Real number
- CBSE · NCERT Class 9, Ch 3 The World of Numbers
A real number is any number that has a place on the number line, whether it is rational, like 3/4, or irrational, like √2.
Put the rational numbers and the irrational numbers together and you get the real numbers. They fill the number line with no gaps. Every point on the line stands for one real number, and every real number has one point.
So natural numbers, whole numbers, integers and fractions are all real numbers. So are √2, √5 and π. Each set sits inside the next, like boxes inside a bigger box.
A small example
Take the numbers 7, -2, 0.6, √3 and π. Sort them:
- 7 is natural, whole, an integer, rational and real.
- -2 is an integer, rational and real.
- 0.6 is 3/5, so it is rational and real.
- √3 and π are irrational, but still real.
All five are real numbers. In school maths, you meet no numbers outside this set until much later.
Why it matters later
Class 10 Chapter 1 is named Real Numbers. In Chapter 4, the discriminant decides whether a quadratic equation has real roots at all. "No real roots" means no point on the number line solves it. You need to know what counts as real to read that answer correctly.
Sources
Facts last checked against these sources on 30 September 2026.
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