Bloch has defined higher Chow groups $CH^q(X, p)$ of a scheme $X$ over a field $k$ by constructing a complex out of the codimension $q$ algebraic cycles on $X \times A^n_k n = 0,1,2 \ldots $ We show that the $\mathbb Q$-vector space $CH^q(X, p)_{\mathbb Q}$ k is naturally isomorphic to the weight $q$ portion of the $p$th $K$-group of $X, K_p(X)^{(q)}$ for $X$ a smooth quasi-projective variety over $k$, generalizing the ical isomorphism $CH^q(X)_{\mathbb Q} \rightarrow K_0 (X)^{(q)}$. We also show that the functors $CH^q(-, \star )_{\mathbb Q}$ satisfy most of the properties of a Bloch-Ogus twisted duality theory. Finally, we show that the alternating cycle groups defined by Bloch agree with the rational higher Chow groups.