### 2.3.3. Discussion

You need the `equal` routine because computers'
floating-point representations are just approximations of most real
numbers, as we discussed in the Introduction to this chapter. Perl's
normal printing routines display numbers rounded to 15 decimal places
or so, but its numeric tests don't round. So sometimes you can print
out numbers that look the same (after rounding) but do not test the
same (without rounding).

This problem is especially noticeable in a loop, where round-off
error can silently accumulate. For example, you'd think that you
could start a variable out at zero, add one-tenth to it ten times,
and end up with one. Well, you can't, because a base-2 computer can't
exactly represent one-tenth. For example:

for ($num = $i = 0; $i < 10; $i++) { $num += 0.1 }
if ($num != 1) {
printf "Strange, $num is not 1; it's %.45f\n", $num;
}

prints out:

*Strange, 1 is not 1; it's 0.999999999999999888977697537484345957636833191*

The `$num` is interpolated into the double-quoted
string using a default conversion format of
"`%.15g`" (on most systems), so it looks like 1. But
internally, it really isn't. If you had checked only to a few decimal
places, for example, five:

!equal($num, 1, 5)

then you'd have been okay.

If you have a fixed number of decimal
places, as with currency, you can often sidestep the problem by
storing your values as integers. Storing `$3.50` as
`350` instead of `3.5` removes the
need for floating-point values. Reintroduce the decimal point on
output:

$wage = 536; # $5.36/hour
$week = 40 * $wage; # $214.40
printf("One week's wage is: \$%.2f\n", $week/100);
*One week's wage is: $214.40*

It rarely makes sense to compare more than 15 decimal places, because
you probably only have that many digits of precision in your
computer's hardware.