  Let $A$ be an amenable separable \CA and $B$ be a non-unital but
$\sigma$-unital simple \CA with continuous scale. We show that two essential
extensions $\tau_1$ and $\tau_2$ of $A$ by $B$ are approximately unitarily
equivalent if and only if $$ [\tau_1]=[\tau_2] {\rm in} KL(A, M(B)/B). $$ If
$A$ is assumed to satisfy the Universal Coefficient Theorem, there is a
bijection from approximate unitary equivalence classes of the above mentioned
extensions to $KL(A, M(B)/B).$ Using $KL(A, M(B)/B),$ we compute exactly when
an essential extension is quasidiagonal. We show that quasidiagonal extensions
may not be approximately trivial. We also study the approximately trivial
extensions.
