Rational number
- CBSE · NCERT Class 9, Ch 3 The World of Numbers
A rational number is any number that can be written as p/q, where p and q are integers and q is not zero.
Every fraction is a rational number, and so is every integer. The integer 5 is rational because it can be written as 5/1. The number -3/4 is rational too. The bottom number q can never be 0, because division by zero has no meaning.
A rational number can be written in many ways. 1/2, 2/4 and 50/100 are all the same number.
A small example
Is 0.375 rational? Yes. It equals 375/1000, which cuts down to 3/8. Is 0.4545... rational, where 45 repeats forever? Yes again. It equals 5/11.
This gives a simple test. Divide p by q and the decimal either stops, like 3/8 = 0.375, or repeats a block of digits, like 5/11. A decimal that never stops and never repeats is not rational.
Why it matters later
Class 10 Chapter 1 proves that numbers such as √2 and √3 are irrational. Each proof begins by supposing the number is rational and writing it as a/b. So the definition above is the first line of the proof. If it is missing or loose, the rest of the proof has nothing to stand on.
Sources
Facts last checked against these sources on 30 September 2026.
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