在 C# 中将双精度数转换为分数作为字符串

Question

我想在 C# 中将双精度值显示为分数，我该怎么做？

谢谢

Answer 1

尝试这个 C# 的 Fraction 类。

/*
 * Author: Syed Mehroz Alam
 * Email: [email protected]
 * URL: Programming Home "http://www.geocities.com/smehrozalam/" 
 * Date: 6/15/2004
 * Time: 10:54 AM
 *
 */

using System;

namespace Mehroz
{
    /// <summary>
    /// Classes Contained:
    ///     Fraction
    ///     FractionException
    /// </summary>


    /// Class name: Fraction
    /// Developed by: Syed Mehroz Alam
    /// Email: [email protected]
    /// URL: Programming Home "http://www.geocities.com/smehrozalam/"
    /// Version: 2.0
    /// 
    /// What's new in version 2.0:
    ///     *   Changed Numerator and Denominator from Int32(integer) to Int64(long) for increased range
    ///     *   renamed ConvertToString() to (overloaded) ToString()
    ///     *   added the capability of detecting/raising overflow exceptions
    ///     *   Fixed the bug that very small numbers e.g. 0.00000001 could not be converted to fraction
    ///     *   Other minor bugs fixed
    /// 
    /// What's new in version 2.1
    ///     *   overloaded user-defined conversions to/from Fractions
    ///     
    /// 
    /// Properties:
    ///     Numerator: Set/Get value for Numerator
    ///     Denominator:  Set/Get value for Numerator
    ///     Value:  Set an integer value for the fraction
    /// 
    /// Constructors:
    ///     no arguments:   initializes fraction as 0/1
    ///     (Numerator, Denominator): initializes fraction with the given numerator and denominator values
    ///     (integer):  initializes fraction with the given integer value
    ///     (long): initializes fraction with the given long value
    ///     (double):   initializes fraction with the given double value
    ///     (string):   initializes fraction with the given string value
    ///                 the string can be an in the form of and integer, double or fraction.
    ///                 e.g it can be like "123" or "123.321" or "123/456"
    /// 
    /// Public Methods (Description is given with respective methods' definitions)
    ///     (override) string ToString(Fraction)
    ///     Fraction ToFraction(string)
    ///     Fraction ToFraction(double)
    ///     double ToDouble(Fraction)
    ///     Fraction Duplicate()
    ///     Fraction Inverse(integer)
    ///     Fraction Inverse(Fraction)
    ///     ReduceFraction(Fraction)
    ///     Equals(object)
    ///     GetHashCode()
    /// 
    /// Private Methods (Description is given with respective methods' definitions)
    ///     Initialize(Numerator, Denominator)
    ///     Fraction Negate(Fraction)
    ///     Fraction Add(Fraction1, Fraction2)
    /// 
    /// Overloaded Operators (overloaded for Fractions, Integers and Doubles)
    ///     Unary: -
    ///     Binary: +,-,*,/ 
    ///     Relational and Logical Operators: ==,!=,<,>,<=,>=
    /// 
    /// Overloaded user-defined conversions
    ///     Implicit:   From double/long/string to Fraction
    ///     Explicit:   From Fraction to double/string
    /// </summary>
    public class Fraction
    {
        /// <summary>
        /// Class attributes/members
        /// </summary>
        long m_iNumerator;
        long m_iDenominator;

        /// <summary>
        /// Constructors
        /// </summary>
        public Fraction()
        {
            Initialize(0,1);
        }

        public Fraction(long iWholeNumber)
        {
            Initialize(iWholeNumber, 1);
        }

        public Fraction(double dDecimalValue)
        {
            Fraction temp=ToFraction(dDecimalValue);
            Initialize(temp.Numerator, temp.Denominator);
        }

        public Fraction(string strValue)
        {
            Fraction temp=ToFraction(strValue);
            Initialize(temp.Numerator, temp.Denominator);
        }

        public Fraction(long iNumerator, long iDenominator)
        {
            Initialize(iNumerator, iDenominator);
        }

        /// <summary>
        /// Internal function for constructors
        /// </summary>
        private void Initialize(long iNumerator, long iDenominator)
        {
            Numerator=iNumerator;
            Denominator=iDenominator;
            ReduceFraction(this);
        }

        /// <summary>
        /// Properites
        /// </summary>
        public long Denominator
        {
            get
            {   return m_iDenominator;  }
            set
            {
                if (value!=0)
                    m_iDenominator=value;
                else
                    throw new FractionException("Denominator cannot be assigned a ZERO Value");
            }
        }

        public long Numerator
        {
            get 
            {   return m_iNumerator;    }
            set
            {   m_iNumerator=value; }
        }

        public long Value
        {
            set
            {   m_iNumerator=value;
                m_iDenominator=1;   }
        }

