Rational numbers

Definition

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.

5 Must Know Facts For Your Next Test

1. Rational numbers include all integers, fractions, and terminating or repeating decimals.
2. The set of rational numbers is denoted by $\mathbb{Q}$.
3. Any rational number can be represented on a number line.
4. Operations like addition, subtraction, multiplication, and division (except by zero) on rational numbers result in another rational number.
5. Every integer is a rational number because it can be expressed as the integer divided by one.

Review Questions

• What is the definition of a rational number?
• Can every terminating decimal be considered a rational number? Why?
• Is the sum of two rational numbers always a rational number? Explain.

Related terms

Irrational Numbers: Numbers that cannot be expressed as a quotient of two integers. Their decimal expansions are non-terminating and non-repeating.

Integers: Whole numbers that can be positive, negative, or zero but do not include any fractional or decimal parts.

$\mathbb{Q}$: The set of all rational numbers.