From Numberphile: Pi is famously calculated to trillions of digits – but Dr. James Grime says 39 is enough.
How you round it off makes a difference:
An extra note from Dr. Grime: “Since pi39 ends in 0, you may think we could use pi38 instead, which has even fewer digits. Unfortunately, the rounding errors of pi38 are ten times larger than the rounding errors of pi39 — more than a hydrogen atom. So that extra decimal place makes a difference, even if it’s 0.”
Denise Gaskins' Let's Play Math 
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