Chibueze Opata - 2 months ago 25

C# Question

I tried writing an algorithm to simplify a decimal to a fraction and realized it wasn't too simple. Surprisingly I looked online and all the codes I found where either too long, or wouldn't work in some cases. What was even more annoying was that they didn't work for recurring decimals. I was wondering however whether there would be a mathematician/programmer here who understands all the involved processes in simplifying a decimal to a fraction. Anyone?

Answer

Well, seems I finally had to do it myself. I just had to create a program simulating the natural way I would solve it myself. I just submitted the code to codeproject as writing out the whole code here won't be suitable. You can download the project from here Fraction_Conversion, or look at the codeproject page here.

Here's how it works:

- Find out whether 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

Code Preview:

```
private static string dec2frac(double dbl)
{
char neg = ' ';
double dblDecimal = dbl;
if (dblDecimal == (int) dblDecimal) return dblDecimal.ToString(); //return no if it's not a decimal
if (dblDecimal < 0)
{
dblDecimal = Math.Abs(dblDecimal);
neg = '-';
}
var whole = (int) Math.Truncate(dblDecimal);
string decpart = dblDecimal.ToString().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;
}
//just a few prime factors for testing purposes
var primes = new[] {41, 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);
}
```

Thanks @ Darius for given me an idea of how to solve the recurring decimals :)