Converting Square Feet to AcresDate: 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 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 Check out our web site! http://mathforum.org/dr.math/ |
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