Rational number

Definition

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. Rational numbers include integers, fractions, and finite or repeating decimals.

5 Must Know Facts For Your Next Test

1. A rational number can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.
2. All integers are rational numbers because they can be expressed as a fraction with a denominator of 1 (e.g., $5 = \frac{5}{1}$).
3. Rational numbers can be positive, negative, or zero.
4. The decimal representation of a rational number either terminates or repeats periodically.
5. Rational numbers are closed under addition, subtraction, multiplication, and division (except by zero).

Review Questions

• What is the definition of a rational number?
• Can all integers be considered rational numbers? Explain why or why not.
• What types of decimal representations do rational numbers have?

Related terms

Integer: An integer is any whole number and its negative counterpart, including zero.

Irrational Number: An irrational number cannot be expressed as a fraction of two integers; its decimal representation is non-terminating and non-repeating.

Real Number: A real number includes all rational and irrational numbers; it represents any point on the number line.