Question

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

Answer 1

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

Further, 

327.7081 can be expressed as \(\frac{3277081}{10000}\) = \(\frac{p}{q}\) 

⇒ q = 1000 = 2³ x 5³ 

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