We report high-precision measurements of the longitudinal double-spin asymmetry, ALL, for midrapidity inclusive jet and dijet production in polarized pp collisions at a center-of-mass energy of $\sqrt{s}$=200 GeV. The new inclusive jet data are sensitive to the gluon helicity distribution, Δg(x,Q2), for gluon momentum fractions in the range from x≃0.05 to x≃0.5, while the new dijet data provide further constraints on the x dependence of Δg(x,Q2). The results are in good agreement with previous measurements at s=200 GeV and with recent theoretical evaluations of prior world data. Our new results have better precision and thus strengthen the evidence that Δg(x,Q2) is positive for x>0.05.