*All rights reserved. Originally published in Smart Access October 1997 by Pinnacle Publishing, Inc.; Revised April 2006, July 2013, December 2014, August 2017, April 2018.*

**All versions of Microsoft Access (and Excel, VBA, Visual Basic 6, C++,
and C# and VB.NET in Visual Studio .NET) share quirks that can result in inaccurate mathematical
calculations in both code and queries. Understanding these issues will
help you avoid unnecessary headaches when the numbers you generate don’t
match the mathematically correct values.**

You'd think that today, software programs like Microsoft Access would handle mathematical calculations properly. For the most part Access, VBA, VB, and .NET do, but there are several areas where they generate unexpected results. In most cases, the discrepancies are minor; however, if you are trying to determine if two values are identical, looking for small differences between values, or performing multiple calculations, these errors can diverge significantly from the correct answer. I first encountered these problems while writing FMS' statistical analysis program, Total Access Statistics. I quickly discovered problems in calculations that used Taylor Series and other iterative calculations as well as in code that attempted to trap for division by zero. A little research revealed more than "rounding error."

Rounding errors aren't uncommon in programs because computers store and perform mathematical calculations using binary representations of decimal numbers. This causes rounding errors in inexact calculations such as division. One can certainly excuse computers for accuracy problems in the 15th significant digit. That’s expected. What I didn’t expect, however, is much larger and more obvious errors that must be corrected for using code.

Subtraction is an area where you shouldn't face rounding problems. By definition, the result of subtraction can't have more decimal places than either of the initial numbers. If binary math results in an inaccurate number, MS Access VBA should round the results accordingly. Unfortunately, this doesn't happen in many cases.

A simple example reveals the problem. Examine the difference between 100.8 and 100.7. You would expect the solution to be 0.1, but look what happens when you try this in the debug window:

? 100.8 - 100.7 9.99999999999943E-02

The error is in the 14th most significant digit.

The error worsens if the numbers are larger:

? 10000.8 - 10000.7 9.99999999985448E-02

The error is now in the 11th digit. Now you may wonder why an error in the 11th digit would be a problem. In most cases it probably isn’t.

However, this error is significant enough to cause unexpected results.

Clearly, you can’t have something like this:

Const X = 100.8 Const Y = 100.7 If X - Y = .1 Then ...

A general rule when working with real number calculations, is to avoid directly comparing two double (or single) numbers to see if they are equal. Due to rounding problems, you'd expect differences in the 15th digit. Therefore, you would normally use a function such as the following to test for identity of two double numbers:

Function IsEqual(dblValue1 As Double, dblValue2 As Double) As Integer Const dblSmall = .000000000000001 If Abs(dblValue1 - dblValue2) <= dblSmall Then IsEqual = True Else IsEqual = False End If End Function

By calculating the absolute difference between two values, you can consider the two values equivalent if the difference is less than a
tiny, non-zero number (in this case 10^{-15}). However, this fails if Access introduces larger differences.

For instance, you might use this function to compare the difference between 100.8 and 100.7 to 0.1:

IsEqual(100.8-100.7, .1)

Unexpectedly, the result is False in Access, which is troublesome. To get around this, you need to increase the dblSmall value in the IsEqual() function. Unfortunately, the value can be increased so much that two numbers that aren't really equal return True.

Not being able to determine if two numbers are equal is especially problematic for division. Here’s a simple function that tries to prevent division by zero:

```
Function CalcDivision(dblNumerator As Double, dblDenominator As Double) As Double
If IsEqual(dblDenominator, 0) Then
' Should be undefined.
CalcDivision = 0
Else
CalcDivision = dblNumerator / dblDenominator
End If
End Function
```

To witness this problem, type the following into the debug window:

? CalcDivision(10, 100.8 - 100.7) 100.000000000006

While it isn't completely accurate, it’s reasonably close with the error in the last digit. But look what happens when division by close-to-zero occurs:

? CalcDivision(10, 100.8 - 100.7 - .1) -1.757502293608E+15

The CalcDivision function should have trapped 100.8-100.7-0.1 as zero. Instead, it used the small error as the divisor and created a huge
resulting answer (10 to the 15^{th} power!).

