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A real estate mogul is developing a new 512-acre (ac) master-planned community.

Use the facts to find the area of the community in square miles [tex]\(\left( mi^2 \right)\)[/tex].

Conversion facts for area:
- 1 acre [tex]\((ac) = 43,560\)[/tex] square feet [tex]\(\left( ft^2 \right)\)[/tex]
- 1 square mile [tex]\(\left( mi^2 \right) = 640\)[/tex] acres (ac)
- 1 hectare (ha) [tex]\(\approx 2.5\)[/tex] acres (ac)

Note: [tex]\(\approx\)[/tex] means "is approximately equal to." For this problem, treat [tex]\(\approx\)[/tex] as if it were [tex]\(=\)[/tex].



Answer :

GinnyAnswer
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]

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