What is Rational Number? Definition, Meaning & Example
A number that can be expressed as a fraction p/q, where p and q are integers and q is not zero.
TL;DR: A number that can be expressed as a fraction p/q, where p and q are integers and q is not zero.
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Rational Number: A number that can be expressed as a fraction p/q, where p and q are integers and q is not zero.
Explanation
Rational numbers include integers, fractions, and repeating or terminating decimals. Any integer can be written as a fraction with denominator 1, so all integers are rational numbers. Rational numbers are closed under addition, subtraction, multiplication, and division (except by zero). The set of rational numbers is denoted by Q. Rational numbers can be represented on a number line between integers. Examples include 1/2, 3/4, -2/3, and 5 (which equals 5/1). Understanding rational numbers is crucial for solving real-world problems involving parts of wholes.
Example
The fraction 3/4 is a rational number representing three-quarters. The decimal 0.75 is also a rational number because it equals 3/4. Both -2 and -2/1 are rational numbers.
Frequently Asked Questions
Are all fractions rational numbers?
Yes, all fractions with integer numerator and non-zero integer denominator are rational numbers by definition.
What about decimals like 0.333...?
Repeating decimals like 0.333... (which equals 1/3) are rational numbers because they can be expressed as fractions.
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