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

Question

Responses

(3×10)+(2×1)+(0×110)+(7×1100)+(5×11,000)
open paren 3 times 10 close paren plus open paren 2 times 1 close paren plus open paren 0 times 1 tenth close paren plus open paren 7 times 1 over 100 close paren plus open paren 5 times the fraction with numerator 1 and denominator 1 comma 000 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

(3×100)+(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)

Answer 1

To write 320.75 in expanded form using decimal expansion, we can break it down into its component parts:

• 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 \(5 \times 0.01\).

Now, let's put this information together. The correct expanded form for 320.75 is:

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

Among the given choices, this matches the option:

(3×100) + (2×10) + (0×1) + (7×1/10) + (5×1/100)

This is the correct expanded form for 320.75.