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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?

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    I don't think the "divided by $x$" part is relevant. If you know $n!$ within one part in $10^{10}$, say, then you know $n! / x$ with the same tolerance, whatever $x$ is.2012-11-21
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    And the way to know the most significant digits of $n!$ is Stirling's approximation.2012-11-22
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    In my case it is relevant because I am interested by the decimal part only and it is important that I can get at least a couple of exact digits. Does the Stirling formula sufficiently accurate to get at least a couple of decimal numbers exactly ?2012-12-05

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