my @keepers;
open my $fh, '<', '/path/to/file.dat' or die $!;
while (<$fh>) {
    while ( /(\d+\.\d+)/g ) {
        push @keepers, $_ and last
            if $1 >= 296.1 && $1 <= 314.0;
    }
}
close $fh or die $!;