Which of the following numbers is the largest in base-6?

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Question: Which of the following numbers is the largest in base-6?

Options:

Correct Answer: 63

Solution:

In decimal, \'54\' = 32, \'45\' = 29, \'63\' = 39, \'36\' = 22. \'63\' is the largest.

Which of the following numbers is the largest in base-6?

Which of the following numbers is the largest in base-6?

Step 1: Understand that we need to compare numbers in base-6.
Step 2: Convert each base-6 number to decimal (base-10) to make comparison easier.
Step 3: Convert '54' from base-6 to decimal: 5 * 6^1 + 4 * 6^0 = 30 + 4 = 34.
Step 4: Convert '45' from base-6 to decimal: 4 * 6^1 + 5 * 6^0 = 24 + 5 = 29.
Step 5: Convert '63' from base-6 to decimal: 6 * 6^1 + 3 * 6^0 = 36 + 3 = 39.
Step 6: Convert '36' from base-6 to decimal: 3 * 6^1 + 6 * 6^0 = 18 + 6 = 24.
Step 7: Now we have the decimal values: '54' = 34, '45' = 29, '63' = 39, '36' = 24.
Step 8: Compare the decimal values: 34, 29, 39, and 24.
Step 9: Identify the largest value, which is 39 from '63'.
Step 10: Conclude that '63' is the largest number in base-6.

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