数を言葉で書き表す

Writing numbers as words is far older than writing them as digits, but the names for the very large ones were invented surprisingly late, and by people we can name. Nicolas Chuquet, a physician and mathematician working in Lyon, set the pattern in a manuscript he finished in 1484, the Triparty en la science des nombres. Chuquet cut long numerals into groups of six digits and coined names for the groups — byllion, tryllion, quadrillion, quyllion and on up to nonyllion. Because his groups were sixes, a byllion was a million millions, 10¹². The manuscript itself went unpublished until Aristide Marre printed it in 1880, but Estienne de la Roche borrowed heavily from it in his Larismethique of 1520, and the names escaped into general use.

The gap at 10⁹ was awkward, and Jacques Peletier du Mans filled it: in his L'arithmetique of 1549 he used milliart, today's milliard, for a thousand million. That is why the long scale, with its alternating -ion and -iard names, is called the Peletier system. French clerks later drifted the other way, regrouping digits in threes so that a billion became 10⁹; this short scale crossed to the United States and stuck there, while Britain kept the long one. France itself went back to the long scale by decree in 1961.

The split lasted until the numbers in question got too large to leave ambiguous. On 20 December 1974 the Prime Minister, Harold Wilson, told the House of Commons in a written answer that British government statistics would from then on use billion to mean a thousand million, in line with American usage. British English followed, and milliard has all but vanished from it — but Spanish, German, Italian, Dutch and European Portuguese still count Chuquet's way, which is why billón, Billion and bilião all mean a million millions.

主な性質

• On the short scale each -illion is a thousand times the one before it: the nth is 10^(3n+3), so a billion is 10⁹ and a trillion 10¹².
• On the long scale each -illion is a million times the one before it: the nth is 10^(6n), so a billion is 10¹² — a million squared, which is where the prefix bi- comes from.
• The first English number word containing the letter “a” is “thousand”: nothing from one to nine hundred and ninety-nine needs one.
• German and Dutch put the units before the tens — 21 is einundzwanzig and eenentwintig, literally “one and twenty”.
• Standard French has no single word for 70, 80 or 90: they are soixante-dix, quatre-vingts and quatre-vingt-dix. Belgian French uses septante and nonante, and parts of Switzerland add huitante.
• Spanish writes 16 to 29 as single words (dieciséis through veintinueve) but from 31 up inserts the conjunction: treinta y uno.
• Turkish is almost perfectly regular: every number from 11 to 99 is the tens word followed by the units word, with nothing between them, so 21 is yirmi bir.
• Integers above 2⁵³ − 1 = 9,007,199,254,740,991 cannot be held exactly in a JavaScript number, so this page spells them with arbitrary-precision arithmetic, up to 36 digits.

登場する場面

• Cheques and other bills of exchange carry the amount twice. Under section 9(2) of the UK Bills of Exchange Act 1882, where the words and the figures disagree, the sum denoted by the words is the amount payable.
• Contracts and invoices repeat a figure in words after the numerals — “one hundred thousand dollars ($100,000)” — on the convention that a single mistyped digit then cannot change the sum on its own.
• House style guides set a threshold for spelling out: Associated Press style spells out one through nine and switches to figures at 10.
• Screen readers and text-to-speech engines expand digits into words before speaking them, which is why a phone number and a price read aloud differently.
• US cheque practice writes the cents as a fraction — “and 45/100” — and conventionally avoids “and” inside the number itself, so the two cannot be confused.