Question

what is the expanded form of 23.75

2x10 + 3x1 + 5 x 1/10 + 7 x 1/100
2x10 + 3x1 + 7 x 1/100 + 5 x 1000
5x10 + 7x1 + 3x1/10 + 2x1/100
2x10 + 3x1 + 7x10 + 5x100

Answer 1

The expanded form of 23.75 can be written by breaking it down into its place values.

Let's analyze the number 23.75:
- The "2" is in the tens place, so it is \(2 \times 10\).
- The "3" is in the ones place, so it is \(3 \times 1\).
- The "7" is in the tenths place, so it is \(7 \times \frac{1}{10}\).
- The "5" is in the hundredths place, so it is \(5 \times \frac{1}{100}\).

Thus, the expanded form of 23.75 is:
\[
2 \times 10 + 3 \times 1 + 7 \times \frac{1}{10} + 5 \times \frac{1}{100}
\]

Now let's compare this with the options you provided:

1. **\(2 \times 10 + 3 \times 1 + 5 \times \frac{1}{10} + 7 \times \frac{1}{100}\)** (Incorrect)
2. **\(2 \times 10 + 3 \times 1 + 7 \times \frac{1}{100} + 5 \times 1000\)** (Incorrect)
3. **\(5 \times 10 + 7 \times 1 + 3 \times \frac{1}{10} + 2 \times \frac{1}{100}\)** (Incorrect)
4. **\(2 \times 10 + 3 \times 1 + 7 \times 10 + 5 \times 100\)** (Incorrect)

The correct expanded form is \(2 \times 10 + 3 \times 1 + 7 \times \frac{1}{10} + 5 \times \frac{1}{100}\), which does not match any of the options provided.

Answer 2

write the expanded form of 357.25

3x100 + 5x10 + 7x1 + 2x1/100
3x100 + 5x10 + 7x1 + 2x1/10 + 5x1000
3x100 + 5x10 + 7x1 + 5x1/10 + 2x1/100
3x100 + 5x10 + 7x1 + 2x1/10 + 5x1/100

Answer 3

To write the expanded form of 357.25, we break it down by its place values:

- The "3" is in the hundreds place, so it is \(3 \times 100\).
- The "5" is in the tens place, so it is \(5 \times 10\).
- The "7" is in the ones place, so it is \(7 \times 1\).
- The "2" is in the tenths place, so it is \(2 \times \frac{1}{10}\).
- The "5" is in the hundredths place, so it is \(5 \times \frac{1}{100}\).

Thus, the complete expanded form of 357.25 is:
\[
3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times \frac{1}{10} + 5 \times \frac{1}{100}
\]

Now let's compare this with the provided options:

1. **\(3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times \frac{1}{100}\)** (Incorrect - the tenths place is wrong)
2. **\(3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times \frac{1}{10} + 5 \times 1000\)** (Incorrect - the last term is wrong)
3. **\(3 \times 100 + 5 \times 10 + 7 \times 1 + 5 \times \frac{1}{10} + 2 \times \frac{1}{100}\)** (Incorrect - the ranks of tenths and hundredths are swapped)
4. **\(3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times \frac{1}{10} + 5 \times \frac{1}{100}\)** (Correct)

The correct option is:
**\(3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times \frac{1}{10} + 5 \times \frac{1}{100}\)**.

Answer 4

what is the expanded form of 8,471.716

8x1,000+4x100+7x10+1x1+7x1/10+6x1/100
8x1000+4x100+7x10+1x1+7x1/10+1x1/100+6x1/1000
8x1000+4x100+7x100+1x10+7x1/100+1x1/100+6x1/1000
8x1000+4x100+7x10+1x1+7x10+1x100

Answer 5

To write the expanded form of the number 8,471.716, we break it down according to its place values:

- The "8" is in the thousands place, so it is \(8 \times 1,000\).
- The "4" is in the hundreds place, so it is \(4 \times 100\).
- The "7" is in the tens place, so it is \(7 \times 10\).
- The "1" is in the ones place, so it is \(1 \times 1\).
- The "7" is in the tenths place, so it is \(7 \times \frac{1}{10}\).
- The "1" is in the hundredths place, so it is \(1 \times \frac{1}{100}\).
- The "6" is in the thousandths place, so it is \(6 \times \frac{1}{1000}\).

Thus, the complete expanded form of 8,471.716 is:
\[
8 \times 1,000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times \frac{1}{10} + 1 \times \frac{1}{100} + 6 \times \frac{1}{1000}
\]

Now, let's compare this to the options you provided:

1. **\(8 \times 1,000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times \frac{1}{10} + 6 \times \frac{1}{100}\)** (Incorrect - “6” in wrong position)
2. **\(8 \times 1000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times \frac{1}{10} + 1 \times \frac{1}{100} + 6 \times \frac{1}{1000}\)** (Correct)
3. **\(8 \times 1000 + 4 \times 100 + 7 \times 100 + 1 \times 10 + 7 \times \frac{1}{100} + 1 \times \frac{1}{100} + 6 \times \frac{1}{1000}\)** (Incorrect - “7” and “1” in wrong positions)
4. **\(8 \times 1000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times 10 + 1 \times 100\)** (Incorrect - “7”s and “1”s in wrong positions)

The correct option is:
**\(8 \times 1000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times \frac{1}{10} + 1 \times \frac{1}{100} + 6 \times \frac{1}{1000}\)**.