Converting a number to normalized scientific notation - vbscript

Question

I'm trying to create a method converting a number to normalized scientific notation, here is the code that I'm using to calculate mantissa and exponent:
ConvNSN 1000, M, P
MsgBox M & "e" & P
Sub ConvNSN(N, M, P)
If N = 0 Then
P = 0
M = 0
Else
P = Int(Log(Abs(N)) / Log(10))
M = N / 10 ^ P
End If
End Sub
The problem I am facing is that this code gives wrong exponent value for some numbers, eg 1000, 10E+6, 10E+9, 10E+12, 10E+13, etc... Exactly for 1000 converted should be 1e3, but not 10e2. It's obvious that the same problem with numbers, whose logarithms are close to an integer value, like Log(1 - 5.55111512312578E-17) / Log(10), which result is 0, however 1 - 5.55111512312578E-17 less then 1, and result has to be negative.
How can I get rid of Double type imprecision, and get this code to work properly?
UPDATE
I assume the fastest and quite accurate method to calculate mantissa and exponent of number in normalized scientific notation may be as follows:
Sub ConvNSN(N, M, P)
Dim A
If N = 0 Then
P = 0
M = 0
Exit Sub
End If
A = Abs(N)
If A < 1 Then
P = Int(Log(A) / Log(10))
Else
P = Int(Log(A) / Log(10) * (2 + Log(.1) / Log(10)))
End If
M = N / 10 ^ P
End Sub
Or another one, based on #Bob's solution:
Sub ConvNSN(N, M, P)
If N = 0 Then
P = 0
M = 0
Else
P = Int(Log(Abs(N)) / Log(10))
M = N / 10 ^ P
End If
If Abs(M) = "10" Then
M = M / 10
P = P + 1
End If
End Sub
First one slightly faster. Both of them process exponent from -322 to 308, but return not normalized mantissa with powers of 10 less then -310. I have not tested them yet with numbers, whose logarithms are a marginally less but very close to an integer values.
UPDATE 2
I decided to attach here an extra Sub ConvEN(), allowing to represent a number in engineering notation with SI prefixes from "p" to "T":
N = .0000456789
ConvNSN N, M, P
M = Round(M, 2)
ConvEN M, P, R, S
MsgBox R & " " & S & "Units"
Sub ConvNSN(N, M, P)
Dim A
If N = 0 Then
P = 0
M = 0
Exit Sub
End If
A = Abs(N)
If A < 1 Then
P = Int(Log(A) / Log(10))
Else
P = Int(Log(A) / Log(10) * (2 + Log(.1) / Log(10)))
End If
M = N / 10 ^ P
End Sub
Sub ConvEN(M, P, R, S)
DIM Q, P3
Q = int(P / 3)
P3 = Q * 3
If Q >= -4 And Q <= 4 Then
S = Array("p", "n", ChrW(&H03BC), "m", "", "k", "M", "G", "T")(Q + 4)
Else
S = "e" & P3 & " "
End If
R = M * 10 ^ (P - P3)
End Sub

Answer 1

Try this:
ConvNSN 1000, M, P
MsgBox M & "E" & P
ConvNSN 0.00000000000000001234, M, P
MsgBox M & "E" & P
ConvNSN -0.00000000000000001234, M, P
MsgBox M & "E" & P
Sub ConvNSN(N, M, P)
P = 0
If N < 0 Then
S = -1
ElseIf N > 0 Then
S = 1
Else
M = 0
Exit Sub
End If
M = Abs(N)
If M >= 10 Then
While M >= 10
M = M / 10
P = P + 1
Wend
M = M * S
Exit Sub
End If
If M < 1 Then
While M < 1
M = M * 10
P = P - 1
Wend
M = M * S
Exit Sub
End If
End Sub
Based on the comments, I re-wrote this my way, ignoring the structure from the OP.
MsgBox NSN(-0.0000000000000000000123456789,4)
MsgBox NSN(1234567890000000000000000000,4)
Function NSN(Number, Accuracy)
Exponent = 0
If Number > 0 Then
Sign = 1
ElseIf Number < 0 Then
Sign = -1
Else
NSN = 0
Exit Function
End If
Number = Number * Sign
If Number >= 10 Then
While Number >= 10
Number = Number / 10
Exponent = Exponent + 1
Wend
ElseIf Number < 1 Then
While Number < 1
Number = Number * 10
Exponent = Exponent - 1
Wend
End If
Number = Round(Number, Accuracy)
If Number = "10" Then
Number = 1
Exponent = Exponent + 1
End If
Number = Number * Sign
If Exponent = 0 Then
NSN = Number
Else
NSN = Number & "E" & Exponent
End If
End Function

Answer 2

Using strings rather than maths can help. Add your own error checking.
Num = "1000000.0005"
NumOfDigits = 4
Mag = Instr(Num, ".")
Num = Replace(Num, ".", "")
MSD = Left(Num, 1)
Rest = Mid(num, 2, NumOfDigits)
msgbox MSD & "." & Rest & " x 10^" & (Mag -2)