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In a proper fraction the numerator is smaller than the denominator. Since every two-digit number is larger than every one-digit number, there must be a one-digit numerator and two-digit denominator comprising 3 digits total. The greatest fraction will be the one with the largest possible numerator and smallest possible denominator. Choose a numerator of 9 (the largest one-digit number) and a denominator of 10 (the smallest 2-digit number). All 3 digits are different. The answer is 9/10.
1/(L+1) where L is equal to the number of digits of the cyclic number
the largest five digit number that can be formed using the digits 7 and 9 is 97,000
987654321 is the highest nine-digit number with no repeated digits.
The largest ten digit number with no repeated digits is '9876543210'.