In a base-5 numeral system, what is the decimal equivalent of the number 243?

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Question: In a base-5 numeral system, what is the decimal equivalent of the number 243?

Options:

Correct Answer: 61

Solution:

The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

In a base-5 numeral system, what is the decimal equivalent of the number 243?

In a base-5 numeral system, what is the decimal equivalent of the number 243?

Step 1: Identify the base-5 number, which is 243.
Step 2: Break down the number 243 into its individual digits: 2, 4, and 3.
Step 3: Assign each digit a power of 5 based on its position from right to left, starting at 0: 2 is in the 5^2 position, 4 is in the 5^1 position, and 3 is in the 5^0 position.
Step 4: Calculate the value of each digit multiplied by its corresponding power of 5: 2 * 5^2 = 2 * 25 = 50, 4 * 5^1 = 4 * 5 = 20, and 3 * 5^0 = 3 * 1 = 3.
Step 5: Add all the calculated values together: 50 + 20 + 3 = 73.
Step 6: The decimal equivalent of the base-5 number 243 is 73.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-5 to decimal.
Exponentiation – Applying the concept of exponents in the context of base systems to calculate the value of each digit.