Floating point errors

Question

I am having trouble with floating points. A the double . 56 in Java, for example, might actually be stored as .56000...1.

I am trying to convert a decimal to a fraction. I tried to do this using continued fractions

Continuous Fractions

but my answers using that method were inaccurate due to how to computer stored and rounded decimals.

I tried an alternative method:

public static Rational rationalize(double a){
        if(a>= 1){
        //throw some exception
    }
    String copOut = Double.toString(a);

    int counter = 0;
    System.out.println(a);
    while(a%1 != 0 && counter < copOut.length() - 2){
        a *= 10;
        counter++;
    }
    long deno = (long)Math.pow(10,counter);//sets the denominator
    Rational frac = new Rational((long)a,deno)//the unsimplified rational number
    long gcd = frac.gcd();
    long fnum = frac.getNumer();//gets the numerator 
    long fden = frac.getDenom();//gets the denominator
    frac = new Rational(fnum/gcd, fden/gcd);
    return frac;    
}

I am using the string to find the length of the decimal to determine how many time I should multiply by 10. I later truncate the decimal. This gets me the right answer, but it does not feel like the right approach? Can someone suggest the 'correct' way to do this?

The first problem here is that the *input* is `double.` So you're already losing precision before any of your code even executes. Have a think about `BigDecimal.` — user207421, Feb 18 '14 at 05:31

AJ. · Answer 1 · 2014-02-18T05:45:28.680

Actually you are doing great.. But this will fail if the Input is something about 11.56. Here you need to to do copOut.length() - 3.

To make it dynamic use String#split()

String decLength = copOut.split("\\.")[1]; //this will result "56" (Actual string after decimal)

Now you just need to do only

while(a%1 != 0 && counter < decLength.length()){
        a *= 10;
        counter++;
    }

If you want to remove the loop then use

long d = (long)Math.pow(10,decLength.length());
 a=a*d;

Floating point errors

1 Answers1