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 from `(p)/(q)` ? Give reason.

Explanation

Let `x = 327.7bar(081)`
`rArr` x = 327.7081081081……
10 x = 3277.081081081……
10000 x = 3277081.081081081………
On subtraction,
9990 x = 3273804
`therefore` `x = (3273804)/(9990) = (60626)/(185)`
Which is of the form `= (p)/(q)`.
Now, `q = 185 = 5 xx 37`,
which cannot be written in the form `2^(m) xx 5^(n)`.
`therefore` It is non-terminating and repeating decimal.