If you are just looking for an elegant, ready-made solution then Scalar::Util::looks_like_number fits the bill:

use strict;
use warnings;

use Scalar::Util 'looks_like_number';
use Test::More;

my @nums = (
    '1.5671',
    '777',
    '0',
    '-4.567',
    '+9.987'
);

my @not = (
    '0777 891 777',
    '121A3D',
    '+9.8.97',
    '+9.8¬97',
    '9.8[97'
);

plan tests => @nums + @not;

for my $i (@nums) {
    ok looks_like_number ($i), "$i is a number";
}

for my $i (@not) {
    ok ! looks_like_number ($i), "$i is not a number";
}
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