In the Dumper output in this example, the single-quotes around the nummbers (e.g., $VAR1 = '5601.57') indicate that Perl still sees these scalars as strings
Actually, one has to be very careful with statements like these - there is no reliable way to ask Perl for the difference between e.g. 1 and "1". Although Data::Dumper has some code that tries to peek under the hood, it's not perfect:
my $str = "1";
print Dumper($str); # $VAR1 = '1';
my $n = $str + 1;
print Dumper($str); # $VAR1 = 1;
Update: Pointed the link above to a better node with more references.