but how do I get to the decimal cents in the first place?

Assuming you start with a string, you have to avoid triggering perl's implied parse to a floating point number.

  my $input= "2.26";
  my ($whole, $frac)= split /\./, $input;
  $frac //= '';
  length $frac < 2 or die "would lose precision on .$frac";
  $frac .= '0'x(2 - length($frac));
  my $cents= "$whole$frac";
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Yes, it's ugly. I'm sure there is some clever way to do this with a regex that runs faster, and would be even uglier. But, you can just stick that in a function named "parse_cents" or "parse_decimal($str,$scale)" and hide the details.

Another option is to use Math::BigRat, which will handle all arbitrary cases, but then the performance of all the math you do on the numbers will be a little slower.