If a number in base 5 is represented as '320', what is its decimal equivalent? (

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Question: If a number in base 5 is represented as \'320\', what is its decimal equivalent? (2023)

Options:

Correct Answer: 80

Exam Year: 2023

Solution:

The decimal equivalent of \'320\' in base 5 is calculated as (3 * 5^2) + (2 * 5^1) + (0 * 5^0) = 75 + 10 + 0 = 80.

If a number in base 5 is represented as '320', what is its decimal equivalent? (2023)

If a number in base 5 is represented as '320', what is its decimal equivalent? (2023)

Step 1: Identify the base of the number. The number '320' is in base 5.
Step 2: Write down the place values for each digit in '320'. The rightmost digit is 5^0, the middle digit is 5^1, and the leftmost digit is 5^2.
Step 3: Break down the number '320' into its digits: 3, 2, and 0.
Step 4: Multiply each digit by its corresponding place value: 3 * 5^2, 2 * 5^1, and 0 * 5^0.
Step 5: Calculate each multiplication: 3 * 5^2 = 3 * 25 = 75, 2 * 5^1 = 2 * 5 = 10, and 0 * 5^0 = 0 * 1 = 0.
Step 6: Add the results of the multiplications together: 75 + 10 + 0 = 85.
Step 7: The decimal equivalent of '320' in base 5 is 85.

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.