If a number can be represented by the quotient of two integers, then it is rational (from "ratio"). Otherwise, the number is irrational. All integers are rational. All fractions are rational. Any decimal fraction that has a finite number of decimal digits is rational. Any decimal fraction that has an infinite number of decimal digits but has a repeating pattern is rational. Everything else, and that includes the majority of real numbers, are irrational.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it