How can we use irrational numbers in math if we don’t know the full number?
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We do know the full number, we just don’t (can’t) know the full decimal that represents that number.
Pi is pi. It’s the ratio of a circle’s circumference to its diameter. 3.14159.. isn’t pi, that’s just an approximation that gets pretty close.
sin(pi) = 0, by definition. sin(3.14159) = 0.00000265.. (at least according to Google).
10 + pi is approximately 13.14159, sure. But ‘10 + pi’ describes the number more accurately and precisely. If we really need to, like we’re doing maths to design a machine or something, we can use the approximation at the end – it’s a lot simpler to tell a machinist to make it 13.14cm long than it is to tell them to make it (10 + pi) cm long. But at that point, it’s stopped being pure mathematics, and so approximations within a certain tolerance are more than good enough.
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