The number seven trillion two million thirty one thousand in numeric form is 7,000,000,002,031. Thanks!
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries and Arabic-speaking countries use the short scale. In all such countries, the number names are translated into the local language, but retain a name similarity due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from the long and short scales.
For integers less than a thousand million (< 109), the two scales are identical. At and above a thousand million (≥ 109), the two scales diverge by using the same words for different number values. These "false friends" can be a source of misunderstanding.
For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that the two systems were often referred to as British and American in the English language. In 1974, the government of the UK switched to the short scale, a change that is reflected in its mass media and official usage. Although some residual usage of the long scale continues in the UK, the phrases British usage and American usage are no longer accurate characterisations. Usage of the two systems can be a subject of controversy. Differences in opinion as to which system should be used can evoke resentment between adherents, while national differences of any kind can acquire jingoistic overtones.
The first recorded use of the terms échelle courte and échelle longue was by the French mathematician Geneviève Guitel in 1975.
At and above a thousand million (≥ 109), the same numerical value has two different names, depending on whether the value is being expressed in the long or short scale. Equivalently, the same name has two different numerical values depending on whether it is being used in the long or short scale.
Each scale has a logical justification to explain the use of each such differing numerical name and value within that scale. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million. In both scales, the prefix bi- refers to "2" and tri- refers to "3", etc. However only in the long scale do the prefixes beyond one million indicate the actual power or exponent (of 1,000,000). In the short scale, the prefixes refer to one less than the exponent (of 1,000).
The relationship between the numeric values and the corresponding names in the two scales can be described as:
The root mil in "million" does not refer to the numeral "one". Rather, it refers to the Latin word for "thousand" (milia).
The relationship between the names and the corresponding numeric values in the two scales can be described as:
The word milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term yard, which derives from milliard, is used on financial markets, as it unlike the term billion is internationally unamboguous and phonetically distinct from million. Likewise, many long scale countries use the word billiard (or similar) for a thousand long scale billions (i.e. 1015), and the word trilliard (or similar) for a thousand long scale trillions (i.e. 1021), etc.
The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when interpreting old documents in countries where the dominant scale has changed over time. For example, British-English, French, and Italian historical documents can refer to either the short or long scale, depending on the date of the document, since each of the three countries has used both systems at various times in its history. Today, the United Kingdom officially uses the short scale, but France and Italy use the long scale.
The pre-1974 former British English word billion, post-1961 current French word billion, post-1994 current Italian word bilione, German Billion; Dutch biljoen; Swedish biljon; Finnish biljoona; Danish billion; Polish bilion, Spanish billón; Slovenian bilijon and the European Portuguese word bilião (with an alternate spelling to the Brazilian Portuguese variant) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 modern British English word: trillion (1012 in the short scale), and not billion (109 in the short scale).
On the other hand, the pre-1961 former French word billion, pre-1994 former Italian word bilione, Brazilian Portuguese word bilhão and the Welsh word biliwn all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 modern British English word billion (109 in the short scale).
The terms billion and milliard both originally meant 1012 when introduced.
The word million derives from the Old French milion from the earlier Old Italian milione, an intensification of mille, a thousand. That is, a million is a "big thousand", much as a "great gross" is a dozen gross or 1728.
The extract from Chuquet's manuscript, the transcription and translation provided here all contain an original mistake: one too many zeros in the 804300 portion of the fully written out example: 745324'8043000 '700023'654321 ...
German hyperinflation in the 1920s Weimar Republic caused 'Eintausend Mark' (1000 Mark = 103 Mark) German banknotes to be over-stamped as 'Eine Milliarde Mark' (109 Mark). This introduced large-number names to the German populace.
The Mark or Papiermark was replaced at the end of 1923 by the Rentenmark at an exchange rate of:
1 Rentenmark = 1 billion (long scale) Papiermark = 1012 Papiermark = 1 trillion (short scale) Papiermark
Although American English usage did not change, within the next 50 years French usage changed from short scale to long and British English usage changed from long scale to short.
