2008 Gauss 8 Problem 17

The decimal expansion of \frac{2}{13} is the repeating decimal 0.\overline{153846}. What digit occurs in the 2008th place after the decimal point?

\textbf{(A)}\ 8\quad \textbf{(B)}\ 6\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 3

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.