Question

A plot of land has an area of 1,089,000 square feet.The conversion factors between different area measures are shown below.27,878,400 square feet = 1 square mile 43,560 square feet = 1 acre 9 square feet = 1 square yard 1 square foot = 144 square inches Part AWhich unit listed above can be used to express the area of the plot of land so that the number of units will be between 10 and 100? Explain your answer. Part BWhat is the area of the plot of land in terms of the unit you chose in Part A? ___________ square mile,acre,square yard ,square inches

Answer 1

Part A) 24.79 acres

1) Since that plot has an area of

$1,089,000ft^2=1.08\times10^6ft^2$

And the number of units must be between 10 and 10² units.

Part A)

$\begin{gathered} 27,878,400ft^2=2.78784\times10^7ft^2=1m^2 \\ 43560ft^2\text{ =4.356 }\times10^4ft^2\text{ = 1 acre} \end{gathered}$

2) Let's convert them to the apparently plausible units, see if it fits within the given interval.

$\begin{gathered} \frac{1.08\times10^6}{4.356\times10^4}=24.79\text{ acres} \\ \frac{1.08\times10^6}{2.78784\times10^7}=0.03m^{2} \end{gathered}$

We can see that 0.03 m² does not belong to the given interval.

3) Hence, the answer is 24.79 acres.