Hyperinflation in Hungary in 1946 led to the introduction of the 1020 pengő banknote.
100 million b-pengő (long scale) = 100 trillion (long scale) pengő = 1020 pengő = 100 quintillion (short scale) pengő.
On 1 August 1946, the forint was introduced at a rate of:
1 forint = 400 quadrilliard (long scale) pengő = 4 x 1029 pengő = 400 octillion (short scale) pengő.
The BBC and other UK mass media quickly followed the government's lead within the UK.
During the last quarter of the 20th century, most other English-speaking countries (the Republic of Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either also followed this lead or independently switched to the short scale use. However, in most of these countries, some limited long scale use persists and the official status of the short scale use is not clear.
Hyperinflation in Yugoslavia led to the introduction of 5 x 1011 dinar banknotes.
500 thousand millions (long scale) dinars = 5 x 1011 dinar banknotes = 500 billions (short scale) dinars.
The later introduction of the new dinar came at an exchange rate of:
1 novi dinar = 1 × 1027 dinars = ~1.3 × 1027 pre 1990 dinars.
Hyperinflation in Zimbabwe led to banknotes of 1014 Zimbabwean dollars being issued in 2009, shortly ahead of the currency being abandoned. As of 2013[update], a new currency has yet to be announced – so foreign currencies are being used instead.
100 trillion (short scale) Zimbabwean dollars = 1014 Zimbabwean dollars = 100 billion (long scale) Zimbabwean dollars = 1027 pre-2006 Zimbabwean dollars.
Most English-language countries and regions use the short scale with 109 = billion. For example:
Most Arabic-language countries and regions use the short scale with 109 = milyar. For example:
Other countries also use a word similar to trillion to mean 1012, etc. While a few of these countries like English use a word similar to billion to mean 109, most like Arabic have kept a traditional long scale word similar to milliard for 109. Some examples of short scale use, and the words used for 109 and 1012, are:
The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Bulgaria, Greece, Romania, and Brazil). These countries use a word similar to billion to mean 1012. Some use a word similar to milliard to mean 109, while others use a word or phrase equivalent to thousand millions.
Most Spanish-language countries and regions use the long scale with 109 = mil millones, for example:
Most French-language countries and regions use the long scale, for example:
With the notable exception of Brazil, a short scale country, most Portuguese-language countries and regions use the long scale, for example:
Most Dutch-language countries and regions use the long scale, for example:
Some examples of long scale use, and the words used for 109 and 1012, are:
Some countries use either the short or long scales, depending on the internal language being used or the context.
The following countries have their own numbering systems and use neither short nor long scales:
The long and short scales are both present on most continents, with usage dependent on the language used. Examples include:
Unambiguous ways of identifying large numbers include:
Orders of magnitude (numbers)
Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems: the Indian (Arabic) system used world-wide and two indigenous systems.
The more familiar indigenous system are Chinese characters that correspond to numerals in the spoken language][. These are shared with other languages of the Chinese cultural sphere such as Japanese, Korean and Vietnamese. Most people and institutions in China primarily use the Indian (Arabic) system for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on checks and banknotes and some ceremonial occasions.][
The other indigenous system is the Suzhou numerals, or huama, a positional system. It is the only surviving form of the rod numerals. They were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but has been gradually supplanted by the Arabic numerals and also the Roman numerals.
The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals. Similar to spelling-out numbers in English (e.g., "one thousand nine hundred forty-five"), it is not an independent system per se. Since it reflects spoken language, it does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not.
There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing and one for use in commercial or financial contexts known as dàxiě (simplified Chinese: ; traditional Chinese: ). The latter arose because the characters used for writing numerals are geometrically simple, so simply using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could easily change everyday characters 三十 (30) to 五千 (5000) by adding just a few strokes. That would not be possible when writing using the financial characters 參拾 (30) and 伍仟 (5000). They are also referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals." For the same reason, rod numerals were never used in commercial records.
