Which of the following is NOT a valid representation of the decimal number 10 in

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Question: Which of the following is NOT a valid representation of the decimal number 10 in any base?

Options:

Correct Answer: 22

Solution:

\'22\' cannot represent 10 in any base since it would require base 3 or higher.

Which of the following is NOT a valid representation of the decimal number 10 in any base?

Which of the following is NOT a valid representation of the decimal number 10 in any base?

Step 1: Understand what a base is. A base is a number system that uses digits to represent values. For example, base 10 uses digits 0-9.
Step 2: Identify the decimal number we are working with, which is 10.
Step 3: Look at the representation '22'. This means 2 in the 'tens' place and 2 in the 'ones' place.
Step 4: Calculate what '22' means in base 3. In base 3, '22' means 2*3^1 + 2*3^0 = 6 + 2 = 8.
Step 5: Since '22' in base 3 equals 8, it does not equal 10. Therefore, '22' cannot represent 10 in base 3.
Step 6: Check if '22' can represent 10 in any base higher than 3. In base 4, '22' means 2*4^1 + 2*4^0 = 8 + 2 = 10, which is valid.
Step 7: Conclude that '22' cannot represent 10 in base 3 or lower, making it an invalid representation in any base lower than 4.

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