In a numeral system where the digits are 0, 1, 2, 3, and 4, what is the value of

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Question: In a numeral system where the digits are 0, 1, 2, 3, and 4, what is the value of \'34\' in decimal?

Options:

Correct Answer: 16

Solution:

\'34\' in base 5 is calculated as 3*5^1 + 4*5^0 = 15 + 4 = 19.

In a numeral system where the digits are 0, 1, 2, 3, and 4, what is the value of '34' in decimal?

In a numeral system where the digits are 0, 1, 2, 3, and 4, what is the value of '34' in decimal?

Step 1: Identify the base of the numeral system. Here, the base is 5 because the digits are 0, 1, 2, 3, and 4.
Step 2: Write down the number '34'. The first digit (3) is in the '5^1' place, and the second digit (4) is in the '5^0' place.
Step 3: Calculate the value of the first digit: 3 * 5^1 = 3 * 5 = 15.
Step 4: Calculate the value of the second digit: 4 * 5^0 = 4 * 1 = 4.
Step 5: Add the values from Step 3 and Step 4 together: 15 + 4 = 19.
Step 6: The final result is that '34' in base 5 equals 19 in decimal.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 5 to decimal.
Place Value – Recognizing the significance of each digit's position in a numeral system.