In a base 6 number system, what is the value of the number 245 in decimal?

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Question: In a base 6 number system, what is the value of the number 245 in decimal?

Options:

Correct Answer: 77

Solution:

To convert from base 6 to decimal, calculate: 2*6^2 + 4*6^1 + 5*6^0 = 2*36 + 4*6 + 5*1 = 72 + 24 + 5 = 101.

In a base 6 number system, what is the value of the number 245 in decimal?

In a base 6 number system, what is the value of the number 245 in decimal?

Step 1: Identify the base of the number system. Here, the base is 6.
Step 2: Write down the number you want to convert, which is 245 in base 6.
Step 3: Break down the number 245 into its individual digits: 2, 4, and 5.
Step 4: Assign each digit a power of 6 based on its position from right to left, starting at 0: 2 is in the 6^2 position, 4 is in the 6^1 position, and 5 is in the 6^0 position.
Step 5: Calculate the value of each digit: 2 * 6^2 = 2 * 36 = 72, 4 * 6^1 = 4 * 6 = 24, and 5 * 6^0 = 5 * 1 = 5.
Step 6: Add all the values together: 72 + 24 + 5 = 101.
Step 7: The final result is that the base 6 number 245 is equal to 101 in decimal.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 6 to decimal.
Exponentiation – Applying the concept of exponents in the context of base systems to calculate the value of each digit.
Place Value – Recognizing the significance of each digit's position in a number based on its base.