If a number in base 5 is represented as 243, what is its decimal equivalent? (20

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Question: If a number in base 5 is represented as 243, what is its decimal equivalent? (2023)

Options:

Correct Answer: 60

Exam Year: 2023

Solution:

The decimal equivalent of the base 5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60.

If a number in base 5 is represented as 243, what is its decimal equivalent? (2023)

If a number in base 5 is represented as 243, what is its decimal equivalent? (2023)

Step 1: Identify the base of the number. Here, the base is 5.
Step 2: Write down the number in base 5, which is 243.
Step 3: Break down the number 243 into its individual digits: 2, 4, and 3.
Step 4: Assign each digit a power of 5 based on its position from right to left, starting at 0. So, 2 is in the 2nd position (5^2), 4 is in the 1st position (5^1), and 3 is in the 0th position (5^0).
Step 5: Calculate the value of each digit multiplied by its corresponding power of 5: 2 * 5^2, 4 * 5^1, and 3 * 5^0.
Step 6: Calculate each term: 2 * 5^2 = 2 * 25 = 50, 4 * 5^1 = 4 * 5 = 20, and 3 * 5^0 = 3 * 1 = 3.
Step 7: Add all the calculated values together: 50 + 20 + 3.
Step 8: The final result is 60, which is the decimal equivalent of the base 5 number 243.

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 numbers to calculate their decimal values.