To convert the area of the masterplanned community from acres to square miles, we need to use the given conversion fact: [tex]\( 1 \text{ square mile (} mi^2) = 640 \text{ acres (ac)} \)[/tex].
We are given that the area of the community is [tex]\( 512 \text{ acres} \)[/tex].
To find the area in square miles, follow these steps:
1. Identify the given area in acres:
[tex]\[
\text{Area} = 512 \text{ acres}
\][/tex]
2. Use the conversion factor:
The conversion from acres to square miles is given by [tex]\( 1 \text{ square mile} = 640 \text{ acres} \)[/tex].
3. Set up the conversion:
To convert acres to square miles, we divide the number of acres by the number of acres per square mile.
4. Perform the calculation:
[tex]\[
\text{Area in square miles} = \frac{\text{Area in acres}}{\text{Acres per square mile}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Area in square miles} = \frac{512 \text{ acres}}{640 \text{ acres/square mile}}
\][/tex]
5. Simplify the fraction:
[tex]\[
\text{Area in square miles} = \frac{512}{640}
\][/tex]
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 128:
[tex]\[
\frac{512 \div 128}{640 \div 128} = \frac{4}{5} = 0.8
\][/tex]
Therefore, the area of the masterplanned community in square miles is:
[tex]\[
0.8 \text{ square miles (} mi^2)
\][/tex]
