将十进制数转换为分数/有理数

Question

在JavaScript中，有没有办法将十进制数（如0.0002）转换为表示为字符串的分数（如“2/10000”）？

如果为此编写了一个名为decimalToFraction的函数，那么decimalToFraction（0.0002）将返回字符串"2/10000"。

Answer 1

我用过这个网站http://mathforum.org/library/drmath/view/51886.html但是正如文章所提到的，你会得到一个不合理的大数，比如偏激或π。

希望能有所帮助。

function Fraction(){}
Fraction.prototype.convert = function(x, improper)
{
    improper = improper || false;
    var abs = Math.abs(x);
    this.sign = x/abs;
    x = abs;
    var stack = 0;
    this.whole = !improper ? Math.floor(x) : 0;
    var fractional = !improper ? x-this.whole : abs;
    /*recursive function that transforms the fraction*/
    function recurs(x){
        stack++;
        var intgr = Math.floor(x); //get the integer part of the number
        var dec = (x - intgr); //get the decimal part of the number
        if(dec < 0.0019 || stack > 20) return [intgr,1]; //return the last integer you divided by
        var num = recurs(1/dec); //call the function again with the inverted decimal part
        return[intgr*num[0]+num[1],num[0]]
    }
    var t = recurs(fractional); 
    this.numerator = t[0];
    this.denominator = t[1];
}

Fraction.prototype.toString = function()
{
    var l  = this.sign.toString().length;
    var sign = l === 2 ? '-' : '';
    var whole = this.whole !== 0 ? this.sign*this.whole+' ': sign;
    return whole+this.numerator+'/'+this.denominator;
}

//var frac = new Fraction()
//frac.convert(2.56, false)
//console.log(frac.toString())
//use frac.convert(2.56,true) to get it as an improper fraction

如果你想要一个只返回分子和分母的自包含函数，那么使用下面的函数。

var toFraction = function (dec) {
    var is_neg = dec < 0;
    dec = Math.abs(dec);
    var done = false;
    //you can adjust the epsilon to a larger number if you don't need very high precision
    var n1 = 0, d1 = 1, n2 = 1, d2 = 0, n = 0, q = dec, epsilon = 1e-13;
    while (!done) {
        n++;
        if (n > 10000) {
            done = true;
        }
        var a = parseInt(q);
        var num = n1 + a * n2;
        var den = d1 + a * d2;
        var e = (q - a);
        if (e < epsilon) {
            done = true;
        }
        q = 1 / e;
        n1 = n2;
        d1 = d2;
        n2 = num;
        d2 = den;
        if (Math.abs(num / den - dec) < epsilon || n > 30) {
            done = true;
        }
    }
    return [is_neg ? -num : num, den];
};
//Usage:
//var frac = toFraction(0.5);
//console.log(frac)
//Output: [ 1, 2 ]

Answer 2

在谷歌上搜索一下“小数到分数”这个词，第一个结果是：

http://wildreason.com/wildreason-blog/2010/javascript-convert-a-decimal-into-a-simplified-fraction/

这似乎有效：

http://jsfiddle.net/VKfHH/

function HCF(u, v) { 
    var U = u, V = v
    while (true) {
        if (!(U%=V)) return V
        if (!(V%=U)) return U 
    } 
}
//convert a decimal into a fraction
function fraction(decimal){

    if(!decimal){
        decimal=this;
    }
    whole = String(decimal).split('.')[0];
    decimal = parseFloat("."+String(decimal).split('.')[1]);
    num = "1";
    for(z=0; z<String(decimal).length-2; z++){
        num += "0";
    }
    decimal = decimal*num;
    num = parseInt(num);
    for(z=2; z<decimal+1; z++){
        if(decimal%z==0 && num%z==0){
            decimal = decimal/z;
            num = num/z;
            z=2;
        }
    }
    //if format of fraction is xx/xxx
    if (decimal.toString().length == 2 && 
            num.toString().length == 3) {
                //reduce by removing trailing 0's
        decimal = Math.round(Math.round(decimal)/10);
        num = Math.round(Math.round(num)/10);
    }
    //if format of fraction is xx/xx
    else if (decimal.toString().length == 2 && 
            num.toString().length == 2) {
        decimal = Math.round(decimal/10);
        num = Math.round(num/10);
    }
    //get highest common factor to simplify
    var t = HCF(decimal, num);

    //return the fraction after simplifying it
    return ((whole==0)?"" : whole+" ")+decimal/t+"/"+num/t;
}

// Test it
alert(fraction(0.0002)); // "1/5000"

Answer 3

你可以用埃里克·加里森的分数。js库来实现这一点和更多的分数运算。

var f = new Fraction(2, 10000);
console.log(f.numerator + '/' + f.denominator);

去做你可以去做

var f = new Fraction(.003);
console.log(f.numerator + '/' + f.denominator);