How can we use irrational numbers in math if we don’t know the full number?

Question

How can we use irrational numbers in math if we don’t know the full number?

In: 232

Answer 1

3.14159265358979323846264338327950288420

These are all the digits of Pi necessary to calculate the circumference of the visible universe to a precision of a hydrogen atoms diameter. As you can see, it is far from infinite digits.

And to get a bit more philosophical, while infinities exist in math, they do not seem to exist physically in our universe, so infinite precision is not only not necessary, it’s probably not possible. So worrying about the “full” number is pointless. And in the math itself you just dismiss the issue by giving the number a symbol and calling it a day.