Why do we need to distinguish between rational and irrational numbers? What’s the importance of knowing where they fall between the two?

Question

Why do we need to distinguish between rational and irrational numbers? What’s the importance of knowing where they fall between the two?

In: Mathematics

Answer 1

As for “Real world applications”, there really aren’t any. Any irrational or transcendental number can be sufficiently calculated to the point of removing any practical error.

For instance, NASA uses ~15 decimal places of Pi for most of their calculations. If you were to look at using Pi to 15 decimal places versus Pi to significantly more decimal places, and were looking at a task like putting an orbiter around Mars (about 55 million kilometers away at closest points), then Pi to 15 decimal places still gives you precision to within a millimeter.