Decimal systems around the world

Decimal numeral systems (base-10) are the most widespread type of counting system across the world's languages. Their ubiquity has often been attributed to presumed functional advantages, including ease of use, cognitive efficiency and arithmetical transparency. In principle, decimal systems represent numbers as compositions involving a form representing 10 and smaller atomic numerals (e.g. Mandarin <i>shí sān</i> 'thirteen', literally 'ten three'). In practice, however, many languages exhibit deviations that obscure this compositional logic-such as allomorphy (<i>fifteen</i> in English, as opposed to <i>five-ten</i>), suppletion (e.g. Russian <i>sorok</i> 'forty', unrelated to <i>četyre</i> 'four' or <i>desjat'</i> 'ten'), or secondary structures involving other compositional elements (e.g. 5). Despite being frequently mentioned in the literature, these violations have not been systematically analysed at scale. Here, we develop a rule-based classification of decimal systems and apply it to a curated, genealogically and geographically balanced sample of 118 languages. We assess each system along three dimensions-<i>transparency</i>, <i>canonicity</i> and <i>compositionality</i>-and show that, while surface-level irregularities are widespread, the underlying mathematical structure of decimal systems remains highly regular and patterned. These results reveal that deviations from perfect decimality are not random but instead reflect structured variation shaped by historical, cognitive and typological constraints.This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.