trillion

trillion
1000000000000
depiction
dual	1110 1000 1101 0100 1010 0101 0001 0000 0000 0000
Octal	16 4324 5121 0000
Duodecimal	1419 81B8 7854
Hexadecimal	E8 D4A5 1000
Morse code	- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Mathematical properties
sign	positive
parity	just
Factorization	${\displaystyle 2^{12}\cdot 5^{12}}$
Divider	<All numbers that are neither divisible by nor by a prime number other than 2 and 5 (see running text). ${\displaystyle 2^{13}}$ ${\displaystyle 5^{13}}$

In international parlance, the number name Billion stands for the number 1000 billion or 1,000,000,000,000 = 10 ¹² , in the decimal system it stands for a one with 12 zeros. 1000 trillion makes one quadrillion . The prefix for units of measurement for the factor one trillion is Tera with the symbol T. It is abbreviated to Bio. or Bill. , whereby the latter can be confused with billiards.

The US-American and partly British billion, on the other hand, corresponds to the German billion , while the German trillion is referred to there as the trillion .

Math

Divider

Factoring is . This results in so ways a power of two ( up ) with a power of five ( to multiply). The number 1,000,000,000,000 has exactly the following 169 factors: ${\displaystyle 2^{12}\cdot 5^{12}}$ ${\displaystyle (12+1)\cdot (12+1)}$ ${\displaystyle (13\cdot 13)=169}$ ${\displaystyle 2^{0}}$ ${\displaystyle 2^{12}}$ ${\displaystyle 5^{0}}$ ${\displaystyle 5^{12}}$

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1,000, 1,024, 1,250, 1,280, 1,600, 2,000, 2,048, 2,500, 2,560, 3,125, 3,200, 4,000, 4,096, 5,000, 5,120, 6,250, 6,400, 8,000, 10,000, 10,240, 12,500, 12,800, 15,625, 16,000, 20,000, 20,480, 25,000, 25,600, 31,250, 32,000, 40,000, 50,000, 51,200, 62,500, 64,000, 78,125, 80,000, 100,000, 102,400, 125,000, 128,000, 156,250, 160,000, 200,000, 250,000, 256,000, 312,500, 320,000, 390,625, 400,000, 500,000, 512,000, 625,000, 640,000, 781,250, 800,000, 1,000,000, 1,250,000, 1,280,000, 1,562,500, 1,600,000, 1,953,125, 2,000,000, 2,500,000, 2,560,000, 3,125,000, 3,200,000, 3,906,250, 4,000,000, 5,000,000, 6,250,000, 6,400,000, 7,812,500, 8,000,000, 9,765,625, 10,000,000, 12,500. 000, 12,800,000, 15,625,000, 16,000,000, 19,531,250, 20,000,000, 25,000,000, 31,250,000, 32,000,000, 39,062,500, 40,000,000, 48,828,125, 50,000,000, 62,500,000, 64,000,000, 78.125,000, 80,000,000, 97.65 6,250, 100,000,000, 125,000,000, 156,250,000, 160,000,000, 195,312,500, 200,000,000, 244,140,625, 250,000,000, 312,500,000, 320,000,000, 390,625,000, 400,000,000, 488,281,250, 500,000,000, 625,000,000, 781,250,000, 800,000,000, 976,562,500, 1,000,000,000, 1,250,000,000, 1,562,500,000, 1,600,000,000, 1,953,125,000, 2,000,000,000, 2,500. 000,000, 3,125,000,000, 3,906,250,000, 4,000,000,000, 5,000,000,000, 6,250,000,000, 7,812,500,000, 8,000,000,000, 10,000,000,000, 12,500,000,000, 15,625,000,000, 20,000,000,000, 25,000,000,000, 31,250,000,000, 40,000,000,000, 50,000,000,000, 62,500,000,000, 100,000,000,000, 125,000,000,000, 200,000,000,000, 250,000,000,000, 500,000,000,000, 1,000,000,000,000

Unit of measure prefixes

When referring to units of measurement , the trillion times the unit of measurement is denoted with the prefix tera (abbreviated: T), whereas the trillionth part (10 ⁻¹² ) is denoted by pico (abbreviated: p). For example, a picometer (pm) is a trillionth of a meter (10 ⁻¹² m).

Even when referring to the unit of measurement byte in computer science , the term terabyte (abbreviated: TB) is understood today in the sense of exactly one trillion bytes. That is 10 ¹² bytes and not 2 ⁴⁰ = 1024 ⁴ = 1,099,511,627,776 bytes, which exceeds a trillion bytes by approx. 9.95%. Today, the designation Tebibyte (TiB) is suggested for naming 2 ⁴⁰ bytes ; Tebi (Ti) is a binary prefix while Tera (T) is a decimal prefix.

