Write this decimal number in the expended form. Use the formula discussed in class (with the place values, positions and the base):

2,850,638.491

To write the decimal number \( 2,850,638.491 \) in expanded form using the place values, positions, and the base (which is 10 for the decimal system), we break it down according to each digit's place value.

### Expanded Form:

\[
2,850,638.491 = 2 \times 10^6 + 8 \times 10^5 + 5 \times 10^4 + 0 \times 10^3 + 6 \times 10^2 + 3 \times 10^1 + 8 \times 10^0 + 4 \times 10^{-1} + 9 \times 10^{-2} + 1 \times 10^{-3}
\]

### Explanation:

1. **Whole Number Part:**
   - \(2\) is in the millions place: \(2 \times 10^6\)
   - \(8\) is in the hundred thousands place: \(8 \times 10^5\)
   - \(5\) is in the ten thousands place: \(5 \times 10^4\)
   - \(0\) is in the thousands place: \(0 \times 10^3\)
   - \(6\) is in the hundreds place: \(6 \times 10^2\)
   - \(3\) is in the tens place: \(3 \times 10^1\)
   - \(8\) is in the ones place: \(8 \times 10^0\)

2. **Decimal Part:**
   - \(4\) is in the tenths place: \(4 \times 10^{-1}\)
   - \(9\) is in the hundredths place: \(9 \times 10^{-2}\)
   - \(1\) is in the thousandths place: \(1 \times 10^{-3}\)

Thus, the decimal number \(2,850,638.491\) is expanded to show the value contributed by each digit according to its position and the base (10).

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### Related Questions:

1. How would you write a different decimal number, such as \(3,672.58\), in expanded form?
2. Can you express \(5.0073\) in its expanded form using the base of 10?
3. What is the significance of zero in the expanded form, and how does it affect the number's value?
4. How do place values change as you move left or right of the decimal point in a base-10 number system?
5. How can expanded forms help in understanding the value of each digit in a number?

**Tip:** When writing numbers in expanded form, always identify each digit's position and corresponding power of 10, moving from left to right.

Write this decimal number in the expanded form. Use the formula discussed in class (with the place values, positions, and the base): 2,850,638.491

Learn how to write the decimal number 2,850,638.491 in expanded form using place values, positions, and the base 10. This guide is ideal for students in Grades 4-6 and covers the key concepts of the decimal system.

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