Chapter 1: Real Numbers
5 lessons
Real Numbers extends Class 8's rational numbers to include irrational numbers — numbers like √2 or π whose decimal expansion never terminates or repeats — and covers plotting them accurately using successive magnification.
A common misconception, cleared up
Not every non-terminating decimal is irrational — a repeating decimal like 0.333... is actually rational, since it equals exactly 1/3. Students also tend to round an irrational number too early in a calculation, which can quietly carry an error through several later steps; keeping √2 as √2, rather than rounding it to 1.41 immediately, usually gives a cleaner final answer.
This chapter is the conceptual foundation for every number system used afterward — irrational side lengths from the Pythagorean theorem, trigonometric ratios, and Class 10's own Real Numbers chapter, which proves several of these irrationality results formally.