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

Question

Responses

(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 the number 320.75 in expanded form using decimal expansion, we can break it down into its place value components:

1. Hundreds place: 3 is in the hundreds place, which is \(3 \times 100\).
2. Tens place: 2 is in the tens place, which is \(2 \times 10\).
3. Units place (ones): 0 is in the ones place, which is \(0 \times 1\).
4. Tenths place: 7 is in the tenths place, which is \(7 \times \frac{1}{10}\) or \(7 \times 0.1\).
5. Hundredths place: 5 is in the hundredths place, which is \(5 \times \frac{1}{100}\) or \(5 \times 0.01\).

Putting it all together, the expanded form of 320.75 is:

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

From the given options, the correct response is:

(3×100) + (2×10) + (0×1) + (7×\frac{1}{10}) + (5×\frac{1}{100})