1983 AHSME Problem 16

Let x = .123456789101112....998999, where the digits are obtained by writing the integers 1 through 999 in order. The 1983rd digit to the right of the decimal point is

\textbf{(A)}\ 2\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 5\qquad \textbf{(D)}\ 7\qquad \textbf{(E)}\ 8

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