Math worksheet for practicing place value, number comparison, and expanded form with the number 8,351,207.

Problem Analysis:

The worksheet involves understanding place values, expanded form, number line representation, and basic arithmetic operations. Let's solve each part step by step.

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#### 1. The special number is 8,351,207

- The value of the digit 5:
- The digit 5 is in the ten-thousands place.
- Its value is \( 5 \times 10,000 = 50,000 \).

- The value of the digit 7:
- The digit 7 is in the ones place.
- Its value is \( 7 \times 1 = 7 \).

- The value of the digit 3:
- The digit 3 is in the hundred-thousands place.
- Its value is \( 3 \times 100,000 = 300,000 \).

- The value of the digit 2:
- The digit 2 is in the hundreds place.
- Its value is \( 2 \times 100 = 200 \).

- The value of the digit 8:
- The digit 8 is in the millions place.
- Its value is \( 8 \times 1,000,000 = 8,000,000 \).

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#### 2. Fill in the empty boxes on the number line

The number line shows two points: one labeled as \( 6,361,207 \) and the other as \( 8,351,207 \). We need to fill in the missing numbers before and after these points.

- Before \( 6,361,207 \):
- Assume a consistent interval between the points. Since the difference between \( 6,361,207 \) and \( 8,351,207 \) is \( 8,351,207 - 6,361,207 = 1,990,000 \), we can divide this interval into smaller segments.
- For simplicity, let’s assume the interval is divided into equal parts. If we take the midpoint or another logical point, the number before \( 6,361,207 \) could be \( 4,361,207 \).

- After \( 8,351,207 \):
- Similarly, the next number after \( 8,351,207 \) could be \( 10,351,207 \) (adding the same interval).

So, the number line would look like:
\[
\boxed{4,361,207 \quad 6,361,207 \quad 8,351,207 \quad 10,351,207}
\]

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#### 3. Write the number in expanded form

The number \( 8,351,207 \) in expanded form is:
\[
8,000,000 + 300,000 + 50,000 + 1,000 + 200 + 7
\]

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#### 4. Arithmetic operations

- 1,000,000 less than 8,351,207:
\[
8,351,207 - 1,000,000 = 7,351,207
\]

- 1,000 more than 8,351,207:
\[
8,351,207 + 1,000 = 8,352,207
\]

- 100,000 less than 8,351,207:
\[
8,351,207 - 100,000 = 8,251,207
\]

- 10 more than 8,351,207:
\[
8,351,207 + 10 = 8,351,217
\]

- 1 less than 8,351,207:
\[
8,351,207 - 1 = 8,351,206
\]

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#### 5. Compare the numbers

- Compare \( 8,513,207 \) and \( 8,351,207 \):
- Both numbers have the same millions and hundred-thousands digits, but \( 8,513,207 \) has a larger ten-thousands digit (5 vs. 3).
- Therefore, \( 8,513,207 > 8,351,207 \).

- Compare \( 8,251,307 \) and \( 8,351,207 \):
- Both numbers have the same millions digit, but \( 8,351,207 \) has a larger hundred-thousands digit (3 vs. 2).
- Therefore, \( 8,251,307 < 8,351,207 \).

- Compare \( 8,351,207 \) and \( 8,351,207 \):
- Both numbers are identical.
- Therefore, \( 8,351,207 = 8,351,207 \).

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Final Answers:

1. Values of digits:
- Digit 5: \( 50,000 \)
- Digit 7: \( 7 \)
- Digit 3: \( 300,000 \)
- Digit 2: \( 200 \)
- Digit 8: \( 8,000,000 \)

2. Number line:
\[
\boxed{4,361,207 \quad 6,361,207 \quad 8,351,207 \quad 10,351,207}
\]

3. Expanded form:
\[
8,000,000 + 300,000 + 50,000 + 1,000 + 200 + 7
\]

4. Arithmetic results:
- 1,000,000 less: \( 7,351,207 \)
- 1,000 more: \( 8,352,207 \)
- 100,000 less: \( 8,251,207 \)
- 10 more: \( 8,351,217 \)
- 1 less: \( 8,351,206 \)

5. Comparisons:
- \( 8,513,207 > 8,351,207 \)
- \( 8,251,307 < 8,351,207 \)
- \( 8,351,207 = 8,351,207 \)

Final Boxed Answer:
\[
\boxed{50,000, 7, 300,000, 200, 8,000,000, 4,361,207, 10,351,207, 8,000,000 + 300,000 + 50,000 + 1,000 + 200 + 7, 7,351,207, 8,352,207, 8,251,207, 8,351,217, 8,351,206, >, <, =}
\]