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Approximation in number use: Roundness and magnitude
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Description: Numbers have mathematically defined, formal meanings, which afford precision and objectivity—at least in principle. In practice, we show that round numbers are often used approximately, increasingly so at higher magnitudes. Across four analyses of American and British English, we demonstrate the following. First, round numbers are used more often at higher magnitudes, revealing an increasingly approximate use of larger numbers. Second, broadeners like ‘about’ and ‘approximately’ are used more often with round numbers, especially at higher magnitudes. Third, the distributional semantics of large round numbers like ‘million’, ‘billion’, and ‘sextillion’ are similar to those of indefinite hyperbolic numbers like ‘gazillion’ and ‘bajillion’, which do not have a precise value. Fourth, an analysis of jigsaw puzzles reveals that, as puzzles grow larger, the stated number of pieces on the packaging (e.g., 13,200) differs by a greater extent from the actual value (e.g., 13,224). These patterns of number use parallel numerical cognition (e.g., our ability to estimate quantities), which becomes increasingly approximate as magnitudes increase.
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