2690: Roman Numeral Fractions May 2, 2024

People tend to be familiar with the notation of Roman numerals like I, V, X and so on. S was used to represent ½ as in XIIS (12½). Other than this, a system of dots (····· or ⁙ for 5/12, and S⁙ for 11/12) was used representing fractions of twelfths, as is attested in coins. Why an S though? While the Roman numeral system is not actually based upon the names of the words for the numbers and only coincidentally resembles numbers usually—a lesson for another day—S is short for ‘semis’, meaning ‘a half’. The half in question was specifically 6⁄12 since there were 12 ounces to an as, a Roman coin. Mentioning that these fractions are named for being parts of 12 is not only relevant to know about a now-obscure coin, but that the names sometimes are derived from this, like 8⁄12 being called ‘bes’ as in ‘twice [a third]’. For most of history the primary setting of Roman numerals was in commerce, not math, so that’s what this system related to mostly, despite the obvious limitations for numbers beyond. Outside of this and a handful of other specific abbreviations, the only way to express other fractions would be in whole words, or in commerce would simply be performed with an abacus, but it could be argued that S is still in the Roman numeral family.