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

Pi isn’t infinite: it’s greater than 3.1 and less than 3.2.

What it isn’t is rational: it’s not equal to a ratio of integers. “3.14159” is, in fact, a ratio of integers: it’s 314159/100000. When we calculate pi to one more decimal place we’re still getting a number that is not equal to pi; it’s just that now we’ve limited how far off we are by another power of ten.