To find the decimal representation of $\frac{3}{11}$, we perform the division and get
$$\begin{array}{c|cc}
\multicolumn{2}{r}{2} & \\
\cline{2-3}
11 & 3 & .\overline{27} \\
\multicolumn{2}{r}{22} & \\
\cline{2-2}
\multicolumn{2}{r}{8} & \\
\multicolumn{2}{r}{} & \\
\cline{2-2}
\multicolumn{2}{r}{80} & \\
\multicolumn{2}{r}{} & \\
\cline{2-2}
\multicolumn{2}{r}{70} & \\
\multicolumn{2}{r}{} & \\
\cline{2-2}
\multicolumn{2}{r}{100} & \\
\end{array}$$
We see that the decimal representation of $\frac{3}{11}$ is $0.\overline{27}$.
The repeating block is $27$, so $a=2$ and $b=7$.
The sum of the digits $a$ and $b$ is $2+7=\boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the sum of the digits $a$ and $b$ in the repeating decimal representation $0.ababab\dots$ of $\frac{3}{11}$?

### Answer:
