### Instruction: What is the reciprocal of the common fraction form of $.\overline{2}$?### Response: I know that the decimal $.\overline{2}$ is equivalent to the fraction $\frac{2}{9}$, because the repeating part is 2 and the denominator is 9, which is one less than the number of digits in the repeating part.
To find the reciprocal of a fraction, I just switch the numerator and the denominator, so the reciprocal of $\frac{2}{9}$ is $\frac{9}{2}$.
This is the answer in fraction form, but I can also convert it to a mixed number or a decimal if I want to.
To convert it to a mixed number, I divide 9 by 2 and get a quotient of 4 and a remainder of 1, so $\frac{9}{2}$ is the same as 4 and $\frac{1}{2}$.
To convert it to a decimal, I divide 9 by 2 using long division and get 4.5, which is the same as 4 and $\frac{1}{2}$.