define irrational numbers on the number line

Irrational numbers are numbers that cannot be expressed as a fraction (ratio) of two integers, and their decimal representations neither terminate nor repeat. On the number line, irrational numbers are located between rational numbers. They span an infinite and dense continuum on the number line, meaning that between any two irrational numbers, there are infinitely many other irrational numbers. Examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).