Wrong friends in other languages

→ Main article : Long and short scale

The different use of the same term in different languages ​​(as a so-called false friend ) often leads to incorrect translations, especially in non-scientific or negligent journalism when specifying costs or assets. The reason for this lies in two systems used in parallel for number names in the decimal system, the so-called long and short scale : In the long scale, which is used in German , French , Italian , Polish , Spanish and Portugal, among others , one trillion has the Meaning of a million to the power of 2 (hence the prefix  bi ), i.e. 10 ¹² . In US English, however, the number “ billion ” stands for 10 ⁹ (= 1000 ^{1+ 2} ), so it corresponds to the billion from the long scale (the German-speaking trillion in US English is correspondingly called trillion ). In British English , billion is used for both 10 ⁹ and traditionally 10 ¹² due to US influence . Therefore, translations from English are not always reliable.

In numismatics, the term trillion silver with base alloy components of at least 50 percent. The trillion coins made from it had a maximum fineness of 500/1000. In German, however, the correct expression is Billon and not Billion.

story

The word trillion came up in France in the 15th century . Originally it certainly stood for the attested bi-million (= 10 ¹² ). This meaning was first described and systematized by the French mathematician Nicolas Chuquet in his work Triparty en la science des nombres (published as a manuscript in 1484). It appears for the first time in English in 1690 ( Oxford English Dictionary ). This is exactly how it is commonly used by science in England today .

In the 17th century there was an attempt at reform in France, according to which one trillion should only be worth 1000 million (10 ⁹ ). The Americans adopted this reformed meaning directly from French advisers. The so-called short scale is also used today in Puerto Rico and Brazil as well as in Russia and Turkey , although the word billion (10 ⁹ ) is firmly anchored in the parlance of the last two countries mentioned . The Greek language, in which the international word billion is not used, is a special case . The number 10 ¹² is called in Greece , according to the model of the short skalla, tri-hundred myriad (tris / ekatom / myrio). The million (10 ⁶ ) “Ekatommyrio” - formed as a compound of 100 times 10,000 - is preceded by an increased cardinal number for each “short step” (times a thousand).

The English Prime Minister Harold Wilson decided that his government would use the word as in American in future. Since 1974 the American meaning for official documents has been taken over by the British government. In everyday use, however, the trillion is still equated with 10 ¹² in England . There is a tendency in Australia , South Africa and other English-speaking countries to subscribe to the American understanding of the trillion.

In all other countries of the world, the original meaning of the trillion according to Chuquet prevailed. The international committees have been recommending this use since 1948, most recently the 11th General Conference on Weights and Measures, 1960. In France itself, the reformed naming of large numbers never really caught on. The French government then confirmed the long scale in 1961 with the Décret 61-501, which also corresponds to the linguistic usage. In Italy, too, this understanding of the trillion is general and, according to an EU directive, official.

The internationally standardized prefixes Giga for 10 ⁹ and Tera for 10 ¹² cannot fully replace the number names.

The reform system, which the French lexicon Littré explicitly describes as "erroneous", has so far been unreservedly valid in three countries around the world (Brazil, the USA and Puerto Rico).

The logic behind the Chuquet trillion and all other zillions is that the prefix always corresponds exactly to the power of the million. (Example: A Tri is llion one million high three .) The Zilliarden call since the transition from six- to triplets very well the intermediate numbers that thousands of zillions .

use

The trillion only rarely plays a role in everyday life, one example being hyperinflation in Germany in 1923 .

• The trillion is rarely used in everyday life. Sometimes the German inflation from 1914 to 1923 is remembered, when banknotes for several trillion Reichsmarks were issued. In the city of Schramberg , the Billionenweg is a reminder of the construction costs at that time.
• The emergency coin with the highest face value of all time is the 1 trillion mark piece from the province of Westphalia from 1923. Since the coin was already devalued by the planned issue date due to hyperinflation, it was only sold after the end of inflation and the stabilization of the currency in 1924 issued as a souvenir.
• The national debt of the Federal Republic of Germany, as shown, for example, on the debt clock, exceeded the 2 trillion euro mark for the first time in 2010.
• The common unit for the storage capacity of large computer hard disk drives is tera byte (TB): 1 tera byte equals 1 trillion bytes = 1 × 10 ¹² bytes. When specifying the storage capacity of hard disks, the discrepancy between decimal and binary prefixes must be taken into account.

Web links

Wiktionary: Billion  - Explanations of meanings, word origins, synonyms, translations

Wiktionary: billion  - explanations of meanings, word origins, synonyms, translations

• How much is a trillion - Handelsblatt , November 21, 2013
• Dossier on "Billion" at Scinexx

Individual evidence

1. ↑ Helmut Kahnt, Bernd Knorr: Old dimensions, coins and weights. A lexicon. Bibliographisches Institut, Leipzig 1986, licensed edition Mannheim / Vienna / Zurich 1987, ISBN 3-411-02148-9 , p. 382.
2. ^ Triparty en la science des nombres
3. ↑ Décret 61-501 (PDF; 1.1 MB) page 14, note 3A
4. ↑ Direttiva CEE / CEEA / CE n.55 (PDF; 1.1 MB) page 12.
5. ^ Peter Menzel: German emergency coins and other money substitute stamps 1873-1932 , Berlin 1982
6. ^ Public debt , sueddeutsche.de
7. ^ Public debt , spiegel.de, April 13, 2011