Rational and Irrational Numbers

Rational and irrational numbers are fundamental concepts in mathematics, representing two distinct categories of real numbers. Rational numbers can be expressed as a ratio of two integers, where the denominator is not zero. These include fractions and terminating or repeating decimals. In contrast, irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal representations. Famous examples of irrational numbers include π (pi) and √2 (the square root of 2). Understanding the properties and distinctions between these two types of numbers is essential in various mathematical applications, from algebra to calculus.