2011 AMC 10B Problem 10

Consider the set of numbers \{1, 10, 10^2, 10^3, \ldots, 10^{10}\}. The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?

\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 9 \qquad\textbf{(C)}\ 10 \qquad\textbf{(D)}\ 11 \qquad\textbf{(E)} 101

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