Let $x=.\overline{2}$. Multiplying both sides of this equation by 10, we get $10x=2.\overline{2}$.
Subtracting the equation $x=.\overline{2}$ from $10x=2.\overline{2}$, we get $9x=2$,
so $x=\frac{2}{9}$.
Therefore, the reciprocal of $.\overline{2}$ is $\frac{1}{.\overline{2}}=\frac{1}{\frac{2}{9}}=\frac{9}{2}=\boxed{\frac{9}{2}}$.
The answer is: \frac{9}{2}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the reciprocal of the common fraction form of $.\overline{2}$?

### Answer:
