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

Answer 1

The correct decimal expansion of 320.75 in expanded form is:

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

This can be interpreted as:

• 3 is in the hundreds place, so \(3 \times 100\)
• 2 is in the tens place, so \(2 \times 10\)
• 0 is in the ones place, so \(0 \times 1\) (which can actually be omitted since it does not contribute)
• 7 is in the tenths place, so \(7 \times \frac{1}{10}\)
• 5 is in the hundredths place, so \(5 \times \frac{1}{100}\)

So the first option you provided is the most accurate, which is:

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

If we disregard the \(0 \times 1\), the equation can also be simplified as:

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

This clearly reflects the structure of decimal expansion for the number 320.75.