        /// <summary>
        /// The function returns the current Fraction object as double
        /// </summary>
        public double ToDouble()
        {
            return ( (double)this.Numerator/this.Denominator );
        }

        /// <summary>
        /// The function returns the current Fraction object as a string
        /// </summary>
        public override string ToString()
        {
            string str;
            if ( this.Denominator==1 )
                str=this.Numerator.ToString();
            else
                str=this.Numerator + "/" + this.Denominator;
            return str;
        }
        /// <summary>
        /// The function takes an string as an argument and returns its corresponding reduced fraction
        /// the string can be an in the form of and integer, double or fraction.
        /// e.g it can be like "123" or "123.321" or "123/456"
        /// </summary>
        public static Fraction ToFraction(string strValue)
        {
            int i;
            for (i=0;i<strValue.Length;i++)
                if (strValue[i]=='/')
                    break;

            if (i==strValue.Length)     // if string is not in the form of a fraction
                // then it is double or integer
                return ( Convert.ToDouble(strValue));
                //return ( ToFraction( Convert.ToDouble(strValue) ) );

            // else string is in the form of Numerator/Denominator
            long iNumerator=Convert.ToInt64(strValue.Substring(0,i));
            long iDenominator=Convert.ToInt64(strValue.Substring(i+1));
            return new Fraction(iNumerator, iDenominator);
        }


        /// <summary>
        /// The function takes a floating point number as an argument 
        /// and returns its corresponding reduced fraction
        /// </summary>
        public static Fraction ToFraction(double dValue)
        {
            try
            {
                checked
                {
                    Fraction frac;
                    if (dValue%1==0)    // if whole number
                    {
                        frac=new Fraction( (long) dValue );
                    }
                    else
                    {
                        double dTemp=dValue;
                        long iMultiple=1;
                        string strTemp=dValue.ToString();
                        while ( strTemp.IndexOf("E")>0 )    // if in the form like 12E-9
                        {
                            dTemp*=10;
                            iMultiple*=10;
                            strTemp=dTemp.ToString();
                        }
                        int i=0;
                        while ( strTemp[i]!='.' )
                            i++;
                        int iDigitsAfterDecimal=strTemp.Length-i-1;
                        while ( iDigitsAfterDecimal>0  )
                        {
                            dTemp*=10;
                            iMultiple*=10;
                            iDigitsAfterDecimal--;
                        }
                        frac=new Fraction( (int)Math.Round(dTemp) , iMultiple );
                    }
                    return frac;
                }
            }
            catch(OverflowException)
            {
                throw new FractionException("Conversion not possible due to overflow");
            }
            catch(Exception)
            {
                throw new FractionException("Conversion not possible");
            }
        }

        /// <summary>
        /// The function replicates current Fraction object
        /// </summary>
        public Fraction Duplicate()
        {
            Fraction frac=new Fraction();
            frac.Numerator=Numerator;
            frac.Denominator=Denominator;
            return frac;
        }

        /// <summary>
        /// The function returns the inverse of a Fraction object
        /// </summary>
        public static Fraction Inverse(Fraction frac1)
        {
            if (frac1.Numerator==0)
                throw new FractionException("Operation not possible (Denominator cannot be assigned a ZERO Value)");

            long iNumerator=frac1.Denominator;
            long iDenominator=frac1.Numerator;
            return ( new Fraction(iNumerator, iDenominator));
        }   


        /// <summary>
        /// Operators for the Fraction object
        /// includes -(unary), and binary opertors such as +,-,*,/
        /// also includes relational and logical operators such as ==,!=,<,>,<=,>=
        /// </summary>
        public static Fraction operator -(Fraction frac1)
        {   return ( Negate(frac1) );   }

        public static Fraction operator +(Fraction frac1, Fraction frac2)
        {   return ( Add(frac1 , frac2) );  }

        public static Fraction operator +(int iNo, Fraction frac1)
        {   return ( Add(frac1 , new Fraction(iNo) ) ); }

        public static Fraction operator +(Fraction frac1, int iNo)
        {   return ( Add(frac1 , new Fraction(iNo) ) ); }

        public static Fraction operator +(double dbl, Fraction frac1)
        {   return ( Add(frac1 , Fraction.ToFraction(dbl) ) );  }

        public static Fraction operator +(Fraction frac1, double dbl)
        {   return ( Add(frac1 , Fraction.ToFraction(dbl) ) );  }

        public static Fraction operator -(Fraction frac1, Fraction frac2)
        {   return ( Add(frac1 , -frac2) ); }

        public static Fraction operator -(int iNo, Fraction frac1)
        {   return ( Add(-frac1 , new Fraction(iNo) ) );    }

        public static Fraction operator -(Fraction frac1, int iNo)
        {   return ( Add(frac1 , -(new Fraction(iNo)) ) );  }

