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.
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