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

(3×100)+(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

(3×100)+(2×10)+(1×1)+(7×110)+(5×1100)

Answer 1

To write the number 320.75 in expanded form using decimal expansion, we break down each digit according to its place value:

• 3 is in the hundreds place: \(3 \times 100\)
• 2 is in the tens place: \(2 \times 10\)
• 0 is in the ones place: \(0 \times 1\)
• 7 is in the tenths place: \(7 \times \frac{1}{10}\) or \(7 \times 0.1\)
• 5 is in the hundredths place: \(5 \times \frac{1}{100}\) or \(5 \times 0.01\)

Therefore, the expanded form can be expressed as:

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

From the options provided, the closest matching choice is:

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

This matches the first option accurately:

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