irrational numbers, that is, real numbers that are not rational numbers, cannot be written as the ratio of two integers. if you write it in decimal form, there are infinite numbers after the decimal point and there will be no loops. common irrational numbers include the square root of an imperfect square number, π and e (the latter two are both transcendental numbers), etc. another characteristic of irrational numbers is infinite continued fraction expressions. legend has it that irrational numbers were first discovered by hibbers, a disciple of the pythagoreans.

an irrational number is a number in the range of real numbers that cannot be expressed as a ratio of two integers. simply put, irrational numbers are infinite non-repeating decimals in base 10. such as pi, √2 (square root 2), etc. rational numbers are composed of all fractions and integers, which can be converted into finite decimals or infinitely recurring decimals. such as 22/7 etc.