**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.

**Solution:**

327.7081 is terminating decimal number. So, it represents a rational number and also its denominator must have the form 2m x5n .

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 factors of q is 2 and 5.