Approximate round number use depends on magnitude

Abstract Numbers have mathematically defined, formal meanings, which afford precision and objectivity. In practice, however, we show that round numbers are frequently used approximately, and this approximate use depends on magnitude. Across three analyses of British and American English, we demonstrate the following: (1) people use round numbers more often, and round to a greater extent, at higher magnitudes; (2) the distributional semantics of larger round numbers resemble those of indefinite hyperbolic numbers such as ‘gazillion’, which lack a precise value; and (3) larger jigsaw puzzles have greater discrepancies between round advertised piece counts and the actual values (e.g., advertising ‘13,200 pieces’ when the actual count is 13,224). We argue that the relationship between roundness, magnitude and approximation derives from the base-10 structure of English numerals, which renders powers of 10 structurally salient, creating hotspots for communicative functions such as approximation. We discuss how these communicative patterns align with the approximate number system, which cognitively represents larger quantities with increasing imprecision, making them harder to estimate and compare.