Irrational / Rational Numbers and Recurring Decimals Every number is either rational or irrational, whether large or small, negative or positive.

Irrational numbers are real numbers that, when expressed as a decimal, go on forever after the decimal and never repeat. (Image credit: Shutterstock) ...

It’s that the golden ratio, among all irrational numbers, is the most irrational one. What can that mean? Either a number is the ratio of two whole numbers or it isn’t*.

A number like 1/7 needs infinitely many decimals to write down - 0.1428571428571… - but the numbers repeat themselves every six places, making it easy to understand.

Many people conceptualize irrational numbers by rounding them to fractions or decimals: estimating π as 3.14, which is equivalent to 157/50, leads to widespread celebration of Pi Day on March 14th.

Notice that none of the other irrational numbers have something like this - a jump much greater than the 'average' except for e and pi.