In a base 6 number system, what is the decimal equivalent of the number '54'?

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Question: In a base 6 number system, what is the decimal equivalent of the number \'54\'?

Options:

Correct Answer: 34

Solution:

\'54\' in base 6 = 5*6^1 + 4*6^0 = 30 + 4 = 34.

In a base 6 number system, what is the decimal equivalent of the number '54'?

In a base 6 number system, what is the decimal equivalent of the number '54'?

Step 1: Identify the base of the number system. Here, the base is 6.
Step 2: Write down the number '54' in base 6. The first digit is 5 and the second digit is 4.
Step 3: Understand the place values in base 6. The leftmost digit (5) is in the '6^1' place, and the rightmost digit (4) is in the '6^0' place.
Step 4: Calculate the value of the leftmost digit: 5 * 6^1 = 5 * 6 = 30.
Step 5: Calculate the value of the rightmost digit: 4 * 6^0 = 4 * 1 = 4.
Step 6: Add the two values together: 30 + 4 = 34.
Step 7: The decimal equivalent of '54' in base 6 is 34.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 6 to decimal.
Place Value – Recognizing the significance of each digit's position in a number based on its base.