Origin and history of billionth

1680s, from French billion (originally byllion in Chuquet's unpublished "Le Triparty en la Science des Nombres," 1484; copied by De la Roche, 1520); see bi- "two" + million.

A million million in Britain and Germany (numeration by groups of sixes), which was the original sense; subsequently altered in French to "a thousand million" (numeration by groups of threes) and picked up in that form in U.S., "due in part to French influence after the Revolutionary War" [David E. Smith, "History of Mathematics," 1925].

France reverted to the original meaning in 1948. British use is truer to the etymology, but U.S. sense is said to be increasingly common there in technical writing.

In Italian arithmetics from the last quarter of the fifteenth century the words bilione or duilione, trilione, quadrilione or quattrilione, quintilione, cinquilione, or quinquilione, sestione or sestilione, settilione, ottilione, noeilione and decilione occur as common abbreviations of due volte millioni, tre volte millione, etc. In other countries these words came into use much later, although one French writer, Nicolas Chuquet, mentions them as early as 1484, in a book not printed until 1881. The Italians had, besides, another system of numeration, proceeding by powers of a thousand. The French, who like other northern peoples, took most if not all their knowledge of modern or Arabic arithmetic from the Italians, early confounded the two systems of Italian numeration, counting in powers of a thousand, but adopting the names which properly belong to powers of a million. [Century Dictionary]

For a time in Britain gillion (1961), based on giga-, was tried as "a thousand million" to avoid ambiguity. Compare milliard.

word-forming element making ordinal numbers (fourth, tenth, etc.), Old English -ða, from Proto-Germanic *-tha- (cognates: Gothic -da, -ta, Old High German -do, -to, Old Norse -di, -ti), from PIE *-to-, also *-eto-, *-oto-, suffix forming adjectives "marking the accomplishment of the notion of the base" [Watkins].

Cognate with Sanskrit thah, Greek -tos, Latin -tus; Sanskrit ta-, Lithuanian and Old Church Slavonic to, Greek to "the," Latin talis "such;" Greek tēlikos "so old, of such an age," Old Church Slavonic toli "so, to such a degree," toliku "so much," Russian toliko "only;" also see -ed.

Physicists coined zeroth by 1896, in describing functions, "coming before the first."