AHSME 1983 Problem 16

Let $x = .123456789101112....998999$, where the digits are obtained by writing the integers $1$ through $999$ in order. The $1983$rd digit to the right of the decimal point is $\textbf{(A)}\ 2 \textbf{(B)}\ 3 \textbf{(C)}\ 5 \textbf{(D)}\ 7 \textbf{(E)}\ 8$