Question

Question 10
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 $\frac{p}{q}$? Give reasons.

Answer 1

327.7081 is terminating decimal number. So, it represents a rational number and also its denominator must have the form $2^m\times 5^n$ .
Thus,
$327.7081=\frac{3277081}{10000}=\frac{p}{q}$
$\therefore q={10}^4=2\times 2\times 2\times 2\times 5\times 5\times 5\times 5=2^4\times 5^4=(2\times 5{)}^4$
Hence, the prime factorization of q contains only factors of 2 and 5.