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 = ~~22 / 7 by definition~~ (the circumference of a circle divided by its diameter)

~~So whatever number comes up next in the string when you work out “twenty-two divided by seven” is the right number~~