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

I am curious if there are any real life scenarios where we actually have a use for the hundreds or thousands of non-repeating digits after the decimal place for pi in base 10.

I mean, for any reasonable calculation where pi is needed, there is literally zero purpose for most of those digits. But I wonder if there are times when those digits are helpful to us.

Maybe something involving cryptography?