T denotes Traditional Chinese characters, S denotes Simplified Chinese characters.
In the PLA, some numbers will have altered names when used for clearer radio communications. They are:
Similar to the long and short scales in the west, there have been four systems in ancient and modern usage. The original one, with unique names for all powers of ten up to the 14th is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu (Arithmetic in Five Classics). In modern Chinese only the second system is used, in which the same ancient names are used but each number is 10,000 (myriad, 萬 wàn) times the previous:
In practice, this situation does not lead to ambiguity, with the exception of 兆 (zhào), which means 1012 according to the second system in common usage throughout the Chinese communities as well as in Japan and Korea, but is also used for 106 in recent years (esp. in mainland China to represent the Megabyte). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 (wànyì) instead. The ROC government in Taiwan uses 兆 (zhào) to mean 1012 in official documents.
Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are mostly found in ancient texts.
The following are characters used to denote small order of magnitude in Chinese historically. With the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse.
攸 (T) or 幺 (S) corresponds to the SI prefix yocto-.
介 (T) or 仄 (S) corresponds to the SI prefix zepto-.
阿 corresponds to the SI prefix atto-.
飛 (T) or 飞 (S) corresponds to the SI prefix femto-.
皮 corresponds to the SI prefix pico-.
奈 (T) or 纳 (S) corresponds to the SI prefix nano-.
still in use, corresponds to the SI prefix milli-.
still in use, corresponds to the SI prefix centi-.
In the People's Republic of China, the translations for the SI prefixes in 1981 were different from those used today. The larger (兆, 京, 垓, 秭, 穰) and smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as translations for the SI prefixes as mega, giga, tera, peta, exa', micro, nano, pico, femto, atto, resulting in the creation of more values for each numeral.
In addition, Taiwanese defined 百萬 as the translation for mega. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz".
Today, both the governments of the People's Republic of China (Mainland China, Hong Kong and Macau) and Republic of China (Taiwan) use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes. The following table lists the two different standards together with the early translation.
Multiple-digit numbers are constructed using a multiplicative principle; first the digit itself (from 1 to 9), then the place (such as 10 or 100); then the next digit.
In Mandarin, the multiplier 兩 (liǎng) is often used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral (although as noted earlier this varies from dialect to dialect and person to person). Use of both 兩 (liǎng) or 二 (èr) are acceptable for the number 200. When writing in the Cantonese dialect, 二 (yi6) is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou (Teochew), 兩 (no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:
For the numbers 11 through 19, the leading "one" (一) is usually omitted. In some dialects, like Shanghainese, when there are only two significant digits in the number, the leading "one" and the trailing zeroes are omitted. Sometimes, the one before "ten" in the middle of a number, such as 213, is omitted. Thus:
In certain older texts like the Protestant Bible or in poetic usage, numbers such as 114 may be written as    (百十四).
For numbers larger than a myriad, the same grouping system used in English applies, except in groups of four places (myriads) rather than in groups of three (thousands). Hence it is more convenient to think of numbers here as in groups of four, thus 1,234,567,890 is regrouped here as 12,3456,7890. Larger than a myriad, each number is therefore four zeroes longer than the one before it, thus 10000 × wàn (萬) = yì (億). If one of the numbers is between 10 and 19, the leading "one" is omitted as per the above point. Hence (numbers in parentheses indicate that the number has been written as one number rather than expanded):
Interior zeroes before the unit position (as in 1002) must be spelt explicitly. The reason for this is that trailing zeroes (as in 1200) are often omitted as shorthand, so ambiguity occurs. One zero is sufficient to resolve the ambiguity. Where the zero is before a digit other than the units digit, the explicit zero is not ambiguous and is therefore optional, but preferred. Thus:
To construct a fraction, the denominator is written first, followed by 分之 ("parts of") and then the numerator. This is the opposite of how fractions are read in English, which is numerator first. Each half of the fraction is written the same as a whole number. Mixed numbers are written with the whole-number part first, followed by 又 ("and"), then the fractional part.
