I've heard that $\pi$ is usually approximated as 3.14, but it can also be approximated as 22/7, which is equal to 3.142857142857142857…. Guess what? $\pi$ can also be approximated as 355/113, which is equal to 3.1415929203539823008849557…. There are 112 numbers after the decimal, which then start repeating. Anyway, let's cut to the chase. Why is $\pi$ usually approximated as 3.14 or 22/7? Maybe they're close to the actual result? Anything else about it? I do know that these can be used to find the circumference or area of a circle.
[Math] How come $\pi$ is usually approximated as 3.14 or 22/7
approximationpi
Best Answer
Say you're trying to approximate a number by rational numbers $p/q$. Usually, the bigger $q$ is, the better your chance of approximating the number closely. On the other hand, the smaller $q$ is, the simpler the approximation.
In the case of $\pi$, if you want to have a better approximation than $22/7$, you have to go all the way up to $q = 57$. (See this.) So $22/7$ is a remarkably accurate approximation, considering how low its denominator is.