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This problem trains for: SAT-I, AMC-8, GMAT.

What is the smallest positive integer n for which the fraction:

equation

terminates when written as a decimal (in base 10)?

For a fraction to yield a terminating decimal (in base 10), the denominator must consist only of powers of 2 and/or 5. The prime factorization of the denominator of the given fraction is:

equation

While the powers of 5 are not relevant, the factor 11 is. By choosing the numerator to be equal to 11, we can simplify the fraction as to get rid of the unwanted factor. If n=11, the fraction becomes:

equation