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## 2.3. Comparing Floating-Point Numbers

### 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.

```\$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.