You can use the num_rows
on the dataset to check the number of rows returned. Example:
$results = $mysqli->query("SELECT ANNOUNCE_NUMBER,ANNOUNCEMENTS,ANNOUNCE_TYPE,POST_DATE FROM home ORDER BY ANNOUNCE_NUMBER DESC");
if ($results->num_rows === 0) {
echo 'No results';
} else {
while ($obj = $results->fetch_object()) {
//output results from database
}
}