How can we use irrational numbers in math if we don’t know the full number?
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In general math very rarely makes statements about individual numbers. Instead it works with “lets say we have a set of objects that have this and that property and we show that some member of this set now has this and that property.”
When we do have to work with individual numbers we can give them a name and then make use of the fact, that each real number can be characterised by at least one sequence of rational numbers converging onto it. We just give whatever this sequence is converging to a name.
For example to find PI you can use something like [https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80](https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80) to get arbitrarily close approximations for it.
If you do numerical calculations you can then in general find some rule that goes like this: “If we use this and that approximation by rational numbers our result will be less them (some other rational number) apart from the the actual result. And this is enough in virtually all case math is put to a practical use.
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