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 
hand and instead made up a computer algorithm that searches for 
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