2015 AMC 12A Problem 15

What is the minimum number of digits to the right of the decimal point needed to express the fraction \frac{123456789}{2^{26}\cdot 5^4} as a decimal?

\textbf{(A)}\ 4\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 104

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