Use the Devel::Peek module's Dump() function to inspect the various compartments within a scalar at whatever stage you wish in the script. Example:

use Devel::Peek;

my $x = "99 bottles of beer on the wall";

Dump( $x );

$x += 1;

Dump( $x );

$x .= "\n";

Dump( $x );

$x += 2;

Dump( $x );
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Have fun exploring what various actions do to your scalar internally. I can't remember where I read a good explanation of the internals of Perl's various data types. It might have been OReilly's Advanced Perl Programming... or it might not. Hopefully someone can help out with a good reference.

PS: To specifically answer the question; once Perl has recognized it in numeric context, it doesn't need to be re-'converted'.