Pi Day is celebrated on March 14th to reflect the three most important digits in the number's decimal form. A lesser known day is Pi Approximation Day, celebrated on July 22nd, since the fraction 22/7 closely resembles the value of pi. How good are these approximations?
The problem in evaluating the approximation arises, given that there is no true correct value for pi. It's an irrational number, and the number of decimals places that have been calculated surges into the range of trillions. Yet, only a few decimal places are needed for even the most precise calculations applicable in the magnitude of the universe. Using 15 decimal approximation given in Microsoft Excel as the accepted value, here is how commonly used approximations fare:
3.14 = 0.0507% error
22/7 = 0.0403% error
3.14159 = 0.0000845% error
The margin of error drastically decreases even further as more decimal places are added, although they become more and more practically trivial in most instances. Although the difference here is very minute, these calculations show that the 22/7 is actually a better approximation for the value of pi. So while 3.14 is still the more preferred and celebrated, Pi Approximation Day does have its legitimacy for being indeed the more accurate approximation.
