How many digits are there in 100!? How many digits are there in 100 factorial?
How does one calculate the number of digits?

Stirling's formula gives a good approximation: $$n!\approx\sqrt{2\pi n}\left(\frac{n}{e}\right)^n$$
That is messier, but it helps because I can take the logarithm:
$$\log(n!)\approx \log(\sqrt{2\pi n})+n\log\left(\frac{n}{e}\right)$$
That was the common base-ten logarithm.
The number of digits in $n!$ equals the next integer above $\log(n!)$.
