People’s preferences for different types of rational numbers in linguistic contexts

Rational numbers, like fractions, decimals, and percentages, differ in the concepts they prefer to express and the entities they prefer to describe as previously reported in display-rational number notation matching tasks and in math word problem compiling contexts. On one hand, fractions and percentages are preferentially used to express a relation between two magnitudes, while decimals are preferentially used to represent a magnitude. On the other hand, fractions and decimals tend to be used to describe discrete and continuous entities, respectively. However, it remains unclear whether these reported distinctions can extend to more general linguistic contexts. It also remains unclear which factor, the concept to be expressed (magnitudes vs. relations between magnitudes) or the entity to be described (countable vs. continuous), is more predictive of people’s preferences for rational number notations. To explore these issues, two corpus studies and a number notation preference experiment were administered. The news and conversation corpus studies detected the general pattern of conceptual distinctions across rational number notations as observed in previous studies; the number notation preference experiment found that the concept to be expressed was more predictive of people’s preferences for number notations than the entity to be described. These findings indicate that people’s biased uses of rational numbers are constrained by multiple factors, especially by the type of concepts to be expressed, and more importantly, these biases are not specific to mathematical settings but are generalizable to broader linguistic contexts.