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 $\frac{p}{q}$?

• A. $q$ has prime factors $2$ or $5$ or both.
• B. $q$ has prime factors except $2$ and $5.$
• C. $q$ has no prime factors
• D. None of these

Answer 1

The correct option is A $q$ has prime factors $2$ or $5$ or both.

We know that the rational number having denominator $3,7,9,11,13,17,23,\mathrm{27...}$ and multiple of these number, will have a non-terminating decimal expansion.
Here the decimal expansion is $327.7081$, which is terminating.
Then, the prime factors of $q$, when this number is expressed in the form $\frac{p}{q}$ will be $2$ or $5$ or both.

Therefore, option $A$ is correct.