To convert a number from base 8 (octal) to decimal, you expand it using powers of 8.

For the octal number 415₈, it represents:

$415₈ = 4 \times 8^2 + 1 \times 8^1 + 5 \times 8^0$

Now, let's calculate each term:

$4 \times 8^2 = 4 \times 64 = 256$ $1 \times 8^1 = 1 \times 8 = 8$ $5 \times 8^0 = 5 \times 1 = 5$

Now, add them up:

$256 + 8 + 5 = 269$

Thus, the decimal equivalent of 415₈ is 269.

Would you like more details or have any further questions? Here are some related questions:

1. How do I convert a number from base 16 to decimal?
2. Can you explain how base conversion works in general?
3. How do you convert decimal numbers to binary?
4. What is the relationship between binary and octal?
5. How do you convert decimal to hexadecimal?

Tip: Always check that the digits of the number are valid for the base you're working with (e.g., for base 8, digits can only be 0-7).