There isn't one.
9/10
99/100
999/1000
9999/10000
99999/100000
999999/1000000
9999999/10000000
You can keep going on and on forever, and each number is slightly larger than the last.
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You can. The greatest fraction in the set {1/2, 1/4, 1/8, 1/16, ... } is 1/2 which is less than 1!
If the numerator is less than the denominator then the fraction is less than 1.
You can tell if a fraction is less than 1% if the denominator of the fraction has its decimal place moved to the right 2 times and is less than the numerator it is less than 1 percent.
If the three digits are to be used once only then the greatest fraction is 54/3. If the required fraction is less than 1 then the solution is 5/34.
If the denominator is positive and the numerator is less than the denominator then the fraction is less than 1. If the denominator is positive and the numerator is greater than the denominator then the fraction is greater than 1.