Math worksheet for practicing place value, expanded form, and number comparison using 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:
The special number given is 8,351,207.

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#### 2. Value of Each Digit:
We need to determine the value of each digit based on its place value.

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

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

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

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

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

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#### 3. Fill in the Empty Boxes on the Number Line:
The number line shows two points: 6,361,207 and 8,351,207. We need to fill in the missing numbers.

- The difference between the two given points is:
\[
8,351,207 - 6,361,207 = 1,990,000
\]
- This suggests that the number line increments by 1,990,000.

- The first box (to the left of 6,361,207) should be:
\[
6,361,207 - 1,990,000 = 4,371,207
\]

- The second box (to the right of 8,351,207) should be:
\[
8,351,207 + 1,990,000 = 10,341,207
\]

So, the number line should be filled as:
\[
\boxed{4,371,207, 6,361,207, 8,351,207, 10,341,207}
\]

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#### 4. Write the Number in Expanded Form:
The expanded form breaks down the number into the sum of its place values.

\[
8,351,207 = (8 \times 1,000,000) + (3 \times 100,000) + (5 \times 10,000) + (1 \times 1,000) + (2 \times 100) + (0 \times 10) + (7 \times 1)
\]

So, the expanded form is:
\[
\boxed{8,000,000 + 300,000 + 50,000 + 1,000 + 200 + 7}
\]

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#### 5. Arithmetic Operations:
We need to perform the following calculations:

- 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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#### 6. Compare Numbers:
We need to compare the given numbers using \( < \), \( > \), or \( = \).

- Compare 8,513,207 and 8,351,207:
- Both numbers have the same millions and hundred-thousands digits.
- The ten-thousands digit of 8,513,207 is 5, while for 8,351,207 it is 3.
- Therefore, \( 8,513,207 > 8,351,207 \).

- Compare 8,251,307 and 8,351,207:
- Both numbers have the same millions digit.
- The hundred-thousands digit of 8,251,307 is 2, while for 8,351,207 it is 3.
- Therefore, \( 8,251,307 < 8,351,207 \).

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

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

2. Number line:
\[
\boxed{4,371,207, 6,361,207, 8,351,207, 10,341,207}
\]

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

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

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Final Boxed Answers:

\[
\boxed{50,000, 7, 300,000, 200, 8,000,000, 4,371,207, 6,361,207, 8,351,207, 10,341,207, 8,000,000 + 300,000 + 50,000 + 1,000 + 200 + 7, 7,351,207, 8,352,207, 8,251,207, 8,351,217, 8,351,206, >, <, =, =}
\]