All questions of A Story of Numbers for Class 8 Exam

Understanding Roman Numerals
Roman numerals are a numeral system originating from ancient Rome, using combinations of letters from the Latin alphabet. The primary letters used are:
- I (1)
- V (5)
- X (10)
- L (50)
- C (100)
- D (500)
- M (1000)
Identifying M
The letter "M" in Roman numerals represents the value 1000. Therefore, to find the numeral that comes just before "M," we need to identify the numeral that equals 999.
Analyzing the Options
Let's evaluate the given options:
- DCMXCIX:
- D (500) + C (100) + M (1000) + X (10) + C (100) + I (1) + X (10) = 999 (Incorrect)
- CMXCIX:
- C (100) + M (1000) + X (10) + C (100) + I (1) + X (10) = 999 (Correct)
- CMXCV:
- C (100) + M (1000) + X (10) + C (100) + V (5) = 995 (Incorrect)
- CMIX:
- C (100) + M (1000) + I (1) + X (10) = 911 (Incorrect)
Conclusion
The correct answer is option 'B' (CMXCIX), which represents 999. Therefore, CMXCIX is indeed the numeral that comes just before M (1000) in Roman numerals.

Understanding Base-8 (Octal) Number System
The base-8, or octal, number system uses digits from 0 to 7. Each digit's position represents a power of 8, similar to how the decimal system (base-10) uses powers of 10.
Converting 345 (base 8) to Base-10
To convert the octal number 345 to decimal (base-10), we evaluate each digit based on its position:
- The rightmost digit (5) is in the 8^0 position.
- The middle digit (4) is in the 8^1 position.
- The leftmost digit (3) is in the 8^2 position.
Calculation Steps
- Breakdown of the value:
- 3 × 8^2 = 3 × 64 = 192
- 4 × 8^1 = 4 × 8 = 32
- 5 × 8^0 = 5 × 1 = 5
- Adding these values together:
- Total = 192 + 32 + 5
Final Calculation
- Total = 229
Conclusion
Thus, the decimal equivalent of the octal number 345 is 229, confirming that the correct answer is option 'A'. This conversion process illustrates how to translate numbers between different bases, providing a solid understanding of the base-8 system.

Understanding Roman Numerals
Roman numerals are a numerical system used in ancient Rome, combining letters from the Latin alphabet. The basic symbols include:

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100

Breaking Down the Number 49
To represent the number 49 in Roman numerals, we analyze it as follows:
1. 50 - 1 = 49:
- The numeral for 50 is L.
- To express the idea of "one less than 50," we place X (which represents 10) before L.
2. Combining Symbols:
- Thus, we write XL for 40 (50 minus 10).
- Next, we need to add 9, which is represented as IX (10 minus 1).
3. Final Combination:
- When we combine these, we get XLIX for 49.
Why the Other Options Are Incorrect
- Option B: IL:
- This is not a valid Roman numeral, as there is no representation for 49 this way.
- Option C: VLIII:
- This represents 48 (5 + 1 + 1 + 1 + 1 = 48), which is incorrect.
- Option D: XLVIII:
- This represents 48 (40 + 5 + 1 + 1 + 1 = 48), so it is not correct for 49.
Conclusion
Thus, the correct Roman numeral for 49 is XLIX, making option 'A' the accurate choice.