NCERT Solutions Class 8 Maths Ganita Prakash Chapter 3 — A Story of Numbers#

Chapter 3 of Ganita Prakash Part I follows how people learnt to write numbers: counting with sticks and names, the Roman numerals, the Egyptian system and the idea of a base, the place-value systems of Mesopotamia, the Mayans and China, and finally the Hindu number system with its digit 0.

Exercises#

• Figure it Out — Page 54 — Arithmetic with sticks, extending a letter-based system, making your own system (3 questions)
• Figure it Out — Page 59 — Writing numbers in Roman numerals (1 question)
• Figure it Out — Page 60 — Counting by 2s (Gumulgal), Hindu vs Roman numerals (4 questions)
• Figure it Out — Page 62 — Writing and reading Egyptian numerals (2 questions)
• Figure it Out — Page 63 — A base-5 system, landmark numbers of base 7 and base n (3 questions)
• Figure it Out — Page 65 — Adding Egyptian and base-5 numerals (2 questions)
• Figure it Out — Page 69 — Limits of the Egyptian system, a base-4 system, multiplying by 5 in base 5 (3 questions)
• Figure it Out — Page 73 — Writing numbers in the Mesopotamian system (1 question)
• Figure it Out — Page 80 — Chinese rod numerals, base 2, base 8 and base 5 (4 questions)

What you will learn#

• A number system is a fixed sequence of objects, names or symbols used for counting.
• Landmark numbers (like I, V, X, L, C, D, M) make large numbers shorter to write.
• In a base-n system the landmark numbers are $1, n, n^2, n^3, \ldots$
• In a place value system the position of a symbol decides its value, and 0 marks an empty place.

Key formulas and results#

• Base-10: $375 = 3 \times 10^2 + 7 \times 10 + 5$
• Base-5: $143 = 1 \times 5^3 + 0 \times 5^2 + 3 \times 5 + 3$
• Base-60 (Mesopotamian): $7530 = 2 \times 60^2 + 5 \times 60 + 30$

Read and revise#

• NCERT Class 8 Maths Chapter 3 (PDF) — the Ganita Prakash Part I chapter itself.
• All Class 8 Maths chapters from Ganita Prakash Part I and Part II.

Frequently asked questions#