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

A thing I would like to point out is that technically speaking to a computer at least pi is a fixed number.

Every equation we do with pi, is only valid to a certain level of accuracy. In short, certain tasks will require a certain level of accuracy for the calculated answer to be valid. For higher thresholds you must use pi to a larger number of decimal places.

An example of this could be using pi to work out the radius of a pizza so you can serve equal amounts. In this situation using something as low as pi = 3 will still yield an accurate answer. In regards to astrophysics however, this level of inaccuracy would result in drastic changes to the result.