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jmc

number theory intermediate

Problem

How many digits does the decimal equal to have to the right of the decimal point?
Solution
We first get the prime factorization of . Therefore, we can rewrite as . If we multiply this fraction by , the denominator is eliminated entirely. Note that multiplying by is insufficient, so since is the smallest power of ten we can multiply this fraction by to get an integer, there are digits to the right of the decimal point.
Final answer
7