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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?

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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!

What are the place values of a base 8 number with 5 digits? Convert these base 8 numbers to decimal numbers.

Understand the place values of a 5-digit base-8 number and learn how to convert base-8 numbers to decimal. This solution covers key concepts of the octal number system and place value structure, including detailed step-by-step conversions.

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