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Seeming paradox when squaring distance depending on units 
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#1
Feb2814, 06:42 PM

P: 115

Hello all
This is probably simple and I'm overlooking something 1 mile = 5280 feet 10% of a mile is 528 feet 528 feet squared is 278,784 feet which is 52.8 miles squared But 0.1 miles squared is .01 miles squared So depending on if you square it as 0.1 miles, or if you convert it to feet, then square it and convert it back, you get wildly different answers Why is this.? Not sure why I thought of this. Thanks in advance 


#2
Feb2814, 06:53 PM

P: 160

First of all, (528 feet)^{2} is not equal to 278784 feet. It is equal to 278784 feet^{2}. In any case, you want to convert this to a value in miles^{2}. Now, the conversion factor between feet^{2} and miles^{2} is not the same as the conversion factor between feet and miles, because feet^{2} are not the same as feet, and miles^{2} are not the same as miles. In fact, the conversion factor is 27878400 feet^{2} = 1 mile^{2}, and if you use this correct conversion factor you will get the correct answer of 0.01 miles^{2}. 


#3
Feb2814, 06:54 PM

P: 392

##\frac{278784 ft^2}{1} \cdot \frac{(1 mi)^2}{(5280ft)^2} = 0.01 mi^2## 


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