Finding Tens Digit of Very Large Number I think I can figure out the leading digit or the units digit, but how would one find the tens digit of, say, $$7^{100}$$ without having a calculator or web app that actually displays the full integer.
Is there a way to find the tens digit given a scientific calculator that can only display the answer in scientific notation?
Also, I have no idea what to tag this question.

The tens digit of $n$ can be read off of $n\pmod {100}$.  In this case, $7^4\equiv 1 \pmod {100}$ so $7^{100}\equiv 1 \pmod {100}$, so the answer is $0$.
