MySQL query not fetching results (PHP)

I have the following script with an SQL problem which is not working.

$servername = "localhost";
$username = "root";
$password = "root";
$dbname = "Freepaste";
$conn = mysqli_connect($servername, $username, $password,$dbname);

if (!$conn) {
    die("Connection failed: " . mysqli_connect_error());
}
echo "Connected successfully";
$user = $_POST['user'];
$pass = $_POST['pass'];

$sql = "SELECT * FROM users where users.username=$user AND users.password=$pass";
//$sql = "SELECT * FROM users";
$result = mysqli_query($conn, $sql);

if (mysqli_num_rows($result) > 0) {
    // output data of each row
    while($row = mysqli_fetch_assoc($result)) {
        echo "<br>id: " . $row["username"]." Password ".$row["password"]. "<br>";
    }
} else {
    echo "0 results";
}

mysqli_close($conn);

The statement without the "where" clause gets me all the results, so I know the keys are right. Also, I ran the query in MySQL and it is working fine. I tried adding "" to $user and $pass, still not working. I checked the names in HTML, they are correct too. What am I missing?