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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!

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

(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.

2
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.

10,000 square feet = 0.2296 acres (approximately)

-Doctor Barrus,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/

Associated Topics:
Middle School Terms/Units of Measurement

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