A prior post showed how to estimate pi using random numbers. The spreadsheet linked to the post can estimate pi correctly to about 3 places; however, since each set of random numbers is different, the results will vary. Readers are encouraged to extend the spreadsheet beyond 1000 random numbers to improve the accuracy of the estimation.
Pi taken out to 50 decimal places is:
3.14159265358979323846264338327950288419716939937510...
Princeton University has a post where the digits of pi are listed to 10 million places. Beyond 100 places does not provide much immediate value. Just using pi to the 50 places listed above, one could calculate the circumference of the observable university to an accuracy smaller than the diameter of a single hydrogen atom. Readers are challenged to verify given that the estimate of the diameter of the observable universe is 8.8 x 10^26 m and the size of a hydrogen atom is about 1 angstrom (1/10,000,000,000 m).
For simple estimations, consider the following approximations and their relative error:
Approximation Relative Error
3 .045
22/7 .0004
355/113 .00000008
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