To see the problem, add

printf("%.16e\n", $dollar1);
printf("%.16e\n", $dollar2);
[download]

Never compare floating point numbers for equality. A lot of common numbers are periodic in binary so they cannot be stored exactly.

>perl -le"printf '%.16e', 0.1"
1.0000000000000001e-001
                 ^
                 |
[download]

You could round the number to two digits before comparing: (Probably should use something less expensive than sprintf)

if (sprintf('%.2f', $dollar1) ne sprintf('%.2f', $dollar2)) {
  print "$dollar1 != $dollar2\n";
}
[download]

You could work with cents instead of dollars. (Only convert back to dollars when printing)

if ($cents1 != $cents2)) {
  print $cents1/100, ' != ', $cents2/100, "\n";
}
[download]