What is the main characteristic of an irrational number?

An irrational number is defined by its decimal expansion, which is infinite and non-repeating. This means that when you try to express an irrational number in decimal form, the digits continue infinitely without forming a repeating pattern. Classic examples of irrational numbers include values like the square root of 2 and π (pi), both of which cannot be expressed as exact fractions.

The nature of an infinite and non-repeating decimal expansion is what fundamentally distinguishes irrational numbers from rational numbers, which can be expressed as fractions and have either repeating or terminating decimal expansions. Understanding this characteristic is essential as it helps differentiate between these two types of numbers in mathematics.