The flow of the code does seem straight forward enough to suggest that it might by a representation issue. Rather than printing the values, you might consider printing the differences - if they are not literally identical, this should reveal what's getting lost (though I thought there was no truncation in an unformatted print statement). If this does prove to be the issue, you can avoid the false positives by setting a tolerance, e.g.:

my $tolerance = 1.0e-16; # Change this value based on observation
if ($tolerance*abs($range_min + $change_min) < abs($range_min - $chang
+e_min)) {
    print "$variable has different minimum value:\n";
    print "  Change list: $changes{$variable}{min} ($changes{$variable
+}{sheet})\n";
    print "  Range file : $range_file{$variable}{min} ($range_file{$va
+riable}{sheet})\n";
    my $difference = $range_min - $change_min
    print "  Difference : $difference\n";
}
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