The decimal expansion of the fraction \( \frac{1}{11} \) is \( 0.090909...\), which can be expressed as \( 0.09\overline{09} \).
Among the options provided, the correct representation of \( \frac{1}{11} \) would not match exactly with any of the choices, but the closest representation of its decimal expansion in those choices is:
A. 0.09
(Note: The repeating decimal is often approximated or truncated in options, leading to \( 0.09 \) being the best representation available in this case.)