Exercise 1.2 — Number Line

Exercise 1.2 — Rational Numbers on the Number Line

Visualising rational numbers on a number line is a skill that connects arithmetic to geometry. Exercise 1.2 in Class 8 Mathematics develops your ability to locate, compare, and insert rational numbers with precision — skills that appear again in coordinate geometry and real numbers.

How to Place Rational Numbers Precisely

• To represent p/q: divide the unit interval into q equal parts and mark the p-th division point from zero.
• Negative rationals lie to the left of zero — −p/q is as far left as p/q is right.
• To insert n rational numbers between a and b, find a+d, a+2d, ..., a+nd where d = (b−a)/(n+1).
• Convert to decimals for quick comparison when ordering a list of rational numbers — especially useful in MCQs.
• The density property guarantees you can always find a rational between any two given rationals using their average (a+b)/2.

Connection to Later Topics

Number line representation is the visual language of mathematics. In Class 9, you will extend this to irrational numbers and real numbers. In Class 10, coordinate geometry uses the two-dimensional version of this skill. Every mark you invest in Exercise 1.2 pays dividends across multiple chapters and years.

How to Use This Lesson

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