What are the two main types of real numbers?

The two main types of real numbers are rational and irrational numbers. Rational numbers can be expressed as a fraction where both the numerator and the denominator are integers, provided the denominator is not zero. This includes integers (like -3, 0, and 4), fractions (like 1/2 and -3/8), and terminating or repeating decimals (like 0.75 and 0.333…).

Irrational numbers, on the other hand, cannot be expressed as a simple fraction. They are non-repeating and non-terminating decimals, such as the square root of 2 or pi (π). These irrational numbers fill the gaps between the rational numbers on the number line, highlighting that there's an infinite number of real numbers that are not rational.

The classification of numbers into these two groups is fundamental in mathematics, as it establishes the complete set of real numbers, where every point on the continuous number line is represented. Understanding this distinction between rational and irrational numbers is crucial for comprehending more complex mathematical concepts and operations that involve real numbers.