How can I convert a decimal to a fraction?

Question

How do I convert a indefinite decimal (i.e. .333333333...) to a string fraction representation (i.e. "1/3"). I am using VBA and the following is the code I used (i get an overflow error at the line "b = a Mod b":

Function GetFraction(ByVal Num As Double) As String

    If Num = 0# Then
        GetFraction = "None"
    Else
        Dim WholeNumber As Integer
        Dim DecimalNumber As Double
        Dim Numerator As Double
        Dim Denomenator As Double
        Dim a, b, t As Double

        WholeNumber = Fix(Num)
        DecimalNumber = Num - Fix(Num)
        Numerator = DecimalNumber * 10 ^ (Len(CStr(DecimalNumber)) - 2)
        Denomenator = 10 ^ (Len(CStr(DecimalNumber)) - 2)
        If Numerator = 0 Then
            GetFraction = WholeNumber
        Else
            a = Numerator
            b = Denomenator
            t = 0

            While b <> 0
                t = b
                b = a Mod b
                a = t
            Wend
            If WholeNumber = 0 Then
                GetFraction = CStr(Numerator / a) & "/" & CStr(Denomenator / a)
            Else
                GetFraction = CStr(WholeNumber) & " " & CStr(Numerator / a) & "/" & CStr(Denomenator / a)
            End If
        End If
    End If
End Function

Answer 1

Google for "decimal to fraction" and you'll get about a gazillion results.

I really like this one, because it's simple, has source code (in RPL, similar to Forth, ~25 lines), and is pretty fast (it's written to run on a 4-bit, 4MHz CPU). The docs say:

In a book called Textbook of Algebra by G. Chrystal, 1st edition in 1889, in Part II, Chapter 32, this improved continued fraction algorithm is presented and proven. Odd to tell, Chrystal speaks of it as if it were ancient knowledge.