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

All it is a division problem that never ends.

The next number will just be the next in the sequence. To that level of pi that number is accurate. The further you go, the more accurate you get. So if you are at the 5th number there will always be an option to go to the 6th….and the 7th…..and so forth.