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For stars with unresolved companions, motions of the centre of light and that of mass decouple, causing a single-source astrometric model to perform poorly. We show that such stars can be easily detected with the reduced chi2 statistic, or RUWE, provided as part of Gaia DR2. We convert RUWE into the amplitude of the image centroid wobble, which, if scaled by the source distance, is proportional to the physical separation between companions (for periods up to several years). We test this idea on a sample of known spectroscopic binaries and demonstrate that the amplitude of the centroid perturbation scales with the binary period and the mass ratio as expected. We apply this technique to the Gaia DR2 data and show how the binary fraction evolves across the Hertzsprung--Russell diagram. The observed incidence of unresolved companions is high for massive young stars and drops steadily with stellar mass, reaching its lowest levels for white dwarfs. We highlight the elevated binary fraction for the nearby Blue Stragglers and Blue Horizontal Branch stars. We also illustrate how unresolved hierarchical triples inflate the relative velocity signal in wide binaries. Finally, we point out a hint of evidence for the existence of additional companions to the hosts of extrasolar hot jupiters.