Percentages are constructed similarly, using 百 (100) as the denominator. The 一 (one) before 百 is omitted.
Decimal numbers are constructed by first writing the whole number part, then inserting a point (simplified Chinese: ; traditional Chinese: ; pinyin: diǎn), and finally the decimal expression. The decimal expression is written using only the digits for 0 to 9, without multiplicative words.
Ordinal numbers are formed by adding 第 ("sequence") before the number.
Negative numbers are formed by adding fù (simplified Chinese: ; traditional Chinese: ) before the number.
In the same way that Roman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the rod numerals, which is a positional system. The Suzhou numerals (simplified Chinese: ; traditional Chinese: ; pinyin: Sūzhōu huāmǎ) system is a variation of the Southern Song rod numerals. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
Ancient Chinese used positional decimal counting rod numerals for calculation since the Spring and Autumn period.
There is a common method of using of one hand to signify the numbers one to ten. While the five digits on one hand can express the numbers one to five, six to ten have special signs that can be used in commerce or day-to-day communication.
In the 1930s, archeologist Pei Wenzhong unearthed Upper Cave Man relics in Zhoukoudian,
Most Chinese numerals of later period were descendants from Shang dynasty oracle numerals of 14th century B.C. The oracle bone script numerals were found on tortoise shell and animal bones.
Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 were passed to Rod numerals.
while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. Sun Tzu wrote that "one is vertical, ten is horizontal."
The counting rod numerals system has place value and decimal numerals for computation, and was used widely by Chinese merchants, mathematicians and astronomers from Han dynasty to 16th century. In early civilizations, the Shang were able to express any numbers, however large with only 9 symbols and a counting board.
Alexander Wylie, Christian missionary to China, in 1853 already refuted the notion that "the Chinese numbers were written in words at length", and stated that in ancient China, calculation was carried out by means of counting rods, and "the written character is evidently a rude presentation of these". After being introduced to the rod numerals, he said "Having thus obtained a simple but effective system of figures, we find the Chinese in actual use of a method of notation depending on the theory of local value [i.e. place-value], several centuries before such theory was understood in Europe, and while yet the science of numbers had scarcely dawned among the Arabs"
During Ming and Qing dynasties (when Arabic numerals were first introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After Qing dynasty, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.
Traditional Chinese numeric characters are also used in Japan and Korea and were used in Vietnam before the 20th century. In vertical text (that is, read top to bottom), using characters for numbers is the norm, while in horizontal text, Arabic numerals are most common. Chinese numeric characters are also used in much the same formal or decorative fashion that Roman numerals are in Western cultures. Chinese numerals may appear together with Arabic numbers on the same sign or document.
The Three Trillion Dollar War
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.
(; 1000−10; short scale: one nonillionth; long scale: one quintillionth)
(; 1000−9; short scale: one octillionth; long scale: one quadrilliardth)
(; 1000−8; short scale: one septillionth; long scale: one quadrillionth)
ISO: yocto- (y)
(; 1000−7; short scale: one sextillionth; long scale: one trilliardth)
ISO: zepto- (z)
(; 1000−6; short scale: one quintillionth; long scale: one trillionth)
ISO: atto- (a)
(; 1000−5; short scale: one quadrillionth; long scale: one billiardth)
ISO: femto- (f)
(; 1000−4; short scale: one trillionth; long scale: one billionth)
ISO: pico- (p)
(; 1000−3; short scale: one billionth; long scale: one milliardth)
ISO: nano- (n)
(; 1000−2; long and short scales: one millionth)
ISO: micro- (μ)
(0.001; 1000−1; one thousandth)
ISO: milli- (m)
(0.01; one hundredth)
ISO: centi- (c)
(0.1; one tenth)
ISO: deci- (d)
ISO: deca- (da)
ISO: hecto- (h)
ISO: kilo- (k)
(; ten thousand or a myriad)
(; one hundred thousand or a lakh)
(; 10002; long and short scales: one million)
ISO: mega- (M)
(; a crore; long and short scales: ten million)
