If $$0.0\overline{216}$$​ is written as a fraction in lowest terms, then what is the difference between the denominator and the numerator of the fraction?

Correct option is C

Given:

​$$0.0\overline{216}$$​​

Solution:

Let x = 0.0216216216..

10x = 0.216216…

10000x = 216.216216..

10000x - 10x = 216

9990x = 216

x = $$\frac{216}{9990}$$​​

​$$= \frac{4}{185}$$​​

Difference between numerator and denominator = 185 - 4 = 181