Rational numbers can be fractions of integers. Irrational numbers cannot be expressed as ratios. Decimal representations help identify them. Pi and Euler's number are irrational.

This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ratio of two whole numbers. When expressed as a decimal, irrational numbers go on ...

Rational numbers, which make up the majority of numbers we use in day-to-day life (although less than half of all possible numbers), can be written in the form of one whole number divided by ...

The golden ratio doesn’t arise only in geometry; in the Fibonacci sequence, where each number is the sum of the two previous ones (1, 1, 2, 3, 5, 8, 13, 21, 34, …), the ratios between ...

The existence of irrational numbers is best explained with an isosceles right triangle—that is, a triangle with two sides of an equal length that form a right angle.

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, ...

However, rather than proving pi is irrational directly, it's also possible to confirm irrationality using a different property of the number.