Although giant clumps of stars are crucial to galaxy formation and evolution, the most basic demographics of clumps are still uncertain, mainly because the definition of clumps has not been thoroughly discussed. In this paper, we study the basic demographics of clumps in star-forming galaxies (SFGs) at 0.5<z<3, using our proposed physical definition that UV-bright clumps are discrete star-forming regions that individually contribute more than 8% of the rest-frame UV light of their galaxies. Clumps defined this way are significantly brighter than the HII regions of nearby large spiral galaxies, either individually or blended, when physical spatial resolution and cosmological dimming are considered. Under this definition, we measure the fraction of SFGs that contain at least one off-center clump (Fclumpy) and the contributions of clumps to the rest-frame UV light and star formation rate of SFGs in the CANDELS/GOODS-S and UDS fields, where our mass-complete sample consists of 3239 galaxies with axial ratio q>0.5. The redshift evolution of Fclumpy changes with the stellar mass (M*) of the galaxies. Low-mass (log(M*/Msun)<9.8) galaxies keep an almost constant Fclumpy of about 60% from z~3.0 to z~0.5. Intermediate-mass and massive galaxies drop their Fclumpy from 55% at z~3.0 to 40% and 15%, respectively, at z~0.5. We find that (1) the trend of disk stabilization predicted by violent disk instability matches the Fclumpy trend of massive galaxies; (2) minor mergers are a viable explanation of the Fclumpy trend of intermediate-mass galaxies at z<1.5, given a realistic observability timescale; and (3) major mergers are unlikely responsible for the Fclumpy trend in all masses at z<1.5. The clump contribution to the rest-frame UV light of SFGs shows a broad peak around galaxies with log(M*/Msun)~10.5 at all redshifts, possibly linked to the molecular gas fraction of the galaxies. (Abridged)
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