        public static Fraction operator -(double dbl, Fraction frac1)
        {   return ( Add(-frac1 , Fraction.ToFraction(dbl) ) ); }

        public static Fraction operator -(Fraction frac1, double dbl)
        {   return ( Add(frac1 , -Fraction.ToFraction(dbl) ) ); }

        public static Fraction operator *(Fraction frac1, Fraction frac2)
        {   return ( Multiply(frac1 , frac2) ); }

        public static Fraction operator *(int iNo, Fraction frac1)
        {   return ( Multiply(frac1 , new Fraction(iNo) ) );    }

        public static Fraction operator *(Fraction frac1, int iNo)
        {   return ( Multiply(frac1 , new Fraction(iNo) ) );    }

        public static Fraction operator *(double dbl, Fraction frac1)
        {   return ( Multiply(frac1 , Fraction.ToFraction(dbl) ) ); }

        public static Fraction operator *(Fraction frac1, double dbl)
        {   return ( Multiply(frac1 , Fraction.ToFraction(dbl) ) ); }

        public static Fraction operator /(Fraction frac1, Fraction frac2)
        {   return ( Multiply( frac1 , Inverse(frac2) ) );  }

        public static Fraction operator /(int iNo, Fraction frac1)
        {   return ( Multiply( Inverse(frac1) , new Fraction(iNo) ) );  }

        public static Fraction operator /(Fraction frac1, int iNo)
        {   return ( Multiply( frac1 , Inverse(new Fraction(iNo)) ) );  }

        public static Fraction operator /(double dbl, Fraction frac1)
        {   return ( Multiply( Inverse(frac1) , Fraction.ToFraction(dbl) ) );   }

        public static Fraction operator /(Fraction frac1, double dbl)
        {   return ( Multiply( frac1 , Fraction.Inverse( Fraction.ToFraction(dbl) ) ) );    }

        public static bool operator ==(Fraction frac1, Fraction frac2)
        {   return frac1.Equals(frac2);     }

        public static bool operator !=(Fraction frac1, Fraction frac2)
        {   return ( !frac1.Equals(frac2) );    }

        public static bool operator ==(Fraction frac1, int iNo)
        {   return frac1.Equals( new Fraction(iNo));    }

        public static bool operator !=(Fraction frac1, int iNo)
        {   return ( !frac1.Equals( new Fraction(iNo)) );   }

        public static bool operator ==(Fraction frac1, double dbl)
        {   return frac1.Equals( new Fraction(dbl));    }

        public static bool operator !=(Fraction frac1, double dbl)
        {   return ( !frac1.Equals( new Fraction(dbl)) );   }

        public static bool operator<(Fraction frac1, Fraction frac2)
        {   return frac1.Numerator * frac2.Denominator < frac2.Numerator * frac1.Denominator;   }

        public static bool operator>(Fraction frac1, Fraction frac2)
        {   return frac1.Numerator * frac2.Denominator > frac2.Numerator * frac1.Denominator;   }

        public static bool operator<=(Fraction frac1, Fraction frac2)
        {   return frac1.Numerator * frac2.Denominator <= frac2.Numerator * frac1.Denominator;  }

        public static bool operator>=(Fraction frac1, Fraction frac2)
        {   return frac1.Numerator * frac2.Denominator >= frac2.Numerator * frac1.Denominator;  }


        /// <summary>
        /// overloaed user defined conversions: from numeric data types to Fractions
        /// </summary>
        public static implicit operator Fraction(long lNo)
        {   return new Fraction(lNo);   }
        public static implicit operator Fraction(double dNo)
        {   return new Fraction(dNo);   }
        public static implicit operator Fraction(string strNo)
        {   return new Fraction(strNo); }

        /// <summary>
        /// overloaed user defined conversions: from fractions to double and string
        /// </summary>
        public static explicit operator double(Fraction frac)
        {   return frac.ToDouble(); }

        public static implicit operator string(Fraction frac)
        {   return frac.ToString(); }

        /// <summary>
        /// checks whether two fractions are equal
        /// </summary>
        public override bool Equals(object obj)
        {
            Fraction frac=(Fraction)obj;
            return ( Numerator==frac.Numerator && Denominator==frac.Denominator);
        }

        /// <summary>
        /// returns a hash code for this fraction
        /// </summary>
        public override int GetHashCode()
        {
            return ( Convert.ToInt32((Numerator ^ Denominator) & 0xFFFFFFFF) ) ;
        }

        /// <summary>
        /// internal function for negation
        /// </summary>
        private static Fraction Negate(Fraction frac1)
        {
            long iNumerator=-frac1.Numerator;
            long iDenominator=frac1.Denominator;
            return ( new Fraction(iNumerator, iDenominator) );

