CBSE Class 8 Annual Assessment

Annual assessment for Class 8 students under CBSE, focusing on advanced concepts in core subjects to prepare for higher secondary education.

A Story of Numbers — Class 8 Mathematics

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Mathematics · 14 chapters
Summary, key terms, important questions and a practice quiz with AI diagnosis for each.

Chapter 3: A Story of Numbers

Summary

This is a historical-mathematical chapter tracing how humans learned to count and to write numbers. Counting begins with one-to-one mapping — matching each object to a stick, a sound, or a symbol — leading to the idea of a number system as a standard ordered sequence. Early systems counted in groups (the Gumulgal of Australia counted in twos) and then used landmark numbers, as in the Roman system with \(I, V, X, L, C, D, M\). A major breakthrough was the idea of a base: choosing landmark numbers that are powers of a fixed number \(n\) gives a base-\(n\) system, of which the Egyptian system (base \(10\)) is an example. The next leap was place value, where a symbol’s position fixes which power of the base it represents — seen in the Mesopotamian (base \(60\)), Mayan and Chinese systems. The crowning idea was the Hindu number system: a base-\(10\) place-value system with ten digits including \(0\), treated as a number in its own right by Aryabhata and codified by Brahmagupta. Because of \(0\), every number can be written unambiguously with finitely many symbols.

Counting and one-to-one mappingEarly number systemsRoman and landmark numbersThe idea of a basePlace value and the role of zero

Key terms

Number system
A standard ordered sequence of objects, names, or symbols used to count and represent quantities.
Numeral
A written symbol that represents a number within a number system, such as \(0, 7\) or \(36\).
Landmark number
A reference number given its own symbol, used to group and build other numbers (e.g. \(V, X, L\) in Roman).
Base-\(n\) system
A system whose landmark numbers are the powers of a fixed number \(n\): \(1, n, n^2, n^3, \ldots\)
Place value system
A system in which a symbol’s position determines which landmark (power of the base) it stands for.
Role of zero
A placeholder and a number in its own right that lets all numbers be written unambiguously with finitely many digits.

Important questions

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Practice quiz

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Class 8 Maths — A Story of Numbers (Practice Quiz)

10 Qs · ~10 min