Alternatively, using XML::TreeBuilder:
use strict;
use warnings;
use XML::TreeBuilder;
my $xml = <<'END';
<inventors type="array">
<inventor>
<city>Aston Clinton</city>
<name>Andy Barth</name>
<number type="integer">1</number>
<country>GB</country>
<upper-name>ANDY BARTH</upper-name>
</inventor>
<inventor>
<city>Aylesbury</city>
<name>Daniele Dall'Acqua</name>
<number type="integer">2</number>
<country>GB</country>
<upper-name>DANIELE DALL'ACQUA</upper-name>
</inventor>
<inventor>
<city>Calne</city>
<name>Nigel Drew</name>
<number type="integer">3</number>
<country>GB</country>
<upper-name>NIGEL DREW</upper-name>
</inventor>
</inventors>
END
my $tree=XML::TreeBuilder->new();
$tree->parse($xml);
my @inventornums=$tree->find_by_tag_name('number');
foreach my $inventornum(@inventornums){
if ($inventornum->as_text()==2){
my $parent=$inventornum->parent();
print $parent->as_XML;
}
}