Class 9 Maths — Real Numbers

Rational numbers: Terminating (e.g., 0.125) or non‑terminating repeating (e.g., 0.3\(\overline{3}\)).
Irrational numbers: Non‑terminating, non‑repeating (e.g., \(\pi=3.14159...\)).
Test for termination: For rational \(\frac{p}{q}\) in lowest terms, decimal terminates iff prime factors of \(q\) are only 2 and/or 5.

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Number Line — Key Points