I found this post on Facebook: Why is it important to know so many digits of pi?.
As someone who started computing with log tables and slide rules, the first question I ask is how many significant digits do the other variables in your calculation have? The smallest such number tells you how many digits of pi you need. With electronic devices there is no harm in using more in your calculation, as many as your device has, but do not let that give you a false idea of the precision of your result.
I learned about significant figures in my high school chemistry in 1967-68. (Thank you, Mr. Wheeler!). Use of appropriate significant figures, also from a chemistry class, clearly explains the concept and its use in practice.
I only first saw Star Trek (TOS) after high school, in reruns. Thanks to that chemistry class I gag every time I hear Mr. Spock reporting some calculation to an absurd number of decimal places. His input data could not possibly be that precise!