The expanded form of the number 9578 is

Options

A. `9 xx 10000 + 5 xx 1000 + 7 xx 10 + 8 xx 1`
B. `9 xx 1000 + 5 xx 100 + 7 xx 10 + 8 xx 1`
C. `9 xx 1000 + 57 xx 10 + 8 xx 1`
D. `9 xx 100 + 5 xx 100 + 7 xx 10 + 8 xx 1`

Answer

To find the expanded form of the number 9578, we will break down the number according to the place value of each digit.

1. **Identify the digits and their place values:**
- The number 9578 has four digits: 9, 5, 7, and 8.
- The place values from left to right are:
- 9 is in the thousands place.
- 5 is in the hundreds place.
- 7 is in the tens place.
- 8 is in the ones place.

2. **Write the expanded form using the place values:**
- For the digit 9 in the thousands place:
- \(9 \times 1000\)
- For the digit 5 in the hundreds place:
- \(5 \times 100\)
- For the digit 7 in the tens place:
- \(7 \times 10\)
- For the digit 8 in the ones place:
- \(8 \times 1\)

3. **Combine all the parts together:**
- The expanded form of 9578 can be written as:
\[ 9 \times 1000 + 5 \times 100 + 7 \times 10 + 8 \times 1 \]

4. **Match with the options provided:**
- Now, we look at the options given in the question:
- Option 1: \(9 \times 10,000 + 5 \times 1000 + 7 \times 10 + 8 \times 1\)
- Option 2: \(9 \times 1000 + 5 \times 100 + 7 \times 10 + 8 \times 1\)
- Option 3: \(9 \times 1000 + 57 \times 10 + 8 \times 1\)
- Option 4: \(9 \times 100 + 5 \times 100 + 7 \times 10 + 8 \times 1\)
- We can see that the expanded form we derived matches with Option 2.

5. **Conclusion:**
- Therefore, the expanded form of the number 9578 is:
\[ 9 \times 1000 + 5 \times 100 + 7 \times 10 + 8 \times 1 \]
- The correct answer is Option 2.