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NCERT Solutions for Class 8th Maths Chapter 3 A Story of Numbers

Updated on 2026-09-19

About this chapter

To count you need a standard sequence of objects, names or written symbols with a fixed order — that sequence is a number system . Counting a collection means making a one-to-one mapping onto it. The written symbols of a number system are called numerals . Numbers that get a symbol of their own and act as reference points are called landmark numbers . If the landmark numbers are 1, n , n 2 , n 3 , … — the powers of one number — the system is a base- n system. Base 10 is called decimal . In a base- n system the product of two landmark numbers is again a landmark number, which is exactly why multiplication is easy there and hard in the Roman system. A system that uses the position of a symbol to decide which landmark it counts is a place value system . Mesopotamia, the Maya, China and India

  • .1 Reema’s Curiosity
  • The Mechanism of Counting
  • .2 III. Number Names Obtained by Counting in Twos
  • .2 IV. The Roman Numerals
  • .3 I. The Egyptian Number System
  • .3 Advantages of a Base-n System
  • .3 Abacus that Makes Use of the Decimal System
  • .3 III. Shortcomings of the Egyptian System
  • .4 I. The Mesopotamian Number System
  • .4 II. The Mayan Number System
Quick revision
Number systemLandmark numbersThe idea it addsHow 27 is written
Sticks / tally marks1 onlyOne-to-one mapping: one mark per object27 marks
Gumulgal (Australia)1, 2Counting in a fixed group size (2s)ukasar repeated 13 times, then urapon (14 words)
Roman1, 5, 10, 50, 100, 500, 1000A sequence of landmark numbers — but not powers of one numberXXVII
Egyptian1, 10, 102, …, 107Landmarks are powers of 10 — a base2 arches + 7 strokes
Our base-5 system1, 5, 25, 125, 625, 3125The same idea with a different base⬡ △△ (25 + 1 + 1)
Mesopotamian (Babylonian)1, 60, 602, 603Place value; later a placeholder for a blank<< YYYYYYY (two 10-wedges, seven 1-wedges)
Mayan1, 20, 360, 7200, 144000Place value written vertically; a shell for 01 dot above; 1 bar + 2 dots below
Chinese rod numeralspowers of 10Place value made readable by alternating Zong and HengHeng-2 above the tens place, Zong-7 in the units
Hindu (Indian)1, 10, 100, 1000, …0 as a digit and as a number; ten symbols for everything27
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Exercises

  1. .1 Reema’s Curiosity — In-text Questions Page 483
  2. The Mechanism of Counting — Math Talk Page 51
  3. The Mechanism of Counting — In-text Questions Page 52 – 53
  4. The Mechanism of Counting — Figure it Out Page 54
  5. .2 III. Number Names Obtained by Counting in Twos — In-text Questions Page 57 – 583
  6. .2 IV. The Roman Numerals — Figure it Out Page 593
  7. .2 IV. The Roman Numerals — In-text Questions Page 603
  8. .2 IV. The Roman Numerals — Figure it Out Page 60 – 613
  9. .3 I. The Egyptian Number System — Figure it Out Page 623
  10. .3 II. Variations on the Egyptian System and the Notion of Base — In-text Questions Page 623
  11. .3 II. Variations on the Egyptian System and the Notion of Base — In-text Questions Page 633
  12. .3 II. Variations on the Egyptian System and the Notion of Base — Figure it Out Page 633
  13. .3 Advantages of a Base-n System — Figure it Out Page 653
  14. .3 Advantages of a Base-n System — In-text Questions Page 663
  15. .3 Advantages of a Base-n System — In-text Questions Page 673
  16. .3 Advantages of a Base-n System — In-text Questions Page 683
  17. .3 Abacus that Makes Use of the Decimal System — In-text Questions Page 693
  18. .3 III. Shortcomings of the Egyptian System — Figure it Out Page 69 – 703
  19. .4 I. The Mesopotamian Number System — In-text Questions Page 723
  20. .4 I. The Mesopotamian Number System — Figure it Out Page 733
  21. .4 I. The Mesopotamian Number System — In-text Questions Page 733
  22. .4 II. The Mayan Number System — In-text Questions Page 763
  23. .4 IV. The Hindu Number System — In-text Questions Page 783
  24. .4 The Hindu Number System — Figure it Out Page 803
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