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

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

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:

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: