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

Because, you can develop a definite value for a rational number, it is exact. Irrational numbers are approximations of the value, the more precise you get with it the closer you are to the true value, but you will never quite reach it. You can take pi to 25 quintillion decimal places, but you still won’t have its exact value.