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

To make it more worse, **approximate PI by random**:

from random import random

def interpolierePI(versuche = 1000000):
pi, im = 0, 0
for loop in range(versuche):
Xcord = random()
Ycord = random()
if(Xcord * Xcord + Ycord * Ycord <= 1):
im += 1
return(4 * im / versuche)

for i in range(10):
test = 10**i
print(test, interpolierePI(test))