Use decimal expansion to write 320.75 in expanded form.(1 point)%0D%0AResponses%0D%0A%0D%0A(3×1,000)+(2×100)+(0×10)+(7×1)+(5×110)%0D%0A(%0D%0A3%0D%0A×%0D%0A1%0D%0A,%0D%0A000%0D%0A)%0D%0A+%0D%0A(%0D%0A2%0D%0A×%0D%0A100%0D%0A)%0D%0A+%0D%0A(%0D%0A0%0D%0A×%0D%0A10%0D%0A)%0D%0A+%0D%0A(%0D%0A7%0D%0A×%0D%0A1%0D%0A)%0D%0A+%0D%0A(%0D%0A5%0D%0A×%0D%0A1%0D%0A10%0D%0A)%0D%0Aopen 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%0D%0A%0D%0A(3×10)+(2×1)+(0×110)+(7×1100)+(5×11,000)%0D%0A(%0D%0A3%0D%0A×%0D%0A10%0D%0A)%0D%0A+%0D%0A(%0D%0A2%0D%0A×%0D%0A1%0D%0A)%0D%0A+%0D%0A(%0D%0A0%0D%0A×%0D%0A1%0D%0A10%0D%0A)%0D%0A+%0D%0A(%0D%0A7%0D%0A×%0D%0A1%0D%0A100%0D%0A)%0D%0A+%0D%0A(%0D%0A5%0D%0A×%0D%0A1%0D%0A1%0D%0A,%0D%0A000%0D%0A)%0D%0Aopen 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%0D%0A%0D%0A(3×100)+(2×10)+(1×1)+(7×110)+(5×1100)%0D%0A(%0D%0A3%0D%0A×%0D%0A100%0D%0A)%0D%0A+%0D%0A(%0D%0A2%0D%0A×%0D%0A10%0D%0A)%0D%0A+%0D%0A(%0D%0A1%0D%0A×%0D%0A1%0D%0A)%0D%0A+%0D%0A(%0D%0A7%0D%0A×%0D%0A1%0D%0A10%0D%0A)%0D%0A+%0D%0A(%0D%0A5%0D%0A×%0D%0A1%0D%0A100%0D%0A)%0D%0Aopen 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%0D%0A%0D%0A(3×100)+(2×10)+(0×1)+(7×110)+(5×1100)

Answer 1

To write 320.75 in expanded form using decimal expansion, we need to break it down based on the place values of each digit.

The number 320.75 can be expanded as follows:

• 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 (first decimal place): \(7 \times \frac{1}{10}\)
• 5 is in the hundredths place (second decimal place): \(5 \times \frac{1}{100}\)

Putting this 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 expanded form of 320.75 is:

\[ (3 \times 100) + (2 \times 10) + (0 \times 1) + (7 \times 0.1) + (5 \times 0.01) \]