1. The problem statement, all variables and given/known data What is the minimum number of digits to the right of the decimal point needed to express the fraction as a decimal? a) 4 b) 22 c) 26 d) 30 e) 104 2. Relevant equations 3. The attempt at a solution One possible solution is: "We can rewrite the fraction as . Since the last digit of the numerator is odd, a is added to the right if the numerator is divided by [PLAIN]https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png, [Broken] and this will continuously happen because [PLAIN]https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png, [Broken] itself, is odd. Indeed, this happens twenty-two times since we divide by https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png twenty-two times, so we will need more digits. Hence, the answer is [PLAIN]https://latex.artofproblemsolving.com/8/9/7/897cab64b41a26c4bf59f579a975ec600cf2441b.png." [Broken] So I understand how they rewrote the fraction, however I'm totally lost by everything after that. I'm not exactly sure why a 5 is added to the right if the numerator is divided by 2 and how that has anything to do with the last digit being odd. Also, a calculator is not allowed on this. If someone could either clarify the explanation given or give a more simplified alternate solution, that would be appreciated.