In a numeral system where the base is 6, what is the value of '34'?

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Question: In a numeral system where the base is 6, what is the value of \'34\'?

Options:

Correct Answer: 24

Solution:

\'34\' in base 6 is calculated as 3*6^1 + 4*6^0 = 18 + 4 = 22.

In a numeral system where the base is 6, what is the value of '34'?

In a numeral system where the base is 6, what is the value of '34'?

Step 1: Identify the base of the numeral system, which is 6.
Step 2: Break down the number '34' into its digits. The first digit is 3 and the second digit is 4.
Step 3: Determine the place values for each digit. The first digit (3) is in the '6^1' place, and the second digit (4) is in the '6^0' place.
Step 4: Calculate the value of the first digit: 3 * 6^1 = 3 * 6 = 18.
Step 5: Calculate the value of the second digit: 4 * 6^0 = 4 * 1 = 4.
Step 6: Add the values from Step 4 and Step 5 together: 18 + 4 = 22.
Step 7: The final value of '34' in base 6 is 22 in decimal.

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 numeral system, where each position represents a power of the base.