Revision Notes: Class 8 Maths Chapter 3 A Story of Numbers

Class 8 Maths Chapter 3: A Story of Numbers — Quick Revision Notes

• Origins of counting: numbers began as one-to-one correspondence (tally marks, pebbles, notches) tied to specific objects, not abstract entities.
• Grouping: Roman numerals introduced special symbols (V, X, L, C, D, M) for ‘landmark’ quantities instead of pure tallying.
• Gumulgal system: a Pacific/Australian indigenous base-2 additive counting method using just two words (urapon=1, ukasar=2).
• Base / landmark numbers: in a base-n system, landmark values are powers of n (1, n, n², n³…); the Egyptian system used base 10 additively (repeat a symbol up to 9 times, then move to the next landmark).
• Place value: pioneered by the Mesopotamians (base 60) — a symbol’s position, not just its shape, determines its value, drastically reducing the number of symbols needed.
• The zero problem: place-value systems without a true zero create ambiguity (e.g. Mesopotamian 60 vs 3605 both need placeholders for empty positions).
• The Hindu (Indian) system: introduced zero as both a placeholder and a number in its own right — the final piece making a place-value system unambiguous and efficient with just 10 symbols.
• Chinese rod numerals: alternated symbol orientation between place values purely to avoid visual misreading in a place-value system without gaps.
• Any base works: numbers can be represented in any base (2, 4, 5, 7, 8…) — this chapter has students convert the same number across several bases to internalise the idea.
• Why it matters today: the Hindu-Arabic base-10 system with zero underlies everyday arithmetic, and binary (base-2) place value underlies all modern computing.

Frequently Asked Questions

What makes rational numbers different from whole numbers and integers?
Rational numbers include all numbers that can be written as a fraction of two integers, including fractions and negative fractions, while whole numbers and integers are limited to whole values without any fractional parts.

Last Updated: September 23, 2026

Why are rational numbers said to be dense on the number line?
Between any two rational numbers, no matter how close together, there always exists another rational number, which means rational numbers can be found infinitely close to one another on the number line.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.