How can we use irrational numbers in math if we don’t know the full number?
In: 232
A flip side to many of the good answers that have been given here
One angle to consider is in what ways do we use irrational numbers?
A lot of the answers here are discussing it’s use in theoretical, or pure maths, an area that likes exact definitions. If you want to know more about that, and why something like pi is usable without the decimal representation, you’re looking for “Group Theory”
In essence, we can use these irrational numbers because the way we express them has defined rules of mathematics that work the same as the rules that we have for decimal numbers.
The flip side is when we want to use maths practically. Say you’re an engineer, and you want to build a bridge. How many decimal places of pi should you use? If you use too few, will the bridge be at risk of breaking?
With only 40 decimal places of pi, you can calculate the circumference of the universe to within the width of an atom.
So in terms of application, our estimates do not need to be exact, since a difference of 0.0000000000000000000000000000000000000001 meters, doesn’t make that much difference
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