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Minimum Number of Digits

Source: 2015 AMC 12A #15

February 4, 2015
number theoryAMC

Problem Statement

What is the minimum number of digits to the right of the decimal point needed to express the fraction 123 456 789226⋅54\dfrac{123\,456\,789}{2^{26}\cdot 5^4} as a decimal?
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>22<spanclass=′latex−bold′>(C)</span>26<spanclass=′latex−bold′>(D)</span>30<spanclass=′latex−bold′>(E)</span>104<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>22\qquad<span class='latex-bold'>(C) </span>26\qquad<span class='latex-bold'>(D) </span>30\qquad<span class='latex-bold'>(E) </span>104
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