perlfaq nodetype
faq_monk
<P>
The infinite set that a mathematician thinks of as the real numbers can
only be approximate on a computer, since the computer only has a finite
number of bits to store an infinite number of, um, numbers.
<P>
Internally, your computer represents floating-point numbers in binary.
Floating-point numbers read in from a file or appearing as literals in your
program are converted from their decimal floating-point representation (eg,
19.95) to the internal binary representation.
<P>
However, 19.95 can't be precisely represented as a binary floating-point
number, just like 1/3 can't be exactly represented as a decimal
floating-point number. The computer's binary representation of 19.95,
therefore, isn't exactly 19.95.
<P>
When a floating-point number gets printed, the binary floating-point representation is converted back to decimal. These decimal numbers are displayed in either the format you specify with
<CODE>printf(),</CODE> or the current output format for numbers (see
[perlman:perlvar|$#] if you use print. <CODE>$#</CODE> has a different default value in Perl5 than it did in Perl4. Changing <CODE>$#</CODE> yourself is deprecated.
<P>
This affects <STRONG>all</STRONG> computer languages that represent decimal floating-point numbers in binary,
not just Perl. Perl provides arbitrary-precision decimal numbers with the
Math::BigFloat module (part of the standard Perl distribution), but
mathematical operations are consequently slower.
<P>
To get rid of the superfluous digits, just use a format (eg,
<U>printf("%.2f", 19.95)</U>) to get the required precision. See [perlman:perlop|Floating-point Arithmetic].
<P>