Class 9 · Chapter 5
I'm Up and Down, and Round and Round
Cyclic and repeating patterns; periodic behaviour.
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Ganita Manjari · Class 9 (2026-27)
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Detailed theory
If for all , we say has period . Smallest such is the fundamental period.
Key concepts & formulas
01
A **periodic** pattern repeats after a fixed interval — the **period**.
02
Real-life periodicity: seasons, clock, tides, days-of-week.
03
Modular arithmetic: gives remainder cycles.
04
Cycles .
05
Fractions produce recurring decimal cycles (period ≤ denom − 1).