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

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

Options:

Correct Answer: 62

Solution:

2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

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

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

Step 1: Identify the digits in the base-5 number '243'. The digits are 2, 4, and 3.
Step 2: Understand the place values in base-5. The rightmost digit is multiplied by 5^0, the next by 5^1, and the leftmost by 5^2.
Step 3: Calculate the value of each digit: 2 is in the 5^2 place, 4 is in the 5^1 place, and 3 is in the 5^0 place.
Step 4: Compute the value of each digit: 2 * 5^2 = 2 * 25 = 50, 4 * 5^1 = 4 * 5 = 20, and 3 * 5^0 = 3 * 1 = 3.
Step 5: Add all the 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 (base-10).
Exponentiation – Applying the concept of exponents in the context of base systems, where each digit's position represents a power of the base.