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Converting Square Feet to Acres

Date: 05/26/98 at 02:04:45
From: jim poarch
Subject: Math conversion

How much acreage is 10,000 square feet of land?

Date: 05/26/98 at 11:57:43
From: Doctor Barrus
Subject: Re: Math conversion

Hi, Jim!

In answering your question, the following conversion facts are useful:

   1 acre = 4840 sq. yd
     1 yd = 3 feet

To answer your question, I'll multiply the starting number 
(10,000 sq. ft.) by conversion factors. This won't change the area. 
It will just change the units. For example, since 1 yard = 3 feet, 
multiplying by:

   1 yard
   3 feet

is equivalent to multiplying by one. It's not exactly the same as
multiplying by one, because the numbers and units aren't equal, so 
what happens is a conversion. 

Okay, so about your problem. Here's what I calculate:

            2     / 1 yd \     10,000 
   10,000 ft   * (--------) = -------- sq. yd = 1111 sq. yd. (approx.) 
                  \ 3 ft /        9

Notice that I squared the conversion factor. This is allowed, because 
we are doing the equivalent of multiplying by one, remember, and 
multiplying by one twice, or multiplying by one squared, doesn't 
change the value of something. I squared the factor because I wanted 
the feet units to divide out. I started out with square feet in the 
numerator of the first term (10,000 sq. ft), so I needed square feet 
units in the denominator of the conversion factor to cancel the square 
feet. When I do this, I only have square yards left over. So now I 
know that:

   10,000 sq. ft = 10,000/9 sq. yd

Now I want to go from square yards to acres. I'll do this by once 
again multiplying by a conversion factor:

   10,000            1 acre      250
   ------ sq. yd * ----------- = ---- acres = 0.2296 acres (approx.)
     9             4840 sq. yd   1089

Notice again how I made sure the units cancelled. I had square yards 
in both the numerator and the denominator that divided out and left me 
with acres. That's the key to this kind of calculation.

So here's your answer:

   10,000 square feet = 0.2296 acres (approximately)

-Doctor Barrus,  The Math Forum
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Associated Topics:
Middle School Terms/Units of Measurement

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