http://www.perlmonks.org?node_id=288845

in reply to Simple math gone wrong

```\$ perldoc -q decimal
Found in /opt/perl/lib/5.8.0/pod/perlfaq4.pod
Why am I getting long decimals (eg, 19.9499999999999)
instead of the numbers I should be getting (eg, 19.95)?

The infinite set that a mathematician thinks of as
the real numbers can only be approximated on a
computer, since the computer only has a finite
number of bits to store an infinite number of, um,
numbers.

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 an
internal binary representation.

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.
When a floating-point number gets printed, the
binary floating-point representation is converted
back to decimal.  These decimal numbers are dis-
played in either the format you specify with
printf(), or the current output format for num-
bers.  (See "\$#" in perlvar if you use print.  \$#
has a different default value in Perl5 than it did
in Perl4.  Changing \$# yourself is deprecated.)

This affects all 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.

If precision is important, such as when dealing
with money, it's good to work with integers and
then divide at the last possible moment.  For
example, work in pennies (1995) instead of dollars
and cents (19.95) and divide by 100 at the end.

To get rid of the superfluous digits, just use a
format (eg, "printf("%.2f", 19.95)") to get the
required precision.  See "Floating-point Arith-
metic" in perlop.