early 15c., numeracioun, "method or process of numbering or calculating," from Latin numerationem (nominative numeratio) "a counting out, paying, payment," noun of action from past-participle stem of numerare "to count, number," from numerus "number" (see number (n.)). Meaning "act or process of counting the number of" is from mid-15c.
1680s, from French billion (originally byllion in Chuquet's unpublished "Le Triparty en la Science des Nombres," 1484; copied by De la Roche, 1520); see bi- "two" + million.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 usage 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.
1680s, from Latin sext-, combining form of sex "six" (see six) + ending from million. Compare billion. In English, and originally Italian, numeration, 1 to the 6th power (one followed by thirty-six zeroes); in French and U.S. use, 1,000 to the 7th power (one followed by twenty-one zeroes). Related: Sextillionth.