These problems stem from VBA’s subtraction inaccuracies for numbers with decimals. Fortunately, there's a way to work around this problem by using the built-in convert decimal function: CDec.

Function FMS_Subtract(dblValue1 As Double, dblValue2 As Double) As Double FMS_Subtract = CDec(dblValue1) - CDec(dblValue2) End Function

With this function, you’ll get the correct result:

? FMS_Subtract(100.8, 100.7) .1

Applying this to the earlier division, you’ll find that division by zero is properly trapped:

Sub TestDivision() ' Perform: CalcDivision(10, 100.8-100.7-.1) which returned ' -1.757502293608E+15 due to subtraction inaccuracies Dim dblDiff As Double ' Rather than setting dblDiff to 100.8-100.7-.1 use the FMS_Subtract function for subtraction dblDiff = FMS_Subtract(100.8, 100.7) dblDiff = FMS_Subtract(dblDiff, .1) Debug.Print (CalcDivision(10, dblDiff)) End Sub

Certainly, you don’t want to call a special function every time you want to perform subtraction. This is needed only when you're calculating the difference between two numbers that include decimals, and need to compare the result with another number or want to use it as a divisor.

Another common numeric problem is associated with expressions passed to functions. Before VBA introduced the Round function, the following was a common function used to round numbers to the nearest decimal place. Numbers on the border, *.5, should be rounded up, but are, in fact, always rounded down (note that this is different from the Banker's Rounding behavior of the VBA Round command):

Function RoundBad(dblNumber As Double, intDecimals As Integer) As Double Dim dblFactor As Double dblFactor = 10 ^ intDecimals RoundBad = Int(dblNumber * dblFactor + .5) / dblFactor End Function

Running this function generates these results:

? RoundBad(100.06, 1) ' Correctly returns 100.1 ? RoundBad(100.04, 1) ' Correctly returns 100.0 ? RoundBad(100.05, 1) ' Incorrectly returns 100.0 instead of 100.1

The problem stems from the way the Int( ) function processes the expression. It actually rounds the number before applying the Integer conversion. Let’s isolate the problem from the debug window.

As expected, this correctly evaluates to 1001:

? 100.05 * 10 + .5 1001

However, using the same expression inside the Int( ) function gives the wrong result:

? Int(100.05 * 10 + .5) 1000

Therefore, it is imperative that you avoid passing expressions involving real numbers to Access/VBA functions. If the expression is assigned to a variable and then passed to the Int( ) function, it usually works fine. However, there are times when that also fails and adding a null string to is fixes the problem. Here’s the correct way to perform rounding:

Function FMS_Round(dblNumber As Double, intDecimals As Integer) As Double Dim dblFactor As Double Dim dblTemp As Double dblFactor = 10 ^ intDecimals dblTemp = dblNumber * dblFactor + .5 FMS_Round = Int(CDec(dblTemp)) / dblFactor End Function

With the simple addition of the CDec conversion, FMS_Round() returns the correct result:

`? FMS_Round(100.05, 1) ' Correctly returns 100.1`

It's sad, but even in this day and age, you can’t assume math is accurate. The problems discussed in this article impact not only module code but also calculations performed in queries, and exists in Microsoft Excel, C++, Visual Basic 6, and VB.NET and C# in Visual Studio .NET. While some of these issues can be considered minor rounding errors, I hope I have shown you that this isn't always the case. Not paying attention to these errors could cause you huge problems in applications that require these types of calculations to be accurate. By recognizing where and how such problems occur, you can take steps to handle or avoid them.

*Luke Chung is the president and founder of FMS, Inc., the world's leading Access
development firm. He has actively participated in designing all of the FMS products, including solutions for SQL Server, VB, and .NET. He also
wrote major portions of Total Access Analyzer,
Total Access Analyzer,
Total Access Emailer,
Total Access Statistics,
Total Visual CodeTools, and
Total Visual SourceBook.*

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