There are two types of real numbers: rational numbers and irrational numbers. Rational numbers can be written as a ratio of two integers and when expressed as decimals are either terminating or repeating. Irrational numbers cannot be written as a ratio of integers and when expressed as decimals are non-terminating and non-repeating. Examples of rational numbers include integers and fractions while examples of irrational numbers include square roots of non-perfect squares and pi.