Converting a float into a string fraction representation

Question

In Java, I am trying to find a way to convert a float number into a fraction string. For example:

float num = 1.33333;
String numStr = Convert(num); // Shoul         


        

Answer 1

Assume you have "0.1234567", then count how many numbers after the decimal point (which is 7). then multiply the number with 10 ^ 7, now you have "1234567".

divide 1234567 over 10 ^ 7. Then, simplify the fraction using the GCD of the two numbers.

0.1234567 * 10000000 = 1234567
=> 1234567 / 10000000
=> System.out.println(1234567 / gcd(1234567,10000000) + "/" + 10000000/gcd(1234567,10000000));

Answer 2

Look into chain fractions. This allows you to determine denominator and fraction within a given accuracy.

For Pi you can get 22/7 or 355/113 depending on when you choose to stop.

Answer 3

Modified the FOR loop to break the loop, when the best denominator is already identified.

if (error2 == 0) break;

public static String toFraction(double d, int factor) {
    StringBuilder sb = new StringBuilder();
    if (d < 0) {
        sb.append('-');
        d = -d;
    }
    long l = (long) d;
    if (l != 0) sb.append(l);
    d -= l;
    double error = Math.abs(d);
    int bestDenominator = 1;
    for(int i=2;i<=factor;i++) {
        double error2 = Math.abs(d - (double) Math.round(d * i) / i);
        if (error2 < error) {
            error = error2;
            bestDenominator = i;
            if (error2 == 0) break;
        }
    }
    if (bestDenominator > 1)
        sb.append(' ').append(Math.round(d * bestDenominator)).append('/') .append(bestDenominator);
    return sb.toString();
}

public static void main(String... args)  {
    System.out.println(toFraction(1.3333, 1000));
    System.out.println(toFraction(1.1428, 1000));
    for(int i=1;i<100000000;i*=10) {
        System.out.println("PI "+i+": "+toFraction(3.1415926535897932385, i));
    }
}

Answer 4

The simplest approach might be to use trial and error.

public static String toFraction(double d, int factor) {
    StringBuilder sb = new StringBuilder();
    if (d < 0) {
        sb.append('-');
        d = -d;
    }
    long l = (long) d;
    if (l != 0) sb.append(l);
    d -= l;
    double error = Math.abs(d);
    int bestDenominator = 1;
    for(int i=2;i<=factor;i++) {
        double error2 = Math.abs(d - (double) Math.round(d * i) / i);
        if (error2 < error) {
            error = error2;
            bestDenominator = i;
        }
    }
    if (bestDenominator > 1)
        sb.append(' ').append(Math.round(d * bestDenominator)).append('/') .append(bestDenominator);
    return sb.toString();
}

public static void main(String... args)  {
    System.out.println(toFraction(1.3333, 1000));
    System.out.println(toFraction(1.1428, 1000));
    for(int i=1;i<100000000;i*=10) {
        System.out.println("PI "+i+": "+toFraction(3.1415926535897932385, i));
    }
}

prints

1 1/3
1 1/7
PI 1: 3
PI 10: 3 1/7
PI 100: 3 14/99
PI 1000: 3 16/113
PI 10000: 3 16/113
PI 100000: 3 14093/99532
PI 1000000: 3 140914/995207
PI 10000000: 3 244252/1725033

Answer 5

This might be of help:

http://www.merriampark.com/fractions.htm

Otherwise you'd need some way of telling Convert() how far out you want to take things. Maybe a maximum reduced demoninator or something like that. That way you'll get "1 1/3" for both of the first two examples you have above rather than "1 33333/100000" for the first and "1 333/1000" for the second.

Answer 6

Extract the fractional part of the number (for example, ((int) 0.5 + 1) - 0.5, then divide one by the result (1 / 0.5). You'll get the denominator of the fraction. Then cast the float to an int, and you'll get the integer part. Then concatenate both.

It's just a simple solution, and will work only if the numerator of the fraction is 1.

double n = 1.2f;

int denominator = 1 / (Math.abs(n - (int) n - 0.0001)); //- 0.0001 so the division doesn't get affected by the float point aproximated representation
int units = (int) n;

int numerator = units * denominator + 1;

System.out.println("" + numerator + "/" + denominator); //6/5
System.out.println("" + units + " 1/" + denominator); //1 1/5