To solve this problem, let’s break it into two parts based on the image content.

Part 1: Place Values of a Base-8 Number with 5 Digits

In base-8 (octal), each digit represents a power of 8, starting from the rightmost digit (which is the $8^0$ place). For a 5-digit base-8 number, the place values from left to right are:

• Leftmost digit: $8^4 = 4096$
• Next digit: $8^3 = 512$
• Middle digit: $8^2 = 64$
• Next digit: $8^1 = 8$
• Rightmost digit: $8^0 = 1$

So, from left to right, the place values are: 4096, 512, 64, 8, 1.

Part 2: Converting Base-8 Numbers to Decimal

To convert each base-8 number to decimal, we use the formula: $\text{Decimal} = \sum (\text{digit} \times 8^{\text{position}})$ where each position is counted from the right, starting at 0.

1. $0_8$: $0$
2. $1_8$: $1$
3. $4_8$: $4$
4. $7_8$: $7$
5. $10_8$: $1 \times 8 + 0 = 8$
6. $11_8$: $1 \times 8 + 1 = 9$
7. $12_8$: $1 \times 8 + 2 = 10$
8. $73_8$: $7 \times 8 + 3 = 56 + 3 = 59$
9. $100_8$: $1 \times 8^2 + 0 \times 8 + 0 = 64$
10. $101_8$: $1 \times 8^2 + 0 \times 8 + 1 = 64 + 1 = 65$
11. $110_8$: $1 \times 8^2 + 1 \times 8 + 0 = 64 + 8 = 72$
12. $525_8$: $5 \times 8^2 + 2 \times 8 + 5 = 320 + 16 + 5 = 341$
13. $1000_8$: $1 \times 8^3 + 0 \times 8^2 + 0 \times 8 + 0 = 512$
14. $1007_8$: $1 \times 8^3 + 0 \times 8^2 + 0 \times 8 + 7 = 512 + 7 = 519$
15. $1040_8$: $1 \times 8^3 + 0 \times 8^2 + 4 \times 8 + 0 = 512 + 32 = 544$
16. $5250_8$: $5 \times 8^3 + 2 \times 8^2 + 5 \times 8 + 0 = 2560 + 128 + 40 = 2728$

Would you like more detailed explanations or have any questions?

Here are some additional related questions:

1. How do place values change in other bases, such as base-10 or base-16?
2. Can you explain how to convert decimal numbers back to base-8?
3. How would the process differ for a base-16 number with 5 digits?
4. What are practical applications of using different bases in mathematics or computer science?
5. How do you represent a base-8 (octal) number in binary?

Tip: To verify a base conversion, try converting your result back to the original base as a quick check!