Actually, I will reformulate the question: how can I find a formula to calculate the nth decimal digit (the non-integer part) of f(x,n) = n!/x ? My idea is a Taylor serie of some kind but I don't know where to start. Any idea?
Formulated this way, the size of n and x is not relevant since I am looking for a formula.
This was the original question:
Consider we got a really big integer number, $n!$ where $n$ is at least $10$ digits long. I would like to calculate the $10$ first decimal digits of $\frac {n!}{x}$. Is there a practical way of doing this?