In a base-5 numeral system, what is the decimal equivalent of the base-5 number

₹0.0

Question: In a base-5 numeral system, what is the decimal equivalent of the base-5 number 243? (2023)

Options:

Correct Answer: 60

Exam Year: 2023

Solution:

The base-5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60 in decimal.

In a base-5 numeral system, what is the decimal equivalent of the base-5 number 243? (2023)

In a base-5 numeral system, what is the decimal equivalent of the base-5 number 243? (2023)

Step 1: Identify the base-5 number, which is 243.
Step 2: Break down the base-5 number into its digits: 2, 4, and 3.
Step 3: Assign each digit a power of 5 based on its position from right to left: 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 4: Calculate 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.
Exponentiation – Applying the concept of exponents in the context of base systems, where each digit's position represents a power of the base.
Place Value – Recognizing the significance of each digit's position in a numeral system and how it contributes to the overall value.