When the approximation $\pi\simeq 3.14$ is NOT sufficent It's common at schools to use $3.14$ as an appropriate approximation of $\pi$. However, here it's stated that for some purposes, $\pi$ should be approximated to $32$ decimal places. I need an example of such a purpose, accessible to a middle school student.
Thanks.

The approximation required for any number depends on the purpose, as you can see. It is a good approximation to take $\pi$ being approximately equal to 3.14.
So, generally in mechanical engineering we can assume this approximation to be true because we take into account the factor safety which serves the purpose causing no damages. However, suppose you want to be build a spaceship you require things to be accurate. So, this approximation won't help!
