NCERT Solutions for Class 8 Maths – Ganita Prakash
Chapter: A Story of Numbers
Exercise 3.3 (Figure it Out – Continued)
1. Why do different sequences of number names exist?
Different sequences are used because:
- Different objects may be counted in culturally meaningful ways.
- It helps in easier grouping and identification of objects.
- It reduces confusion when counting different categories (like fish, coconuts, tools).
- It reflects the traditions and practical needs of the community.
Conclusion: It makes counting more organized and meaningful.
2. Operations in the Gumulgai system:
Understanding:
- “ukasar” represents 2
- “urapon” represents 1
(i)
(ukasar-ukasar-ukasar-ukasar-urapon) = 2+2+2+2+1 = 9
(ukasar-ukasar-urapon) = 2+2+1 = 5
9 + 5 = 14 = ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar
Answer: ukasar repeated 7 times
(ii)
9 − 6 = 3 = ukasar + urapon
Answer: ukasar-urapon
(iii)
9 × 4 = 36
36 = 2×18 → ukasar repeated 18 times
Answer: ukasar repeated 18 times
(iv)
Total = ukasar repeated 8 times = 16
Divided by ukasar-ukasar (4)
16 ÷ 4 = 4 = ukasar-ukasar
Answer: ukasar-ukasar
3. Features of Hindu number system:
- Place Value System: Value depends on position.
- Use of Zero: Helps represent large numbers easily.
- Compact Representation: Uses only 10 digits.
- Easy Calculations: Arithmetic operations are simple.
- Scalability: Can represent very large numbers.
Conclusion: It is more efficient than the Roman system.
4. Refining your number system:
Improved System Example:
- Use symbols: 0–9 (base-10 system)
- Introduce place value (units, tens, hundreds)
- Use zero as a placeholder
Example:
- 245 = 2×100 + 4×10 + 5
Conclusion:
A refined system should:
- Be easy to write
- Be easy to calculate
- Represent large numbers efficiently