Question

Use decimal expansion to write 320.75 in expanded form.(1 point)
Responses

(3×100)+(2×10)+(1×1)+(7×110)+(5×1100)
open paren 3 times 100 close paren plus open paren 2 times 10 close paren plus open paren 1 times 1 close paren plus open paren 7 times 1 tenth close paren plus open paren 5 times 1 over 100 close paren

(3×100)+(2×10)+(0×1)+(7×110)+(5×1100)
open paren 3 times 100 close paren plus open paren 2 times 10 close paren plus open paren 0 times 1 close paren plus open paren 7 times 1 tenth close paren plus open paren 5 times 1 over 100 close paren

(3×1,000)+(2×100)+(0×10)+(7×1)+(5×110)
open paren 3 times 1 comma 000 close paren plus open paren 2 times 100 close paren plus open paren 0 times 10 close paren plus open paren 7 times 1 close paren plus open paren 5 times 1 tenth close paren

(3×10)+(2×1)+(0×110)+(7×1100)+(5×11,000)

Answer 1

To write 320.75 in expanded form using decimal expansion, we break it down by place value:

- The digit 3 is in the hundreds place, so it represents \(3 \times 100\).
- The digit 2 is in the tens place, so it represents \(2 \times 10\).
- The digit 0 is in the ones place, so it represents \(0 \times 1\).
- The digit 7 is in the tenths place, so it represents \(7 \times \frac{1}{10}\) (or \(7 \times 0.1\)).
- The digit 5 is in the hundredths place, so it represents \(5 \times \frac{1}{100}\) (or \(5 \times 0.01\)).

Putting it all together, we get:

\[
(3 \times 100) + (2 \times 10) + (0 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]

So the correct response is:

**(3×100)+(2×10)+(0×1)+(7×110)+(5×1100)**
open paren 3 times 100 close paren plus open paren 2 times 10 close paren plus open paren 0 times 1 close paren plus open paren 7 times 1 tenth close paren plus open paren 5 times 1 over 100 close paren.