TITLE: A calculation that goes awfully wrong if we let $\pi=22/7$
QUESTION [8 upvotes]: Me and one of my friends had an argument and he said that using $22/7$ as value of $\pi$ is sufficient for any calculation. Can we always take it $22/7$, or is there some example of some calculation in which if we use $\pi=22/7$, some noticeable error which makes quite a significant difference, appears. Kind of calculative contradiction.
Thanks!

REPLY [2 votes]: What quadrant is $1\ 000\ 000$ radians in?  The answer you get to that question is wrong if you use $22/7$ as an approximation to $\pi$.