my usage of perl is almost entirely for web-development, so i have a lot of experience w/compatability issues etc. - but to sum up...
~yes, you should always nest tags the 'correct way' -> <TABLE><TR><TD></TD></TR></TABLE>, but unless you're using something like XML (which is particularly adamant on this point) or really jumbled up the tags - usually the browsers will still render it as expected.
~quoting strings is good, but in my experience, only necessary, when working with something other than pixels. (The percentages "100%" should be quoted.)

BUT... when it comes down to answering your question, those things are irrelevant. AFAIK, browsers will not chop up your long strings - unless they reach some arbitrary limit, that the browser sets for max. widths of pages - which could be thousands of characters. This problem is quite common w/people posting huge links and messing up your nicely designed webpages. :-P

What i do is what frodo72 touched on. I first dice large strings into arrays. (Which we don't have to do here, since you already have the data in @cut). Then, i'd do something like this...

# please note: i always miss some punctuation mark or some other overs
+ight
# so this may/may not work, but you get the idea...

print "<TR><TD WIDTH='100%'>The annotated sequence is given below alon
+g with the digested sequence<BR>";
print "<B>Annotated:</B>$anotate<BR>";
print "<B>Digested:</B>";

my $printcounter = 1;
foreach $_(@cut){
    print "$_";
    $printcounter++;
    # you can put whatever number you want in here and substitute <WBR
+> for <BR>
    # if you like (maybe use $printcounter of 4 with <WBR> or somethin
+g)
    if ($printcounter==16){    print "<BR>";
                $printcounter=1;}}
print "</TD></TR>";
[download]

If you don't explicity put in the optional break <WBR> or definitive break <BR>, browsers usually will not take it upon themselves to do it for you.

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