The decimal expansion of the fraction \( \frac{1}{11} \) is \( 0.\overline{09} \). This means the digits "09" repeat indefinitely. Thus, it can be expressed as:
\[ \frac{1}{11} = 0.0909090909\ldots \]
You can also write it as \( 0.09\overline{09} \) to indicate that "09" repeats.