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

Our methods of calculating pi also produce upper and lower bounds for what pi is. If the upper bound is 3.1416 and lower bound is 3.1415 for example then we know that the digits 3.141 100% are correct values in pi.