Converting a float into a string fraction representation
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); // Should return "1 1/3"
float num2 = 1.333;
String numStr2 = Convert(num2); // Should also return "1 1/3"
float num3 = 0.5开发者_C百科;
String numStr3 = Convert(num3); // Should return "1/2"
float num4 = 2.25;
String numStr4 = Convert(num4); // Should return "2 1/4"
Any ideas how to do this in Java?
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
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.
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.
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
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));
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));
}
}
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