To find the equivalent in base 10 of the last 3-digit number in base 8, follow these steps:

1. Identify the last 3-digit number in base 8:
   The largest 3-digit number in base 8 is $777_8$.

2. Convert $777_8$ to base 10:
   The base 10 equivalent can be calculated using the formula: $777_8 = 7 \times 8^2 + 7 \times 8^1 + 7 \times 8^0$ Let's compute this step by step: $7 \times 8^2 = 7 \times 64 = 448$ $7 \times 8^1 = 7 \times 8 = 56$ $7 \times 8^0 = 7 \times 1 = 7$ $777_8 = 448 + 56 + 7 = 511$

So, the equivalent in base 10 of the last 3-digit number in base 8 is 511.

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert a number from base 10 to base 8?
2. What is the largest 4-digit number in base 8, and its base 10 equivalent?
3. What is the smallest 3-digit number in base 8, and its base 10 equivalent?
4. How does base 8 (octal) relate to binary (base 2)?
5. How would you subtract $777_8$ from $1000_8$ in base 10?
6. What are common uses of the octal (base 8) number system?
7. How do you add numbers in base 8?
8. Can you explain how base 8 was historically used in computing?

Tip: When converting between different bases, it's helpful to remember the powers of the base you're working in.