Practice30Create account

Class 8 Number Bases and Old Numeral Systems — practice questions with answers

Number System · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. In our base-10 (Indian) numeral system, what is the place value of 7 in 4,705?
Show answer
Answer: C) 700
4,705 = 4 thousands + 7 hundreds + 0 tens + 5 ones. The 7 stands in the hundreds place, so its value is 700.
2. What is the largest number (in base 10) you can write with three binary digits?
Show answer
Answer: C) 7
The largest 3-digit binary numeral is 111₂ = 4 + 2 + 1 = 7. The next number, 8, needs four digits: 1000₂.
3. How many binary digits does the number 100 need?
Show answer
Answer: B) 7
64 ≤ 100 < 128, and 64 = 2⁶ is the 7th place (1, 2, 4, 8, 16, 32, 64). Indeed 100 = 1100100₂, 7 digits.
4. What is 102 in base 3 equal to in base 10?
Show answer
Answer: A) 11
Base-3 places are 9, 3, 1. 102₃ = 1 × 9 + 0 × 3 + 2 = 11.
5. A Mesopotamian tablet shows a 1, then an empty gap where a place is skipped, then another 1, all in base 60. What is the value?
Show answer
Answer: B) 3601
The gap is an empty sixties place. Value = 1 × 3600 + 0 × 60 + 1 = 3601. Without a clear zero symbol, scribes could confuse this with 61, which is why a true zero matters.
Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.