Extra Questions: Class 8 Maths Chapter 3 A Story of Numbers

Practice questions beyond the textbook exercises, testing deeper understanding of number systems and place value for Class 8 Maths Chapter 3: A Story of Numbers. These Class 8 Mathematics Chapter 3 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Extra Questions: Class 8 Maths Chapter 3 A Story of Numbers

1. 1 (Short Answer). What are the landmark numbers of a base-3 system?
   Solution: 3⁰=1, 3⁹=3, 3²=9, 3³=27, 3⁴=81…
2. 2 (Numerical). Convert the base-10 number 50 into base-8.
   Solution: 50 = 6×8+2 → 62 (base 8).
3. 3 (Assertion-Reason). Assertion: Roman numerals are unsuitable for large calculations. Reason: Roman numerals have no place value and no symbol for zero.
   Solution: Both true, and the reason correctly explains the assertion.
4. 4 (Applied). Represent the number 1948 in Roman numerals.
   Solution: MCMXLVIII (1000+900+40+8).
5. 5 (Synthesis). Why couldn’t a purely additive system like the Egyptian one ever represent negative numbers, while a place-value system with zero could eventually be extended to do so?
   Solution: An additive system only combines positive quantities of symbols with no concept of ‘direction’ or a zero reference point; once zero exists as a true number and reference point in a place-value system, negative numbers can be defined as positions ‘below’ zero.
6. 6 (Numerical). Convert 100 (base 5) back into base 10.
   Solution: 1×25+0×5+0×1 = 25.
7. 7 (Short Answer). Name two ancient civilisations mentioned in this chapter that used a place-value system.
   Solution: The Mesopotamians (base 60) and the Chinese (rod numerals); the Hindu (Indian) system later perfected it with true zero.
8. 8 (Applied). Convert 25 into base 4.
   Solution: 25 = 1×16+2×4+1×1 → 121 (base 4).
9. 9 (Assertion-Reason). Assertion: Zero is essential in a place-value system. Reason: Zero acts as a placeholder to distinguish numbers like 60 and 600.
   Solution: Both true, and the reason correctly explains the assertion.
10. 10 (Numerical). Convert the binary number 11001 back to base 10.
    Solution: 16+8+0+0+1 = 25.

Frequently Asked Questions

How can you find a rational number that lies exactly between two given rational numbers?
A rational number lying between two given rational numbers can be found by adding the two numbers together and dividing the result by two, which gives their average, a value that always lies exactly between them.

Why is zero considered a rational number even though it does not appear to be a fraction?
Zero can be expressed as a fraction with zero as the numerator and any non-zero integer as the denominator, such as zero over one, satisfying the definition of a rational number.

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