You don’t. It very rarely matters in practice that pi has infinite digits. A few dozen will get you calculations accurate enough to be within a speck of dust sized error on a circle the size of our galaxy. If you just give it a name like pi, or x, or a, or whatever, you can just use that, the math will check out fine without you writing out the digits.
> The concept alone is as irrational as the numbers…
You better get used to it, because they outnumber rational numbers. In fact, in the set of real numbers (rational+irrational numbers), the rational numbers make up 0% of the total.
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