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How to convert decimal numbers to fractions (Views: 100)

 Problem/Question/Abstract:I'm looking for a function that I can pass in a decimal and return a fraction.Answer:Solve 1:The "Denominators" parameter is an array of potential denominators that would be acceptable. For example, to get a fractional inch dimension with a power of 2 denominator, you'd pass [2, 4, 8, 16, 32] for that parameter, and the function will figure out which potential denominator will work best.function ConvertFloatToFraction(const Value: Double;  const Denominators: array of Integer): string;var  Index: Integer;  TempDelta: Double;  MinDelta: Double;  TempNumerator: Integer;  FracValue: Double;  Numerator: Integer;  Denominator: Integer;  IntValue: Integer;begin  IntValue := Trunc(Value);  FracValue := Abs(Frac(Value));  MinDelta := 0;  Numerator := 0;  Denominator := 0;  for Index := 0 to High(Denominators) do  begin    TempNumerator := Round(FracValue * Denominators[Index]);    TempDelta := Abs(FracValue - (TempNumerator / Denominators[Index]));    if ((Index = 0) or (TempDelta < MinDelta)) then    begin      MinDelta := TempDelta;      Numerator := TempNumerator;      Denominator := Denominators[Index];    end;  end;  if (Numerator = Denominator) then  begin    IntValue := IntValue + Sign(IntValue);    Numerator := 0;  end;  Result := '';  if ((IntValue <> 0) or (Numerator = 0)) then    Result := IntToStr(IntValue);  if ((IntValue <> 0) and (Numerator <> 0)) then    Result := Result + ' ';  if (Numerator <> 0) then    Result := Result + IntToStr(Numerator) + '/' + IntToStr(Denominator);end;Solve 2:This function takes the number to convert, the fraction scale you want returned such as 8 for eighths or 10 for tenths, etc. and a boolean to tell it to round up or down the nearest fraction. It returns a string with the integer portion, a space and then the fraction portion. It will also reduce the fraction to the smallest common denominator. You can use the ErrorFactor variable to adjust the percentage of when to consider a number close enough to the next level to be close enough. I use 4 percent of the fractional scale value.function ToFraction(num: double; scale: integer; RoundUp: boolean): string;{Function to find greatest common denominator}  function GCD(A, B: integer): integer;  begin    if (B mod A) = 0 then      result := A    else if (B mod A) = 1 then      result := 1    else      result := GCD((B mod A), A);  end;var  x, y: integer;  ScaleFrac,    NumFrac,    ErrorFactor: double;begin  ScaleFrac := 1 / scale;  NumFrac := Frac(Num);  ErrorFactor := ScaleFrac * 0.04; {error factor of 4 percent}  x := 0;  while (((x + 1) * ScaleFrac) < (NumFrac + ErrorFactor)) do    inc(x);  if RoundUp then    if (((((x + 1) * ScaleFrac) - NumFrac) / 2) > (ScaleFrac / 2)) then      inc(x);  if (x = 0) then {no fraction, just the integer portion}  begin    result := IntToStr(Trunc(Num))  end  else  begin {reduce the fraction as much as possible}    y := GCD(x, scale);    while (y <> 1) do    begin      x := x div y;      scale := scale div y;      y := GCD(x, scale);    end;    result := IntToStr(Trunc(Num)) + ' ' + IntToStr(x) + '/' + IntToStr(scale);  end;end;

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