re: question 2, try, a few lines below your kluge, the following fix:

  $fr[$exp][$digit] ||= 0;
  print "$fr[$exp][$digit]\t";
[download]

That is, if you never actually saw any digits at a certain power of ten, then set it to zero before printing it out.

Cool idea. I love applying computers to existential mathematical questions.

g r i n d e r