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### Converting Decimals to Fractions

Date: 10 Jul 1995 11:31:28 -0400
From: Michelle Arseneau
Subject: fractions

Question: A certain fraction is converted to a decimal and
the decimal representation is 0.6428571428571428571...
What is the fraction?

Date: 11 Jul 1995 22:13:25 -0400
From: Dr. Ken
Subject: Re: fractions

Hello there!

There are other ways to do your problem than the one I chose,
but I kind of wanted to get in some experience with doing computer
searches, so I tried not to try to figure out your problem by
the answer.  I wrote it in a program called Mathematica.  Here's
the algorithm that I used:

For[
n=1; d=2,
Abs[n/d - 0.6428571428571428571] >
.000000000000000001,
If[n<d, n++, n=1; d++],

];
Print[n, "/", d]

If you're not familiar with Mathematica (boy, is it a neat
program.  Very cool), here's an explanation of what the algorithm
does.  Basically, n is the numerator and d is the denominator.
The first line says to start out with the fraction 1/2.  Then it
checks to see whether the fraction it's checking is within
.000000000000000001 of .6428571428571428571, and if it is, the
algorithm stops.  If it's not, it tries another fraction.  First
it tries all the fractions with a denominator of 2, then with a
denominator of 3, and so on.  That's what that "If[...]" stuff is
all about, it sets n and d to the next fraction's numerator and
denominator.

Then when it finds what it's looking for, it stops and prints out
n and d with a / between them.  And the answer is....(drum roll)....
9/14 !!

There you have it.

-K

Associated Topics:
Middle School Fractions

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