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Which of the following is the correct representation of the decimal number 10 in

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Question: Which of the following is the correct representation of the decimal number 10 in base-3?

Options:

  1. 101
  2. 110
  3. 100
  4. 111

Correct Answer: 110

Solution: 

To convert 10 to base-3, divide by 3: 10 ÷ 3 = 3 remainder 1, 3 ÷ 3 = 1 remainder 0, 1 ÷ 3 = 0 remainder 1. Reading the remainders from bottom to top gives 110.

Which of the following is the correct representation of the decimal number 10 in

Practice Questions

Q1
Which of the following is the correct representation of the decimal number 10 in base-3?
  1. 101
  2. 110
  3. 100
  4. 111

Questions & Step-by-Step Solutions

Which of the following is the correct representation of the decimal number 10 in base-3?
  • Step 1: Start with the decimal number 10 that you want to convert to base-3.
  • Step 2: Divide 10 by 3. The result is 3 with a remainder of 1. (10 ÷ 3 = 3, remainder 1)
  • Step 3: Take the quotient from the previous step (which is 3) and divide it by 3 again. The result is 1 with a remainder of 0. (3 ÷ 3 = 1, remainder 0)
  • Step 4: Now take the new quotient (which is 1) and divide it by 3. The result is 0 with a remainder of 1. (1 ÷ 3 = 0, remainder 1)
  • Step 5: You have now reached a quotient of 0, which means you can stop dividing.
  • Step 6: Write down the remainders from the last division to the first. The remainders are 1, 0, and 1.
  • Step 7: Reading the remainders from bottom to top gives you 110, which is the representation of the decimal number 10 in base-3.
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