## Introduction

Simplifying decimals to fractions come in handy when you are making programs that solve mathematics. Presenting long and recurring decimals in fractions are much more cleaner than their decimal forms.

## Background

After studying the available algorithms for determining fractions from decimals, mostly culled from a paper written in 1991, which seemed a bit complex to me, and asking questions on stackoverflow, I decided to write a simpler code that could do the same job in a clean manner. However this code has some drawbacks as it focuses mainly on using `string `

manipulation (a more natural way) to achieve its purpose.

## Using the Code

The code is quite simple to use. There's the method called `dec2frac `

which accepts a `double `

parameter. A call to this method returns the `string `

representation of the equivalent fraction of the simplified decimal.

Here's how it works:

- Find out whether the given decimal is negative.
- Convert decimal to absolute value.
- Get integer part of given decimal.
- Get the decimal part.
- Check whether decimal is recurring. If decimal is recurring, we then return the exact recurring decimal.
- If decimal is not recurring, start reduction by changing numerator to 10^no. of decimal, else we subtract 1 from numerator.
- Then reduce fraction.

Let's look at the `dec2frac `

method:

private static string Dec2Frac(double dbl)
{
char neg = ' ';
double dblDecimal = dbl;
if (dblDecimal < 0)
{
dblDecimal = Math.Abs(dblDecimal);
neg = '-';
}
var whole = (int) Math.Truncate(dblDecimal);
if (whole == dbl) {
return String.Format("{0} because supplied value is not a fraction", dbl);
}
string decpart = dblDecimal.ToString(CultureInfo.InvariantCulture).Replace(Math.Truncate(dblDecimal) + ".", "");
double rN = Convert.ToDouble(decpart);
double rD = Math.Pow(10, decpart.Length);
string rd = Recur(decpart);
int rel = Convert.ToInt32(rd);
if (rel != 0)
{
rN = rel;
rD = (int) Math.Pow(10, rd.Length) - 1;
}
var primes = new[] {47, 43, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2};
foreach (int i in primes) reduceNo(i, ref rD, ref rN);
rN = rN + (whole*rD);
return string.Format("{0}{1}/{2}", neg, rN, rD);
}

First, we note if the decimal is a negative, then we get the integer part of the decimal. We then proceed to simplify the decimal part by dividing number by power of 10 appropriately.

Next, we check if it's a recurring decimal using the `recur`

method which will return the recurring decimal in a `string `

format if it exists. This is because the decimal part may start with a zero as in 1 / 11. Here:

private static string Recur(string db)
{
if (db.Length < 13) return "0";
var sb = new StringBuilder();
for (int i = 0; i < 7; i++)
{
sb.Append(db[i]);
int dlength = (db.Length/sb.ToString().Length);
int occur = Occurence(sb.ToString(), db);
if (dlength == occur || dlength == occur - sb.ToString().Length)
{
return sb.ToString();
}
}
return "0";
}

## Points of Interest

While I was developing this class, I discovered the C# `String`

class was not powerful enough (Currently this no longer holds though as LINQ provides a lot of methods for any kind of manipulation). For instance, I couldn't find a method to find the number of times a `string `

or character occurs in a `string`

, and had to develop one myself as in the `occurrence `

method:

private static int Occurence(string s, string check)
{
int i = 0;
int d = s.Length;
string ds = check;
for (int n = (ds.Length/d); n > 0; n--)
{
int si = ds.IndexOf(s, StringComparison.Ordinal);
if (si != -1)
{
i++;
ds = ds.Remove(si, d);
}
}
return i;
}

It may be worthy of note that this method does *not *do what you *may* think it's doing. This method checks to see how many times a particular number is occurring inside another number in other to get if a number is recurring.

## History

This is the first successful attempt to write a simple fraction conversion class, written and published on 6^{th} March, 2011. The code will be updated if I happen to refine it later.