2014 AMC 12A Problem 23

The fraction \dfrac1{99^2}=0.\overline{b_{n-1}b_{n-2}\ldots b_2b_1b_0}, where n is the length of the period of the repeating decimal expansion. What is the sum b_0+b_1+\cdots+b_{n-1}?

\textbf{(A) }874\qquad \textbf{(B) }883\qquad \textbf{(C) }887\qquad \textbf{(D) }891\qquad \textbf{(E) }892\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.