如何精确的表达无限小数呢？这在计算机中是一个不可能完成的事情；但是无限循环小数是可以转化成分数，从而精确表达的；那问题来了，如何将无限循环小数转化成分数？例如0.(3)，括号中是循环体，可以用1/3或3/9来表示。当然，我们想要的是分子分母不能再约分的最简分数。好吧：)来看看如何实现吧！import java.math.*;

public class Decimal2Fraction {

public String Repeating2Smallest(String repeating, String separate){

String separate_l = separate.substring(0,1);

String separate_r = separate.substring(1,2);

String separate_p = ".";

int index_p = repeating.indexOf(separate_p);

int index_l = repeating.indexOf(separate_l);

int index_r = repeating.indexOf(separate_r);

BigInteger number = new BigInteger(repeating.substring(0,index_p));

int n = index_l-index_p-1;

BigInteger a = BigInteger.ZERO;

if(n>0)a = new BigInteger(repeating.substring(index_p+1,index_l));

int m = index_r-index_l-1;

BigInteger b = BigInteger.ZERO;

if(m<=0) return "请输入正确的循环体";

if(m>0)b= new BigInteger(repeating.substring(index_l+1,index_r));

BigInteger numerator = NumeratorFormula(n, m, a, b);

BigInteger denominator = DenominatorFormula(n , m);

BigInteger GCD = BigInteger.ZERO;

while(!GCD.equals(BigInteger.ONE)){

GCD = numerator.gcd(denominator);

numerator = numerator.divide(GCD);

denominator = denominator.divide(GCD);

}

return number+" "+numerator+"/"+denominator;

}

public BigInteger NumeratorFormula(int n,int m,BigInteger a,BigInteger b){

return BigInteger.TEN.pow(m).subtract(BigInteger.ONE).multiply(a).add(b);

}

public BigInteger DenominatorFormula(int n,int m){

return BigInteger.TEN.pow(m).subtract(BigInteger.ONE).multiply(BigInteger.TEN.pow(n));

}

public static void Console(Object o){System.out.println(o.toString());}

public static void main(String[] args) {

Decimal2Fraction d2f = new Decimal2Fraction();

String s = "0.2[22]";

Console(d2f.Repeating2Smallest(s,"[]"));

}

}