In this case sprintf is your friend (and coming from a C background an asset). It might slow you down somehow but if you throw in $val= sprintf( "%f6.2", $val); before using $val, you will get back the proper precision.

Here is an example:

 #!/usr/bin/perl -w
use strict;

my @rows=<DATA>;

my $val=0;
   for (@rows) {
     chomp;
     if (/([\d.]+)/) {
       $val += $1;
       $val= sprintf( "%6.2f", $val);
       warn "Added $1 from $_ and set it to $val\n";
     }
   }

__DATA__
we get to $6257.65
now we add $33.4099999999999999
we add $37.24
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outputs:

Added 6257.65 from we get to $6257.65 and set it to 6257.65
Added 33.4099999999999999 from now we add $33.4099999999999999 and set it to 6291.06
Added 37.24 from we add $37.24 and set it to 6328.30