Decimals, fractions, or percentages: a multivariate approach to rational number alternations in English

Abstract Rational numbers can be expressed as decimals, fractions, and percentages, each serving distinct functions. The differences among the three forms have been examined in terms of structural distinction and the cognitive effort required for their processing. Using a multivariate approach, this study integrates cognitive and linguistic factors to explore how these representations alternate in diverse linguistic contexts. A total of 2,217 rational number tokens were coded for eight features. Their relative importance in predicting notation choice was assessed using random forests, with conceptual interpretation and syntactic structure as the most influential predictors, followed by entity type, genre, grammatical function, semantics of verbs, and definiteness, while approximation contributed little predictive information. The findings suggest that the three notations function as members of a prototype-based category, each showing a typical usage core with peripheral cases. Individuals select numerical forms in an effort-saving manner, favoring fractions over decimals and percentages for precise enumeration. Furthermore, these forms are also found to evolve and develop varied grammatical functions and syntactic structures in actual use.