将小数转换为分数

Question

我正在开发一个 "toy problem"，我应该在其中编写一个 JavaScript 函数，将小数转换为分数并将其 return 转换为字符串。例如：fractionConverter(2.75) 应该 return "11/4".

这是我的代码：

function fractionConverter (number) {
  if (number > 0) {
    var isNegative = false;
  } else if (number < 0) {
    var isNegative = true;
  }

  number = Math.abs(number);

  if (number % 1 === 0) {
    var finalFrac = number + "/1";
  } else {
    for (var i = 2; i < 10000000000; i++) {
      if ((i * number) % 1 === 0) {
        var finalFrac = (i * number) + "/" + i;
      }
      if (finalFrac) { break; }
    }
  }

  var getFrac = function(numString, bool) {
    if (!bool) {
      return numString;
    } else {
       return "-" + numString;
    }
  }

  return getFrac(finalFrac, isNegative);
}

抱歉格式问题。无论如何，我遇到了一个奇怪的规范失败。函数 return 为以下数字提供了正确的值：0.5、3、2.5、2.75、-1.75 和 .88。然而，出于某种原因，它在 0.253213 上失败了。它是 returning 1266065/5000000 而不是 253213/1000000。不太清楚为什么。

谢谢

Answer 1

Javascript 没有准确处理浮点数。

我尝试将其输入节点：

0.253213 * 1000000

我得到了这个：

253213.00000000003

这是测试乘数的另一种方法

var bigNumber = Math.pow(10,8);

var isDivisible = (Math.round(i * number * bigNumber)/bigNumber % 1) == 0;

这将对您有所帮助。

如果您希望将 0.333333333 视为 1/3，这也可以按照您预期的方式工作。

一个问题是您可以拥有的最大整数 javascript 介于 10^15 和 10^16 之间。

如果 ((number * bigNumber) > 2^53) 这将不起作用。

Answer 2

我完全改变了你的代码结构，但这个解决方案确实有效。它基于来自 this 线程的代码。希望对您有所帮助。

function fractionConverter(number) {
  var fraction = number - Math.floor(number);
  var precision = Math.pow(10, /\d*$/.exec(new String(number))[0].length);
  var getGreatestCommonDivisor = function(fraction, precision) {
    if (!precision)
      return fraction;
    return getGreatestCommonDivisor(precision, fraction % precision);
  }
  var greatestCommonDivisor = getGreatestCommonDivisor(Math.round(fraction * precision), precision);
  var denominator = precision / greatestCommonDivisor;
  var numerator = Math.round(fraction * precision) / greatestCommonDivisor;

  return numerator + "/" + denominator;
}

document.getElementById("output").innerHTML = fractionConverter(0.253213);

<!DOCTYPE html>
<html>

<body>
  <p id="output"></p>
</body>

</html>

Answer 3

这个答案的警告是 ECMAscript 不能充分处理小数。另请注意，以下大部分是伪代码，但应该可以进行较小的修复。

这里有一个javascript解决这个问题的方法：

var decimal_to_fraction = {
  "numerator": 0,
  "denominator": 0,
  "simplified_numerator": this.numerator,
  "simplified_denominator": this.denominator,
  "init": function(numerator, denominator){
    this.numerator = numerator
    this.denominator = denominator
  },
  "get_divisor": function(numerator, denominator){
    var divisor = 0;
    var divisors = [1, 2, 3, 4, 5];

    for (i in divisors) {
      if (!(numerator % divisor) && !(denominator % divisor)) {
        divisor = i;
        break
      }
    }

    return divisor
  },
  "calculate_fraction": function() {
    var simplified = false;
    divisor = this.get_divisor(numerator_denominator);

    if (divisor) {
      while (simplified == false) {
        if (this.simplfieid_numerator / divisor and this.simplified_denominator / divisor) {
          this.simplified_numerator = simplified_numerator / divisor
          this.simplified_denominator = simplified_denominator / divisor
        } else {
          simplified = true
        }
      }
    }

    return (this.simplified_numerator, this.simplfieid_denominator)
  },
  "get_fraction": function() {
    this.calculate_fraction()

    fraction = "{0} / {1}".format(this.simplfieid_numerator, this.simplified_denominator"

    return fraction
  }

}

decimal_to_fraction.get_fraction()

如果您感到好奇，这里有一个 Python 解决您的问题的方法：

class DecimalToFraction(object):
    def __init__(decimal):
        self.numerator = decimal * 100
        self.denominator = 100
        self.simplified_numerator = self.numerator
        self.simplified_denominator = self.denominator

    def get_divisor(self, numerator, denominator):
        divisor = 0

        for i in range(0,5):
            if not numerator % divisor and not denominator % divisor:
                divisor = i
                break

        return divisor

    def calculate_fraction(self):
        simplified = False

        divisor = get_divisor(self.numerator, self.denominator)

        if divisor:
            while simplified == False:
                if self.simplified_numerator / divisor and self.simplfieid_denominator / divisor:
                    self.simplified_numerator = simplified_numerator / divisor
                    self.simplified_denominator = simplified_denominator / divisor
                else:
                    simplified = True

        return (self.simplified_numerator, self.simplified_denominator)


    def get_fraction(self):
        self.calculate_fraction()

        fraction = "{0} / {1}".format(self.simplified_numerator, self.simplified_denominator)

        return fraction


#d2f = DecimalToFraction(<decimal>)
#d2f.get_fraction()

Answer 4

您可以使用 Erik Garrison 的 fraction.js 库来执行此操作以及更多小数运算。

To to do 1.75 , you can just do

var f = new Fraction(1.75);
console.log(f.toFraction()); // Results "1 3/4" 
console.log(f.s * f.n + " / " + f.d); // Results "7 / 4"
console.log(f.toString()); // Results "1.75

Answer 5

我只是在改进@william 的回答，我认为这个脚本给你更多的减少分数。

function fractionConverter(number) {
  var fraction = number - Math.floor(number);
  var precision = Math.pow(10, /\d*$/.exec(new String(number))[0].length);
  var getGreatestCommonDivisor = function(fraction, precision) {
    if (!precision)
      return fraction;
    return getGreatestCommonDivisor(precision, fraction % precision);
  }
  var greatestCommonDivisor = getGreatestCommonDivisor(Math.round(fraction * precision), precision);
  var denominator = precision / getGreatestCommonDivisor(Math.round(fraction * precision), precision);
  var numerator = Math.round(fraction * precision) / greatestCommonDivisor;

  function reduce (numer,denom) {
    for (var i = 2; i >= 9; i++) {
      if ((numer%i===0) && (denom%i)===0) {
        numerator=numer/i;
        denominator=denom/i;
        reduce(numerator,denominator);
      };
    };
  }
reduce(numerator,denominator);
  return numerator + "/" + denominator;
}

document.getElementById("output").innerHTML = fractionConverter(0.24888);

这是HTML

<body>
  <p id="output"></p>
</body>

</html>

将小数转换为分数

Converting a Decimal to a Fraction

javascript

numbers

decimal

fractions