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I could not do the work that I have been doing without xlPrecision. A special edition of xlPrecision created at the request of a number theorist provides over 2 Billion significant digits of precision. Don't be held back by Excel's limitation of only 15 significant digits!

With xlPrecision, you can use gigantic numbers with over TIMES as many digits as Excel allows, as well as extremely tiny numbers with over times as many zeroes to the right of the decimal.

Finally, xlPrecision offers many additional features that take you beyond Excel's capabilities in other ways. Save valuable time with xlPrecision's powerful Excluder functions.

View your sorted data at a glance with the exceptional sorting function. Take control of your fractional data with the versatile fraction reducer. These functions provide vastly greater precision than Excel's built-in mathematical operators. Excel does not allow changing the behavior of its built-in operators and worksheet functions, so it is not possible for xlPrecision to apply high precision to your existing worksheet formulas. Using xlPrecision requires modifying your worksheet formulas by replacing Excel's built-in operators and functions with xlPrecision's custom worksheet functions.

Of course, you only have to modify those formulas from which you want high precision. See the Function Reference for a complete list of xlPrecision functions and more information about using them. Without xlPrecision, Excel provides a maximum of 15 digits of precision, or " significant digits ".

For example, if you divide 67 by 89, the result is an infinite number of digits long. But Excel rounds it off to 15 significant digits: But "significant digits" does not simply mean the number of decimal places. Significant digits is the quantity of digits from the left-most non-zero digit to the right-most non-zero digit.

That series of digits can be anywhere relative to the decimal point. For example, if you multiply ,,,, by ,,,,, the correct answer is an integer 30 digits long. Excel rounds it off to 15 digits: It is intended for use in your programming code rather than within Excel worksheets, as it can return more characters than Excel can accept in a worksheet cell. The 2,,, SD Edition was created at the request of a number theorist.

The 2,,, SD Edition is also in use for combinatorics , another branch of pure mathematics. Without xlPrecision, Excel truncates your numbers to 15 significant digits. For example, if you enter this number in Excel: Excel truncates it to this. Notice that Excel doesn't even round it correctly; instead it just replaces all digits after the 15th digit with zeros: Even if you preserve all the digits by typing a leading apostrophe or pre-formatting the cell as text, Excel still truncates it to 15 digits before doing any arithmetic or any other kind of numeric analysis.

For example, if you type this into cell A1, including the leading apostrophe: Excel truncated your number down to 15 digits to do even the simplest imaginable arithmetic operation, adding zero. Like all other spreadsheet programs, Excel converts your numbers to binary before sending them to the microprocessor to do the arithmetic.

But the conversion is often approximate. Then, when the microprocessor completes the arithmetic and returns the binary result, Excel converts it back to base That conversion, too, is often approximate. Though each error is small, they can still cause incorrect spreadsheet results. Subtract 1, from 1, The result looks like 0. To reveal the hidden error, right-click the cell, choose Format Cells, select the Number category on the Number tab, increase Decimal Places to 15 or more, and click OK.

Now it says 0. Formulas in dependent cells are given the incorrect number no matter how that cell is formatted. Let's look at another example of a binary conversion error, this time taken from an xlPrecision customer's real, production worksheet. Let's get the Matrix Determinant of those numbers.

On a square array of four cells, the Matrix Determinant formula looks like this: Using Excel's built-in multiply and subtract operators returns this: Excel's two multiplications return numbers that are different by only one digit: Those two numbers are exactly apart.

Subtracting them should result in But instead Excel returns 10 The " " is false precision due to binary conversion errors. Even worse is trying to use Excel's "Precision as Displayed" feature to get around binary conversion errors, because that can cause errors in other parts of the spreadsheet and workbook, and requires constant monitoring of most formulas to make sure that as many digits are displayed as possible or as required, without showing a binary conversion error.

Binary conversion errors may seem small, but they are stealthy and cause unexpected problems without warning. During the Gulf War, a binary conversion error led to the deaths of 28 American soldiers and around injured on February 25th, when an American Patriot missile failed to intercept an Iraqi SCUD missile headed toward their Army barracks.

Though each conversion error was tiny, the error accumulated enough to make the Patriot's navigation software miss the SCUD, which then reached its target. Never underestimate the insidious, destructive power of binary conversion errors. The largest number Excel can accept, use, or return is 1. This number is formatted in "scientific notation". The largest number xlPrecision in Excel can accept, use, or return is 32, 9's, which for comparison purposes here could be rounded off to 9.

One example of what a difference this can make is that the largest factorial Excel can calculate is ! The smallest number Excel can accept, use, or return is 2. That's 32, digits longer and therefore that much closer to zero than Excel's smallest, or again over times as many digits.

If your spreadsheet calculations go beyond Excel's ability to store tiny numbers, Excel automatically and without warning converts the number to 0 instead of returning an error, as it correctly does if your spreadsheet calculations go beyond Excel's ability to store huge numbers.

In addition to allowing vastly smaller numbers than Excel, xlPrecision does not convert to 0 if you exceed even xlPrecision's ability to use tiny numbers. Instead, xlPrecision correctly returns an error in that case. Excel returns exactly zero in cell A2, because the result is too small of a number for Excel, and because Excel does not return an error as it should when the result is too small for Excel: That number is extremely closer to zero than Excel can go.

Just to show only one example of what a difference this can make, the largest factorial Excel can calculate is ! However, this is how Microsoft Excel does it. By duplicating the way Microsoft Excel handles currency internationalization, xlPrecision allows you to internationalize currency in the same way you always have with Microsoft Excel. Other worksheet functions, whether built-in or provided by an add-in, do not use the xlPrecision worksheet functions, and so do not gain precision from them.

If you're building a cell formula that uses other worksheet functions, and use xlPrecision functions instead of operators in the formula, then you gain precision between those other functions, but not within them.

It's possible for add-in worksheet functions to use xlPrecision instead of operators. If that code uses xlPrecision functions instead of mathematical operators, it can gain precision. Unless, of course, that same code also calls other functions that, in turn, use mathematical operators, at which point the extra precision is discarded. Microsoft is unlikely to ever be interested in using xlPrecision to add high precision to Excel's built-in formulas.

However, in a future version of xlPrecision I plan to duplicate all of the relevant built-in Excel functions with equivalent high-precision xlPrecision functions.

If you want high precision in custom functions provided by another Excel Add-In, you might want to contact the authors of that other Add-In and suggest that they use xlPrecision in a future version. For information on how the programming code that is used to build add-in worksheet functions can call xlPrecision functions to gain precision, click here. Excel's limitation of 15 significant digits is not caused by Excel or Microsoft.

All other spreadsheet programs, including Lotus and Corel Quattro Pro, have the same limitation. The limitation is enforced by the microprocessor. The 15 significant digit limitation is part of an industry standard called "IEEE ", which was created to achieve faster processing by sacrificing precision. IEEE was ratified in , by which time it had already become a de facto standard.

Ready to try the Free Edition of xlPrecision? You can use it for as long as you like. There are only 3 types of people in the world -- those who understand binary and those who don't.