Rational number

Definition

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. They can be either positive, negative, or zero.

5 Must Know Facts For Your Next Test

1. All integers are rational numbers because they can be written as a fraction with a denominator of 1.
2. The set of rational numbers is denoted by the symbol Q.
3. Rational numbers include terminating and repeating decimals.
4. The sum or product of two rational numbers is always a rational number.
5. A rational number cannot have a non-repeating, non-terminating decimal expansion.

Review Questions

• What distinguishes a rational number from an irrational number?
• Can the decimal representation of a rational number be non-repeating and non-terminating? Why or why not?
• Is the sum of two rational numbers always a rational number? Explain.

Related terms

Integer: Whole numbers that can be positive, negative, or zero without any fractional part

Irrational Number: Numbers that cannot be expressed as a quotient of two integers and have non-repeating, non-terminating decimal expansions

Real Number: The set of all rational and irrational numbers