decimal to fraction coversions

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decimal to fraction coversions

Postby mark » Fri Mar 26, 2004 12:39 am

for example I've converted 3m to 9.843 ft. It'd be nice to be able to find the fractional measure for .843 so I can go to the tape measure and start building. Thanks for a fantastically useful site.
mark
 

Re: decimal to fraction coversions

Postby Knight » Wed Apr 07, 2004 9:08 pm

mark wrote:for example I've converted 3m to 9.843 ft. It'd be nice to be able to find the fractional measure for .843 so I can go to the tape measure and start building. Thanks for a fantastically useful site.
Well, After getting the 9 feet, we've still got .843 feet left. There are 12 inches to the foot, so 0.843 x 12 gives us 10.116 inches. This leaves us with 0.116 inches.

Converting a decimal to a fraction is something we all hated in grade school, but its really pretty easy. Since anything over one is itself, we place 0.116 over one. Then we start moving the decinal point on the top and the bottom (the numerator and denominator) until the numerator (the top) is a whole number - Like this:

Code: Select all
0.116 | 1.16 | 11.6 | 116  |
------|------|------|------|
  1   |  10  |  100 | 1000 |
Since we've moved the decimal point on both the top and the bottom, we haven't really changed the number, just how it looks. But now we can reduce the fraction.
To do this, we need to find the greatest common factor.

First, we find the factors of both numbers - Like this:

116 = 1x116, 2x58, 4x29

1000 = 1x1000, 2x500, 4x250, 5x100, 8x125, 10x100 20x50, 25x40

The common factors of these two numbers are 1, 2, and 4, the greatest of them is 4, making 4 the greatest common factor.

Next, we divide both numbers by 4:

Code: Select all
 116 ÷ 4 =  29
----       ---
1000 ÷ 4 = 250


So we're looking for 29/250ths. Unfortunately your not likely to find 29/250ths on a measuring tape. Sometimes these things work out good. Sometimes we get bagged.

Fractions of an inch are generally going to be in multiples of two. 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64th are generally the ones you might see. 32nds and 64ths are not that common, but you will see them in detail work.

I know that 1/8 = 0.125, which is a bit too big. The next smaller common fractional size is 7/64, which is 0.109 - a bit too small. however, these two bracket the number. So your looking for a little less than 1/8 of an inch. Hopefully with a nine foot measurement, you can deal with a few fractions of an inch of slop.

Your total measurement works out to be nine feet, ten inches, plus a bit less than 1/8th of an inch.

Again, this exersize is an excellent example of why some of us Americans will be very happy when we finally switch over to the metric system!
William J. Knight
Health Physicist
Los Alamos National Labs
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