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. Rational numbers can be positive, negative, or zero.
2. Every integer is a rational number because it can be expressed as itself divided by one.
3. A rational number can always be written in the form $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$.
4. The decimal representation of a rational number either terminates or eventually repeats.
5. When solving linear equations in one variable, solutions are often sought in the set of rational numbers.

Review Questions

• How would you express the rational number $-3.75$ as a fraction?
• Is the number $0.333...$ (repeating) a rational number? Why?
• Can every integer be considered a rational number? Explain your answer.

Related terms

Integer: An integer is any whole number, positive or negative, including zero.

Irrational Number: An irrational number cannot be expressed as a simple fraction; its decimal form does not terminate or repeat.

Linear Equation: $A linear equation$ is an equation between two variables that gives a straight line when plotted on a graph. In one variable, it has the form $ax + b = c$.