        }   

        /// <summary>
        /// internal functions for binary operations
        /// </summary>
        private static Fraction Add(Fraction frac1, Fraction frac2)
        {
            try
            {
                checked
                {
                    long iNumerator=frac1.Numerator*frac2.Denominator + frac2.Numerator*frac1.Denominator;
                    long iDenominator=frac1.Denominator*frac2.Denominator;
                    return ( new Fraction(iNumerator, iDenominator) );
                }
            }
            catch(OverflowException)
            {
                throw new FractionException("Overflow occurred while performing arithemetic operation");
            }
            catch(Exception)
            {
                throw new FractionException("An error occurred while performing arithemetic operation");
            }
        }

        private static Fraction Multiply(Fraction frac1, Fraction frac2)
        {
            try
            {
                checked
                {
                    long iNumerator=frac1.Numerator*frac2.Numerator;
                    long iDenominator=frac1.Denominator*frac2.Denominator;
                    return ( new Fraction(iNumerator, iDenominator) );
                }
            }
            catch(OverflowException)
            {
                throw new FractionException("Overflow occurred while performing arithemetic operation");
            }
            catch(Exception)
            {
                throw new FractionException("An error occurred while performing arithemetic operation");
            }
        }

        /// <summary>
        /// The function returns GCD of two numbers (used for reducing a Fraction)
        /// </summary>
        private static long GCD(long iNo1, long iNo2)
        {
            // take absolute values
            if (iNo1 < 0) iNo1 = -iNo1;
            if (iNo2 < 0) iNo2 = -iNo2;

            do
            {
                if (iNo1 < iNo2)
                {
                    long tmp = iNo1;  // swap the two operands
                    iNo1 = iNo2;
                    iNo2 = tmp;
                }
                iNo1 = iNo1 % iNo2;
            } while (iNo1 != 0);
            return iNo2;
        }

        /// <summary>
        /// The function reduces(simplifies) a Fraction object by dividing both its numerator 
        /// and denominator by their GCD
        /// </summary>
        public static void ReduceFraction(Fraction frac)
        {
            try
            {
                if (frac.Numerator==0)
                {
                    frac.Denominator=1;
                    return;
                }

                long iGCD=GCD(frac.Numerator, frac.Denominator);
                frac.Numerator/=iGCD;
                frac.Denominator/=iGCD;

                if ( frac.Denominator<0 )   // if -ve sign in denominator
                {
                    //pass -ve sign to numerator
                    frac.Numerator*=-1;
                    frac.Denominator*=-1;   
                }
            } // end try
            catch(Exception exp)
            {
                throw new FractionException("Cannot reduce Fraction: " + exp.Message);
            }
        }

    }   //end class Fraction


    /// <summary>
    /// Exception class for Fraction, derived from System.Exception
    /// </summary>
    public class FractionException : Exception
    {
        public FractionException() : base()
        {}

        public FractionException(string Message) : base(Message)
        {}

        public FractionException(string Message, Exception InnerException) : base(Message, InnerException)
        {}
    }   //end class FractionException


}   //end namespace Mehroz

---

正如@Tillito 在评论中指出的那样，我仔细检查了以下代码：

using System.IO;
using System;
using Mehroz;

class Program
{
    static void Main()
    {
        double d = .5;
        string str = new Fraction(d).ToString();

        Console.WriteLine(str);
    }
}

输出：

1/2

Answer 2

将后面的代码放入静态类中以创建扩展，然后使用：

var number = 2.83;
var result = number.ToFractions(4);

预期结果：“2 3/4”

代码：

public static string ToFractions(this double number, int precision = 4)
{
    int w, n, d;
    RoundToMixedFraction(number, precision, out w, out n, out d);
    var ret = $"{w}";
    if (w > 0)
    {
        if (n > 0)
            ret = $"{w} {n}/{d}";
    }
    else
    {
        if (n > 0)
            ret = $"{n}/{d}";
    }
    return ret;
}

static void RoundToMixedFraction(double input, int accuracy, out int whole, out int numerator, out int denominator)
{
    double dblAccuracy = (double)accuracy;
    whole = (int)(Math.Truncate(input));
    var fraction = Math.Abs(input - whole);
    if (fraction == 0)
    {
        numerator = 0;
        denominator = 1;
        return;
    }
    var n = Enumerable.Range(0, accuracy + 1).SkipWhile(e => (e / dblAccuracy) < fraction).First();
    var hi = n / dblAccuracy;
    var lo = (n - 1) / dblAccuracy;
    if ((fraction - lo) < (hi - fraction)) n--;
    if (n == accuracy)
    {
        whole++;
        numerator = 0;
        denominator = 1;
        return;
    }
    var gcd = GCD(n, accuracy);
    numerator = n / gcd;
    denominator = accuracy / gcd;
}

static int GCD(int a, int b)
{
    if (b == 0) return a;
    else return GCD(b, a % b);
}