If a number in base 5 is represented as '243', what is its equivalent in decimal

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Question: If a number in base 5 is represented as \'243\', what is its equivalent in decimal?

Options:

Correct Answer: 62

Solution:

\'243\' in base 5 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

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

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

Step 1: Identify the base of the number. The number '243' is in base 5.
Step 2: Write down the place values for each digit in '243'. The rightmost digit is 5^0, the middle digit is 5^1, and the leftmost digit is 5^2.
Step 3: Multiply each digit by its corresponding place value. For '243':
- The leftmost digit is 2, so calculate 2 * 5^2.
- The middle digit is 4, so calculate 4 * 5^1.
- The rightmost digit is 3, so calculate 3 * 5^0.
Step 4: Calculate each multiplication:
- 2 * 5^2 = 2 * 25 = 50.
- 4 * 5^1 = 4 * 5 = 20.
- 3 * 5^0 = 3 * 1 = 3.
Step 5: Add all the results together: 50 + 20 + 3.
Step 6: The final result is 73, which is the decimal equivalent of '243' in base 5.

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 equivalents.