Precision and Mathematical Form in First and Subsequent Mentions of Numerical Facts and their Relation to Document Structure

In a corpus study we found that authors vary both mathematical form and precision1 when expressing numerical quantities. Indeed, within the same document, a quantity is often described vaguely in some places and more accurately in others. Vague descriptions tend to occur early in a document and to be expressed in simpler mathematical forms (e.g., fractions or ratios), whereas more accurate descriptions of the same proportions tend to occur later, often expressed in more complex forms (e.g., decimal percentages). Our results can be used in Natural Language Generation (1) to generate repeat descriptions within the same document, and (2) to generate descriptions of numerical quantities for different audiences according to mathematical ability.