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Qus: Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?

A. Rational Number, Prime factor of q will be only 2.
B. Rational Number, Prime factor of q will have a factor other than 2 or 5.
C. Not rational number
D. Rational Number, Prime factors of q will have either 2 or 5 or both

Solution

D. Rational Number, Prime factors of q will have either 2 or 5 or both

Explanation

It is rational because decimal expansion is terminating. Therefore, it can be expressed in p/q form where factors of q are of the form. and n and m are non-negative integers.