Rational numbers

Definition

Rational numbers are any numbers that can be expressed as the quotient or fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. They include fractions, integers, and finite or repeating decimals.

5 Must Know Facts For Your Next Test

1. All integers are rational numbers because they can be expressed as fractions with a denominator of 1.
2. Rational numbers can be either positive or negative.
3. Any finite decimal or repeating decimal is a rational number.
4. The set of rational numbers is denoted by the symbol $\mathbb{Q}$.
5. Operations such as addition, subtraction, multiplication, and division (except by zero) on rational numbers result in another rational number.

Review Questions

• Is every integer a rational number? Explain why or why not.
• Can a non-repeating, non-terminating decimal be considered a rational number? Why?
• Express the repeating decimal $0.3333\ldots$ as a fraction.

Related terms

Integers:

Whole numbers that can be positive, negative, or zero; denoted by the symbol $\mathbb{Z}$.

Irrational Numbers:

Numbers that cannot be expressed as fractions; their decimal expansions are non-repeating and non-terminating.

$\mathbb{Q}$: The set of all rational numbers, including both positive and negative fractions and integers.