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NCERT Solutions for Ganita Prakash (Part 1) Chapter 3 A Story of Numbers

Updated on 2026-09-05

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
  • – 53The Mechanism of Counting
  • – 583.2 III. Number Names Obtained by Counting in Twos
  • .2 IV. The Roman Numerals
  • – 613.2 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
  • – 703.3 III. Shortcomings of the Egyptian System
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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. – 53The Mechanism of Counting — In-text Questions Page 52
  4. The Mechanism of Counting — Figure it Out Page 54
  5. – 583.2 III. Number Names Obtained by Counting in Twos — In-text Questions Page 57
  6. .2 IV. The Roman Numerals — Figure it Out Page 593
  7. .2 IV. The Roman Numerals — In-text Questions Page 603
  8. – 613.2 IV. The Roman Numerals — Figure it Out Page 60
  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. – 703.3 III. Shortcomings of the Egyptian System — Figure it Out Page 69
  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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