Trollathon #3.14 : A Fraction

The clue x100 suggests us to multiply the numerator and denominator by $100$ . This guess is confirmed by the fact that $10! = 3628800$ . Now, the fraction becomes $\frac{1000000}{3628800}$ .

Actually, the problem asks us for the 1000000th lexicographic permutation of the digits 0, 1,2 , ..., 9. So, using an algorithm (See this ), or doing it by hand gives $2783915460$ .