The set of rational numbers contains all numbers that can be written as fractions, or quotients of integers.
Integers are also rational numbers since they can be represented as fractions.
All decimals that repeat or terminate belong to the set of rational numbers. The irrational numbers are nonrepeating, nonterminating decimals. They cannot be represented as the quotient of two integers. The set of real numbers consists of all the rational numbers together with all the irrational numbers. Start with the innermost and work outward.