If a number like Pi is infinite, how do we know each decimal that is newly calculated is valid?

Question

Not a mathematician here at all so perhaps my question is phrased incorrectly.

Let’s say through thorough testing in reality, we can prove with certainty Pi is correct up until 5 decimal places,

3.14159

The computers that are calculating Pi to an endless degree, how do they validate new values that are calculated as correct and cannot be otherwise?

In: 434

Answer 1

To put it very simply, the way to calculate Pi is exact and known. It just takes more and more effort the longer you go on. They way you can validate each new digit is to simply calculate it again.

It is actually possible to calculate the N-th digit of pie, so its not like we have to keep calculating it from the start over and over again.