I remember learning in school that, for most practical purposes, 22/7 is a good approximation of pi.

I decided to play around with an Excel spreadsheet to see if I could find a better approximation.

First of all, Excel says that pi equals 3.14159265358979. Therefore I assume that the limit of Excel's accuracy is 14 decimal places, so that's how I displayed my results.

22/7 equals 3.14285714285714, which differs from pi by 0.00126448926735.

I verified that 22/7 is the best approximation you can get if you are limited to an integer fraction with a 1-digit denominator.

The best approximation you can get with a 2-digit denominator is 311/99. That equals 3.14141414141414, which differs from pi by 0.00017851217565.

The best approximation you can get with a 3-digit denominator is 355/113. That equals 3.14159292035398, which differs from pi by 0.00000026676419.

I'm not interested in pursuing this any further, but if anyone else does, I would be interested in the results.