Question

Write the expanded form of 357.25(1 point)
Responses

(3×100)+(5×10)+(7×1)+(2×110)+(5×11,000)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 1,000 End Fraction right parenthesis

(3×100)+(5×10)+(7×1)+(5×110)+(2×1100)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis

(3×100)+(5×10)+(7×1)+(2×1100)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis

(3×100)+(5×10)+(7×1)+(2×110)+(5×1100)

Answer 1

To express the number 357.25 in expanded form, we break it down based on the place value of each digit.

For 357.25:
- The '3' is in the hundred's place, so it contributes \(3 \times 100\).
- The '5' is in the ten's place, so it contributes \(5 \times 10\).
- The '7' is in the one's place, so it contributes \(7 \times 1\).
- The '2' is in the tenths place (0.2), so it contributes \(2 \times \frac{1}{10}\) (or \(2 \times 0.1\)).
- The '5' is in the hundredths place (0.05), so it contributes \(5 \times \frac{1}{100}\) (or \(5 \times 0.01\)).

So the 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, looking at the provided options:

1. \((3×100)+(5×10)+(7×1)+(2×110)+(5×11,000)\)
2. \((3×100)+(5×10)+(7×1)+(5×110)+(2×1100)\)
3. \((3×100)+(5×10)+(7×1)+(2×\frac{1}{100})\)
4. \((3×100)+(5×10)+(7×1)+(2×110)+(5×1100)\)

None of the responses fully match the correct expanded form described above. **However**, option 3 is the closest, except that it has \(2 \times \frac{1}{100}\) instead of \(2 \times \frac{1}{10}\).

If we also consider the full correct interpretation including all elements, it should look like this:
\[
(3 \times 100) + (5 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]

In conclusion, none of the provided options are entirely correct for the expanded form of 357.25 within standard numerical representation, but option 3 is the closest representation of the whole number side of it.