Test: A Story of Numbers - Class 8 MCQ

M = 1000, CM = 900, XC = 90, IV = 4 → 1994.

The symbol for 60 is important in various number systems, especially in the Mesopotamian sexagesimal system. H

99 is correctly written as XCIX, not IC.

49 = 40 (XL) + 9 (IX) → XLIX.

To find the 4th landmark number in a base-7 system:

• The landmark numbers are the powers of the base.
• Starting from 1 (which is 7⁰):
• The first landmark number is 7⁰ = 1.
• The second landmark number is 7¹ = 7.
• The third landmark number is 7² = 49.
• The fourth landmark number is 7³ = 343.

Thus, the 4th landmark number after 1 in a base-7 system is 343.

999 = 900 (CM) + 90 (XC) + 9 (IX) → CMXCIX.

376 = 300 (CCC) + 70 (LXX) + 6 (VI) → CCCLXXVI

Solution:

To convert the number 345 from base-8 to base-10, follow these steps:

• Identify the place values in base-8:
  • 3 in the hundreds place (8²)
  • 4 in the tens place (8¹)
  • 5 in the units place (8⁰)
• Calculate the value of each digit:
  • 3 × 8² = 3 × 64 = 192
  • 4 × 8¹ = 4 × 8 = 32
  • 5 × 8⁰ = 5 × 1 = 5
• Add these values together:
  • 192 + 32 + 5 = 229

Thus, the value of 345 in base-10 is 229.

45 + 25 = 70 → LXX.

In a base-5 system, the third landmark number after 1 is:

The landmark numbers in a base-5 system are calculated as powers of 5, starting from:

• 5⁰ = 1
• 5¹ = 5
• 5² = 25
• 5³ = 125
• 5⁴ = 625

The sequence indicates that:

• The first landmark number is 1.
• The second landmark number is 5.
• The third landmark number is 25.

Therefore, the third landmark number after 1 in a base-5 system is 25.