An irrational number is a type of real number that cannot be expressed as a simple fraction. This means that it cannot be written in the form of \fracab , where a and b are integers and b is not zero. Instead, irrational numbers have non-repeating and non-terminating decimal expansions. Examples include numbers like π (pi) and √2 (the square root of 2). Irrational numbers are important in mathematics because they help describe quantities that cannot be precisely represented by fractions. They appear in various areas, such as geometry, where π is used to calculate the circumference of a circle. Understanding irrational numbers expands our knowledge of the number system beyond just rational numbers.