If a number in base-6 is represented as 405, what is its decimal equivalent?

If a number in base-6 is represented as 405, what is its decimal equivalent?

Step 1: Identify the base of the number. Here, the base is 6.
Step 2: Write down the number in base-6, which is 405.
Step 3: Break down the number 405 into its individual digits: 4, 0, and 5.
Step 4: Assign each digit a power of 6 based on its position from right to left, starting at 0. So, 4 is in the 2nd position (6^2), 0 is in the 1st position (6^1), and 5 is in the 0th position (6^0).
Step 5: Calculate the value of each digit: 4 * 6^2 = 4 * 36 = 144, 0 * 6^1 = 0 * 6 = 0, and 5 * 6^0 = 5 * 1 = 5.
Step 6: Add all the values together: 144 + 0 + 5 = 149.
Step 7: The decimal equivalent of the base-6 number 405 is 149.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-6 to decimal.
Exponentiation – Applying the correct powers of the base (6 in this case) to each digit based on its position.
Positional Notation – Recognizing that each digit's value is determined by its position in the number.