What Is a Rational Number?
A rational number is any number that can be written in the form , where and are integers and .
The word rational comes from "ratio" — a rational number is simply one number compared to another as a fraction. This family of numbers is huge! It includes:
- Whole numbers (e.g. ) — because
- Fractions (e.g. )
- Decimals that terminate (e.g. )
- Decimals that repeat (e.g. )
The denominator can never be zero. Division by zero is undefined, so is not a rational number — it is not a number at all!
Numbers that cannot be written as a fraction of two integers are called irrational numbers (e.g. and ). Together, rational and irrational numbers make up all the real numbers — every single point on the number line.
The Number Line — Your Map of All Real Numbers
A number line is a straight line where every point corresponds to exactly one real number. It stretches infinitely in both directions.
- Numbers increase as you move to the right
- Numbers decrease as you move to the left
- Zero sits in the middle, separating positive numbers (right) from negative numbers (left)
Think of a number line like a street with house numbers. The positive side is to the right of the town centre (zero), and the negative side is to the left. Every address on the street belongs to a unique number — rational or irrational.
Because rational numbers include fractions and decimals, the gaps between whole numbers are filled with infinitely many rational points. No matter how small a gap you pick, you can always find a rational number inside it.
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