If 'x' is a number in base 5 represented as '320', what is its decimal equivalen

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

Options:

Correct Answer: 75

Solution:

\'320\' in base 5 = 3*5^2 + 2*5^1 + 0*5^0 = 75.

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

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

Step 1: Understand that '320' is a number in base 5.
Step 2: Identify the place values for each digit in '320'. The rightmost digit is the '5^0' place, the middle digit is the '5^1' place, and the leftmost digit is the '5^2' place.
Step 3: Write down the value of each digit multiplied by its place value: 3 is in the '5^2' place, 2 is in the '5^1' place, and 0 is in the '5^0' place.
Step 4: Calculate the value of each digit: 3 * 5^2 = 3 * 25 = 75, 2 * 5^1 = 2 * 5 = 10, and 0 * 5^0 = 0 * 1 = 0.
Step 5: Add all the values together: 75 + 10 + 0 = 85.
Step 6: 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.