  We prove a "quantified" version of the Weyl-von Neumann theorem, more
precisely, we estimate the ranks of approximants to compact operators appearing
in the Voiculescu's theorem applied to commutative algebras. This allows
considerable simplifications in uniform K-homology theory, namely it shows that
one can represent all the uniform K-homology classes on a fixed Hilbert space
with a fixed *-representation of C_0(X), for a large class of spaces X.
