2015 AMC 12A Problem 15

The numerator and denominator share no common factors. To write the fraction as a decimal, rewrite it with a power of $10$ in the denominator; the smallest that works is $10^{26}:$ $$\dfrac{123456789}{2^{26}\cdot 5^4} = \dfrac{123456789\cdot 5^{22}}{10^{26}}.$$ Since the numerator $123456789\cdot 5^{22}$ is not divisible by $10,$ the decimal has exactly $26$ places after the point. Thus, the correct answer is C.