We report high-precision measurements of the longitudinal double-spin asymmetry, $A_{LL}$, for midrapidity inclusive jet and dijet production in polarized $pp$ collisions at a center-of-mass energy of $sqrt{s}=200,mathrm{GeV}$. The new inclusive jet data are sensitive to the gluon helicity distribution, $Delta g(x,Q^2)$, for gluon momentum fractions in the range from $x simeq 0.05$ to $x simeq 0.5$, while the new dijet data provide further constraints on the $x$ dependence of $Delta g(x,Q^2)$. The results are in good agreement with previous measurements at $sqrt{s}=200,mathrm{GeV}$ and with recent theoretical evaluations of prior world data. Our new results have better precision and thus strengthen the evidence that $Delta g(x,Q^2)$ is positive for $x > 0.05$.
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