In a certain number system, the base is 5. What is the decimal equivalent of the

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Question: In a certain number system, the base is 5. What is the decimal equivalent of the number 243 in base 5?

Options:

Correct Answer: 62

Solution:

To convert from base 5 to decimal, calculate: 2*5^2 + 4*5^1 + 3*5^0 = 2*25 + 4*5 + 3*1 = 50 + 20 + 3 = 73.

In a certain number system, the base is 5. What is the decimal equivalent of the number 243 in base 5?

In a certain number system, the base is 5. What is the decimal equivalent of the number 243 in base 5?

Step 1: Identify the base of the number system, which is 5.
Step 2: Write down the number you want to convert, which is 243 in base 5.
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 with 0: 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 * 25 = 50, 4 * 5 = 20, and 3 * 1 = 3.
Step 7: Add all the calculated values together: 50 + 20 + 3.
Step 8: The final result is 73, which is the decimal equivalent of the number 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 values.