my $numerator;
      my $denominator;
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Here both $numerator and $denominator contain undef.

         if ($indicator eq "SH"){
    $numerator = $last_element;
      }
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If that branch is true, $numerator will contain the value of $last_element, which may be undef. $denominator will still contain undef.

      elsif ($indicator eq "SL"){
    $denominator = $last_element;
      }
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If that branch is true (and it will only be true if the first branch is false, in which case $numerator will still contain undef), $denominator will contain the value of $last_element, which may be undef.

      else {
    print "\nError: There has been an unexpected string within the sec
+ond to last element of the array\n";
      }
[download]

If this branch is true, both $numerator and $denominator contain undef.

At this point, at least one of those two variables does contain undef. Both may.