Question

A rational number in its decimal expansion is 327.7081. what can you say about the prime factors of q. where this number is expressed in the form of p/q? Give reasons ​

Answer 1

$\huge\fbox{\textrm{{{\color{navy}{An}}{\purple{sw}}{\pink{er࿐}}{\color{pink}{:}}}}}$

Since, 327.7081 has a terminating decimal expansion its denominator should be of the form 2^m x 5^n, 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