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How to convert decimal numbers to fractions Turn on/off line numbers in source code. Switch to Orginial background IDE or DSP color Comment or reply to this aritlce/tip for discussion. Bookmark this article to my favorite article(s). Print this article
19-Oct-02
Category
Algorithm
Language
Delphi 2.x
Views
84
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Publisher:
DSP, Administrator
Reference URL:
DKB
			Author: Jonas Bilinkevicius

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.
1   
2   function ConvertFloatToFraction(const Value: Double;
3     const Denominators: array of Integer): string;
4   var
5     Index: Integer;
6     TempDelta: Double;
7     MinDelta: Double;
8     TempNumerator: Integer;
9     FracValue: Double;
10    Numerator: Integer;
11    Denominator: Integer;
12    IntValue: Integer;
13  begin
14    IntValue := Trunc(Value);
15    FracValue := Abs(Frac(Value));
16    MinDelta := 0;
17    Numerator := 0;
18    Denominator := 0;
19    for Index := 0 to High(Denominators) do
20    begin
21      TempNumerator := Round(FracValue * Denominators[Index]);
22      TempDelta := Abs(FracValue - (TempNumerator / Denominators[Index]));
23      if ((Index = 0) or (TempDelta < MinDelta)) then
24      begin
25        MinDelta := TempDelta;
26        Numerator := TempNumerator;
27        Denominator := Denominators[Index];
28      end;
29    end;
30    if (Numerator = Denominator) then
31    begin
32      IntValue := IntValue + Sign(IntValue);
33      Numerator := 0;
34    end;
35    Result := '';
36    if ((IntValue <> 0) or (Numerator = 0)) then
37      Result := IntToStr(IntValue);
38    if ((IntValue <> 0) and (Numerator <> 0)) then
39      Result := Result + ' ';
40    if (Numerator <> 0) then
41      Result := Result + IntToStr(Numerator) + '/' + IntToStr(Denominator);
42  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.
43  
44  function ToFraction(num: double; scale: integer; RoundUp: boolean): string;
45  
46  {Function to find greatest common denominator}
47    function GCD(A, B: integer): integer;
48    begin
49      if (B mod A) = 0 then
50        result := A
51      else if (B mod A) = 1 then
52        result := 1
53      else
54        result := GCD((B mod A), A);
55    end;
56  
57  var
58    x, y: integer;
59    ScaleFrac,
60      NumFrac,
61      ErrorFactor: double;
62  begin
63    ScaleFrac := 1 / scale;
64    NumFrac := Frac(Num);
65    ErrorFactor := ScaleFrac * 0.04; {error factor of 4 percent}
66    x := 0;
67    while (((x + 1) * ScaleFrac) < (NumFrac + ErrorFactor)) do
68      inc(x);
69    if RoundUp then
70      if (((((x + 1) * ScaleFrac) - NumFrac) / 2) > (ScaleFrac / 2)) then
71        inc(x);
72    if (x = 0) then {no fraction, just the integer portion}
73    begin
74      result := IntToStr(Trunc(Num))
75    end
76    else
77    begin {reduce the fraction as much as possible}
78      y := GCD(x, scale);
79      while (y <> 1) do
80      begin
81        x := x div y;
82        scale := scale div y;
83        y := GCD(x, scale);
84      end;
85      result := IntToStr(Trunc(Num)) + ' ' + IntToStr(x) + '/' + IntToStr(scale);
86    end;
87  end;


			
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