use strict;
use warnings;
use 5.010;

my $x = '23';
my $y = '17';

say $x > $y;   # 1
say $x >= $y;  # 1
say $x + $y;   # 40

Even if the numbers contain a decimal point or an exponential part:

use strict;
use warnings;
use 5.010;

my $x = '23.2e2';
my $y = '17.1';

say $x > $y;   # 1
say $x >= $y;  # 1
say $x + $y;   # 2337.1

Perl automatically converts the strings into numbers that are exactly the same as what we had in the string. No warnings were emitted. (Think about writing numbers on a paper. Are those strings or numbers? Who cares. They look like numbers.)

Not numbers

On the other hand if one of the values cannot be converted without disregarding some part of it then Perl will emit a warning. (Of course only if use warnings is effect.)

use strict;
use warnings;
use 5.010;

my $x = '23';
my $y = '17x';

say $x > $y;   # 1
say $x >= $y;  # 1
say $x + $y;   # 40

Even before the normal output of the script there is a warning:

Argument "17x" isn't numeric in numeric gt (>) at ... line 8.
1
1
40

'17x' was converted to the number 17, at the first comparison. Please note, there is only one warning. Once the string was converted to its numerical representation Perl stores this numerical value along the original string value and so in the next expression it does not need to make an imperfect conversion again. Therefore no further warnings are emitted. If we remove the first comparison:

use strict;
use warnings;
use 5.010;

my $x = '23';
my $y = '17x';

say $x >= $y;  # 1
say $x + $y;   # 40

The warning would be now on the greater-than-or-equal comparison.

Argument "17x" isn't numeric in numeric ge (>=) at ... line 8.
1
40

If we removed even that, then the warning is on the addition operation.

use strict;
use warnings;
use 5.010;

my $x = '23';
my $y = '17x';

say $x + $y;   # 40

Argument "17x" isn't numeric in addition (+) at ... line 8.
40

Each warning has a slightly different wording, but they have the same general layout.

If both arguments are 'dirty' and cannot be converted to numbers flawlessly, then each one of them will generate a warning:

use strict;
use warnings;
use 5.010;

my $x = '23y';
my $y = '17x';

say $x + $y;   # 40

Argument "17x" isn't numeric in addition (+) at ... line 8.
Argument "23y" isn't numeric in addition (+) at ... line 8.
40

Solution

The solution of course is that we need to make sure values that cannot be fully converted to numbers are not used in numeric operations. If you encounter the above problem, add a print-statement in front of the line emitting the warning to display the variables involved in the operation. That will help you track down the source of the problem.

Alternatively you can use the looks_like_number function from Scalar::Util to check if a variable can be used as a number.