2015 AMC 12A Problems/Problem 15

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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?

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}}\ 30\qquad\textbf{(E)}\ 104$ (Error compiling LaTeX. Unknown error_msg)

Solution

The fraction is equivalent to $\frac{123456789 \cdot 5^{22}}{10^{26}}.$ The answer is clearly $\textbf{(D)}.$