327.7081 has a terminating decimal expansion its denominator should be of the form 2m x 5n, where m, n are non-negative integers.

Further,

327.7081 can be expressed as

3277081/10000 = p/q

⇒ q = 10000 = 23 x 53

Hence, the prime factors of q has only factors of 2 and 5.

Thank you!!

@itzshivani