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How to convert decimal numbers to fractions


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.

Código Delphi [-]
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.

Código Delphi [-]
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;