I don't think you can get rid of them, you just have to manage it. If you swap in the following line you'll get the results as you expect.

    my $frac = sprintf("%.9g", ($num - $int) );
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This is simply rounding to an arbitrary 9 decimal points. Obviously you need to look at the formulas you're working with but this should serve in a lot of cases.

UPDATE: I didn't notice you actually gave a sprintf example. So, Yes, that is the easiest way to get rid of this problem. Infact the O'Reilly Perl CookBook gives examples just like this.