TITLE: Compute an arbitrary decimal place of $\pi$
QUESTION [8 upvotes]: Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?

REPLY [11 votes]: Yes, there are such algorithms.
-- See e.g. Xavier Gourdon: Computation of the $n$-th decimal digit of $\pi$ with low memory.
There also is the Bailey-Borwein-Plouffe formula already mentioned by Geoff Robinson in a comment -- see https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml.