Converting Decimals to Fractions

Here's shorter code...
Code: 
Function GetFraction(ByVal Number As Single, Denominator As Integer) As String
    Dim i As Integer
    
    Number = RoundToNearest(Number, 1 / Denominator)
    
    If Number <= 0 Or Number >= 1 Then
        Err.Raise 5, "GetFraction()", "Number must be between zero and one"
    Else
        For i = 1 To Denominator - 1
            If CInt(i / Number) = i / Number Then
                GetFraction = i & "/" & i / Number
                Exit For
            End If
        Next
    End If
End Function

Function RoundToNearest(Number As Single, Optional RoundTo As Single = 1)
    RoundToNearest = CLng(Number / RoundTo) * RoundTo
End Function
You can specify precision with the denominator parameter.
 
As @MarkK pointed out there is no need for a table or a select case. This can be solved in closed form using the Euclidean Algorithm for finding greatest common divisor. There are several forms of the algorithm. There is a subtraction method, division method, and the recursive which is shown. The only trick is you have to define the accuracy (precision to which to report your denominator).

Here is another version with a couple of additional features. You can do compound values with whole numbers and fraction parts. Also you can return the whole portion, numerator, and denominator instead of simply a string.

Code: 
Public Type Fraction
  WholeNumber As Long
  Numerator As Long
  Denominator As Long
End Type
Public Function GetFraction(ByVal TheDecimal As Double, Optional ByVal Accuracy As Double = 0.0078125) As Fraction
  'Lets go 10 places
  Const places = 1000000000
  Dim GCD As Long
  Dim decimalPart As Double
  GetFraction.WholeNumber = Fix(TheDecimal)
  decimalPart = TheDecimal - GetFraction.WholeNumber
  decimalPart = Accuracy * CLng(decimalPart / Accuracy)
  GetFraction.Numerator = Fix(decimalPart * places)
  GetFraction.Denominator = places
  GCD = GetGCD(GetFraction.Numerator, GetFraction.Denominator)
  GetFraction.Numerator = GetFraction.Numerator / GCD
  GetFraction.Denominator = GetFraction.Denominator / GCD
End Function
Public Function GetGCD(ByVal a As Long, ByVal b As Long) As Long
    Do While a <> b
        If a > b Then
            a = a - b
        Else
            b = b - a
        End If
    Loop
    GetGCD = a
End Function
Public Function GetFractionToString(TheDecimal As Double, Optional Accuracy As Double = 0.0078125) As String
  Dim TheFraction As Fraction
  TheFraction = GetFraction(TheDecimal, Accuracy)
  GetFractionToString = CStr(TheFraction.Numerator) & "/" & CStr(TheFraction.Denominator)
  If TheFraction.WholeNumber <> 0 Then GetFractionToString = TheFraction.WholeNumber & " " & GetFractionToString
End Function

Public Sub tet()
 Dim x As Double
 Dim acc As Double
 acc = 1 / 8
 x = 3 + 1 / 2
 Debug.Print GetFractionToString(x, acc)
End Sub
 
MajP said:
As @MarkK pointed out there is no need for a table or a select case.
Click to expand...
this won't do, on your test try x=3.021
you'll end up in never ending loop.

the original Function on this thread is about converting decimal inches
to fraction equivalent. not any number system. that's is why there is 1/64", etc.
that is why my sample is to put the data in table.

getting back to the Test sub, it is still running...
 
My turn. Here's a function that converts centigrade to celsius:

Code: 
Public Function to_Celsius(ByVal in_Centigrade As Double) As Double
' converts Centigrade temperature to Celsius

    Dim ret As Double                   ' return value
    Dim int_Counter As Integer          ' counter variable for looping to calculate Celsius value
    Dim int_CounterMax As Integer       ' maximum value of Counter for looping
    Dim int_Decimal As String           ' determines where decimal point is in in_Centigrade

    ret = 0
    ' default return value

    int_CounterMax = Int(Abs(in_Centigrade))
    ' gets positive integer part of Centigrade so can loop and get Celsius

    int_Decimal = InStr(in_Centigrade, ".")
    If int_Decimal > 0 Then
      ' Centigrade has decimal value, will extract it to return value
      ret = Mid(in_Centigrade, int_Decimal) * 1
    End If

    If (in_Centigrade < 0) Then
       ' submitted value is less than 0, will compute Celsius for it
        For int_Counter = 1 To int_CounterMax
            ret = ret + 1
        Next
        ret = ret * -1
    End If

    If (in_Centigrade > 1) Then
    ' submitted value is more than 1, will compute Celsius for it
        int_Counter = 2 * int_CounterMax
        Do While int_Counter > int_CounterMax
            ret = ret + 1
            int_Counter = int_Counter - 1
        Loop
    End If

    to_Celsius = ret

End Function

Discuss and try and outdo, but hold any thanks until 2029 so that we can revisit this then.
 
this won't do, on your test try x=3.021
you'll end up in never ending loop.

the original Function on this thread is about converting decimal inches
to fraction equivalent. not any number system. that's is why there is 1/64", etc.
that is why my sample is to put the data in table.
Click to expand...
It does not matter if you want fractional inches, meters, centimeters etc. Something measured to 1/64th or 1/32 has nothing to do with units.

If you set your accuracy to 128 then you will get fractional values measured to 1/128th accuracy, but you can set it to 1/64, 1/32, 1/16 etc. You can call it fractional inches or whatever you want. And since these can all be further reduced you will get values like 1/2, x/3, x/4, x/16, x/32, x/64

I did not test his version but mine does not go into a loop, unless the accuracy is bigger than then fractional value. So I put in an error check for that.

Code: 
Public Sub tet()
Dim X As Double
Dim acc As Double
acc = 1 / 64
X = 3.021
Debug.Print GetFractionToString(X, acc)
End Sub
returns
3 1/64
if I am measuring more exact to 128 th then i get
3 3/128

Code: 
Public Function GetFraction(ByVal TheDecimal As Double, Optional ByVal Accuracy As Double = 0.0078125) As Fraction
  'Lets go 10 places
  Const places = 1000000000
  Dim GCD As Long
  Dim decimalPart As Double
  GetFraction.WholeNumber = Fix(TheDecimal)
  decimalPart = TheDecimal - GetFraction.WholeNumber
  If Accuracy > decimalPart Then
    MsgBox "Accuracy greater than decimal. Changing to 1/128th"
    Accuracy = 1 / 128
    If Accuracy > decimalPart Then
      MsgBox "Your measurement is very small round up to accuracy or reset accuracy"
      Exit Function
    End If
  End If
  decimalPart = Accuracy * CLng(decimalPart / Accuracy)
  GetFraction.Numerator = Fix(decimalPart * places)
  GetFraction.Denominator = places
  GCD = GetGCD(GetFraction.Numerator, GetFraction.Denominator)
  GetFraction.Numerator = GetFraction.Numerator / GCD
  GetFraction.Denominator = GetFraction.Denominator / GCD
End Function
 
Last edited:
X = 3.9999
 
@plog
I assume you're taking the proverbial....Centigrade to Celsius! 🤣
 
X = 3.9999
Click to expand...
As written my code returns
3 1/1
which although technically correct does not read well. So here is an update.
Code: 
Public Type Fraction
  WholeNumber As Long
  Numerator As Long
  Denominator As Long
End Type
Public Function GetFraction(ByVal TheDecimal As Double, Optional ByVal Accuracy As Double = 0.0078125) As Fraction
  'Lets go 10 places
  Const places = 1000000000
  Dim GCD As Long
  Dim decimalPart As Double
  GetFraction.WholeNumber = Fix(TheDecimal)
  decimalPart = TheDecimal - GetFraction.WholeNumber
  If Accuracy > decimalPart Then
    MsgBox "Accuracy greater than decimal. Changing to 1/128th"
    Accuracy = 1 / 128
    If Accuracy > decimalPart Then
      MsgBox "Your measurement is very small round up to accuracy or reset accuracy"
      Exit Function
    End If
  End If
  decimalPart = Accuracy * CLng(decimalPart / Accuracy)
  GetFraction.Numerator = Fix(decimalPart * places)
  GetFraction.Denominator = places
  GCD = GetGCD(GetFraction.Numerator, GetFraction.Denominator)
  GetFraction.Numerator = GetFraction.Numerator / GCD
  GetFraction.Denominator = GetFraction.Denominator / GCD
  If GetFraction.Denominator = GetFraction.Numerator Then
    GetFraction.WholeNumber = GetFraction.WholeNumber + 1
    GetFraction.Numerator = 0
  End If
End Function
Public Function GetGCD(ByVal a As Long, ByVal b As Long) As Long
    Do While a <> b
        If a > b Then
            a = a - b
        Else
            b = b - a
        End If
    Loop
    GetGCD = a
End Function
Public Function GetFractionToString(TheDecimal As Double, Optional Accuracy As Double = 0.0078125) As String
  Dim TheFraction As Fraction
  TheFraction = GetFraction(TheDecimal, Accuracy)
  If TheFraction.Numerator = 0 Then
    GetFractionToString = CStr(TheFraction.WholeNumber)
  Else
    GetFractionToString = CStr(TheFraction.Numerator) & "/" & CStr(TheFraction.Denominator)
    If TheFraction.WholeNumber <> 0 Then GetFractionToString = TheFraction.WholeNumber & " " & GetFractionToString
  End If
End Function

Public Sub tet()
 Dim X As Double
 Dim acc As Double
 acc = 1 / 128
 X = 3.99999
 Debug.Print GetFractionToString(X, acc)
End Sub
Returns 4
 
To verify using @arnelgp data

Code: 
SELECT
 conversionTable.[Decimal Inches],
 conversionTable.[Fraction Inches],
 GetFractionToString([decimal inches]) AS MajP_Fraction
FROM conversionTable;
Query1 Query1

Decimal InchesFraction InchesMajP_Fraction
0.015625​
1⁄64"1/64
0.03125​
1⁄32"1/32
0.046875​
3⁄64"3/64
0.0625​
1⁄16"1/16
0.078125​
5⁄64"5/64
0.09375​
3⁄32"3/32
0.109375​
7⁄64"7/64
0.125​
1⁄8"1/8
0.140625​
9⁄64"9/64
0.15625​
5⁄32"5/32
0.171875​
11⁄64"11/64
0.1875​
3⁄16"3/16
0.203125​
13⁄64"13/64
0.21875​
7⁄32"7/32
0.234375​
15⁄64"15/64
0.25​
1⁄4"1/4
0.265625​
17⁄64"17/64
0.28125​
9⁄32"9/32
0.296875​
19⁄64"19/64
0.3125​
5⁄16"5/16
0.328125​
21⁄64"21/64
0.34375​
11⁄32"11/32
0.359375​
23⁄64"23/64
0.375​
3⁄8"3/8
0.390625​
25⁄64"25/64
0.40625​
13⁄32"13/32
0.421875​
27⁄64"27/64
0.4375​
7⁄16"7/16
0.453125​
29⁄64"29/64
0.46875​
15⁄32"15/32
0.484375​
31⁄64"31/64
0.5​
1⁄2"1/2
0.515625​
33⁄64"33/64
0.53125​
17⁄32"17/32
0.546875​
35⁄64"35/64
0.5625​
9⁄16"9/16
0.578125​
37⁄64"37/64
0.59375​
19⁄32"19/32
0.609375​
39⁄64"39/64
0.625​
5⁄8"5/8
0.640625​
41⁄64"41/64
0.65625​
21⁄32"21/32
0.671875​
43⁄64"43/64
0.6875​
11⁄16"11/16
0.703125​
45⁄64"45/64
0.71875​
23⁄32"23/32
0.734375​
47⁄64"47/64
0.75​
3⁄4"3/4
0.765625​
49⁄64"49/64
0.78125​
25⁄32"25/32
0.796875​
51⁄64"51/64
0.8125​
13⁄16"13/16
0.828125​
53⁄64"53/64
0.84375​
27⁄32"27/32
0.859375​
55⁄64"55/64
0.875​
7⁄8"7/8
0.890625​
57⁄64"57/64
0.90625​
29⁄32"29/32
0.921875​
59⁄64"59/64
0.9375​
15⁄16"15/16
0.953125​
61⁄64"61/64
0.96875​
31⁄32"31/32
0.984375​
63⁄64"63/64
1​
1"1
 
So the question may be if you should use a table of values or a function to do this.

For speed and efficiency you should use a table.
Pros:
very fast in a query
Cons:
you can make mistakes
takes a while to populate
limited to a specific accuracty

Function
Pros: Flexible to support any accuracy
do not have to input lots of information where mistakes are possible
Cons: any UDF is slower than pure SQL. OK for single value not OK for thousands of values.
 
MajP said:
So the question may be if you should use a table of values or a function to do this.

For speed and efficiency you should use a table.
Pros:
very fast in a query
Cons:
you can make mistakes
takes a while to populate
limited to a specific accuracty

Function
Pros: Flexible to support any accuracy
do not have to input lots of information where mistakes are possible
Cons: any UDF is slower than pure SQL. OK for single value not OK for thousands of values.
Click to expand...

So given the above, presumably store the conversion table(s) of the required accuracy, and populate it carefully with a one-time process.
 
gemma-the-husky said:
So given the above, presumably store the conversion table(s) of the required accuracy, and populate it carefully with a one-time process
Click to expand...
If speed is an issue I would guess so. Lets say you have a table for 100k measurements and want to convert then the table would be very fast.
If you are calculating and reducing the fractions dynamically they all use some version of Euclids Algorithm for greatest common divisor. There are several implementations, but all have loops or recursion. So I put a counter in to print how many loops using the data in post 34. You can see the function loops from 3 to 63 times for the below. So without trying a large dataset, I am assuming it could be slow although they are very simple loops.
63
31
23
15
16
12
15
7
15
9
11
7
16
8
10
3
 
arnelgp said:
on my new db it is returning 3-63/64 (64 graduation).
this is consistent on my qryRange.
Click to expand...
3 63/64 = 3.984375 a difference of .015624 from 3.999999
so 4 is a more accurate answer with a difference of .000001
 
MajP said:
so 4 is a more accurate answer with a difference of .000001
Click to expand...
it would "seem" correct but, you are converting something with decimal fraction and expect the result to be whole number?
even windows calculator would not do that?
 
it would "seem" correct but, you are converting something with decimal fraction and expect the result to be whole number?
Click to expand...
Maybe I do not understand. But I cannot think of any real world application where 3.9999 should be represented as 3 63/64 instead of 3 64/64 (4) if my accuracy is to the nearest 1/64.
 
you compare your result with my table, compare it with the query inside that has range.
 
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