Answer:
To subtract $0.\overline{02}$ from $0.02$, we can write $0.\overline{02}$ as a fraction using the method of infinite geometric series.
Let x = $0.\overline{02}$, then multiplying both sides by 100 gives:
$100x = 2.\overline{02}$
Subtracting x from 100x gives:
$99x = 2$
Solving for x, we get:
$x = \frac{2}{99}$
Therefore, $0.\overline{02}$ is equal to $\frac{2}{99}$.
Subtracting $\frac{2}{99}$ from $0.02$ gives:
$0.02 - \frac{2}{99} = \frac{198}{9900} - \frac{2}{99} = \frac{196}{9900}$
So the difference is $\frac{196}{9900}$, which can be simplified to $\frac{49}{2475}$.
Therefore, the result of subtracting $0.\overline{02}$ from $0.02$ and expressing the result as a fraction is $\frac{49}{2475}$.
This was a bit complicated...