Find the equivalent in base 10 of the last 3-digit number in base 8

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.

Learn how to convert the last 3-digit number in base 8 to base 10 with a step-by-step explanation. This problem covers key concepts in number systems and base conversion. Suitable for Grades 7-9.

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