Q28164: Unexpected PRINT USING ".##" Rounding for .xx5

Article: Q28164
Product(s): See article
Version(s): 4.00 4.00b 4.50
Operating System(s): MS-DOS
Keyword(s): ENDUSER | B_BasicCom | mspl13_basic
Last Modified: 14-FEB-1991

This article describes a case where the PRINT USING statement appears
to round numeric constants to unexpected values. This information
applies to Microsoft QuickBASIC versions 4.00, 4.00b, and 4.50 for
MS-DOS; to Microsoft BASIC Compiler versions 6.00, 6.00b for MS-DOS
and MS OS/2; and to Microsoft BASIC Professional Development System
(PDS) versions 7.00 and 7.10 for MS-DOS and MS OS/2.

For the following statement

   PRINT USING " ###.##"; .245, .255, .265, .275, .285

the above BASIC versions give the following output

   0.25  0.25  0.26  0.28  0.28

while you might have expected the following rounding

   0.25  0.26  0.27  0.28  0.29

or with IEEE rounding (to the nearest even integral value), you would
expect the following:

   0.24  0.26  0.26  0.28  0.28

This behavior occurs because the internal representation of the
numbers used by BASIC (IEEE floating-point format) differs slightly
from the decimal numbers typed into the source code.

IEEE floating-point format cannot accurately represent numbers that
are not of the form 1.x to the power of y (where x and y are base 2
numbers). The internal representation will be slightly more or
slightly less than the decimal numbers typed into the source code.

The internal representations are correctly rounded and displayed in
the above program. This is not a software problem.

If you want floating-point constants in the source code to be exactly
stored, you can append the constant with the CURRENCY type-cast
operator, an "at sign" (@) character. The CURRENCY data type is only
found in Microsoft BASIC PDS 7.00 and 7.10. The following example
rounds to 0.25, 0.26, 0.27, 0.28, 0.29 as you may have wanted:

   PRINT USING " ###.##"; .245@, .255@, .265@, .275@, .285@

Note that the CURRENCY data type can store 19 digits, but only 4
digits can be used after the decimal point.

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