They are a way of approximating Real (the set not as an adjective) numbers, though. Real numbers are exact when they are equal to an integer or a rational, beca

They are a way of approximating Real (the set not as an adjective) numbers, though. Real numbers are exact when they are equal to an integer or a rational, because, depending on how you construct them, either that's what the cut contains or that's where the series converges. And also because that's what the most common spec demands.