(; long and short scales: one hundred million)
(; 10003; short scale: one billion; long scale: one thousand million, or one milliard)
ISO: giga- (G)
(; short scale: ten billion; long scale: ten thousand million, or ten milliard)
(; short scale: one hundred billion; long scale: hundred thousand million, or hundred milliard)
(; 10004; short scale: one trillion; long scale: one billion)
ISO: tera- (T)
(; 10005; short scale: one quadrillion; long scale: one thousand billion, or one billiard)
ISO: peta- (P)
(; 10006; short scale: one quintillion; long scale: one trillion)
ISO: exa- (E)
(; 10007; short scale: one sextillion; long scale: one thousand trillion, or one trilliard)
ISO: zetta- (Z)
(; 10008; short scale: one septillion; long scale: one quadrillion)
ISO: yotta- (Y)
(; 10009; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)
(; 100010; short scale: one nonillion; long scale: one quintillion)
(; 100011; short scale: one decillion; long scale: one thousand quintillion, or one quintilliard)
(; 100012; short scale: one undecillion; long scale: one sextillion)
(; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)
(; 100014; short scale: one tredecillion; long scale: one septillion)
The Three Trillion Dollar War is a 2008 book by Nobel Prize laureate Joseph Stiglitz and Harvard Professor Linda Bilmes, both of whom are American economists.
The book examines the full cost of the Iraq War, including many hidden costs. The book also discusses the extent to which these costs will be imposed for many years to come, paying special attention to the enormous expenditures that will be required to care for very large numbers of wounded veterans. The authors conclude by illustrating the opportunity cost of the resources spent on waging the war. The book was a New York Times and international best-seller and has been translated into 22 languages.
The total cost of $3 trillion is consistent with numerous government studies. These include the Joint Economic Committee of Congress, which estimated that the war will cost $3.5 trillion, and the non-partisan Congressional Budget Office, which has projected that the total cost will reach between $1.4 and $2.2 trillion. The Stiglitz-Bilmes work builds on an earlier study by Yale economist William Nordhaus, who predicted in 2002 that the war could reach $2 trillion if it went badly. Numerous economists, including James K. Galbraith of the University of Texas and Nobel Laureate Lawrence Klein have supported the methodology in the book. Economist Fred Foldvary also wrote a positive review of the book in Econ Journal Watch. He believes better knowledge of both the budgeted and implicit costs of the war as spelled out in the book will further a more coherent dialogue on present and future related policy matters.
Alan B. Krueger argued the estimate was too high for three reasons. First, it counts future interest payments on the debt created by military spending as well as the direct expenditures, which is double counting. Second, it counts increased military recruitment costs that incorporate a premium for higher risk of death or injury and the direct cost of the deaths and injuries, which is also double counting. Third, it attributes to the war an increase in the price of oil, and loss to the American economy of almost half a trillion dollars.
Other academics, including John Lott, Richard Zerbe, and Edgar Browing, echo those criticisms, and in addition challenge the Lancet surveys of Iraq War casualties to determine the number of Iraqi deaths. Recent studies by Brown University, published online at  confirm the high costs of the war identified by Stiglitz and Bilmes.
Chronology of computation of π
The cubic metre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: m3) or cubic meter (American spelling) is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère. Another alternative name, not widely used any more, is the kilolitre.
1 cubic metre is equivalent to:
A cubic metre of pure water at the temperature of maximum density (3.98 °C) and standard atmospheric pressure (101.325 kPa) has a mass of 1,000 kg, or one tonne. At 0 °C, the freezing point of water, a cubic metre of water has slightly less mass, 999.972 kilograms.
It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, cbm when superscript characters or markup cannot be used (e.g. in some typewritten documents and postings in Usenet newsgroups).
Abbreviated CBM and cbm in the freight business and MTQ (or numeric code 49) in international trade.
See 1 E-3 m³ for a comparison with other volumes.
Global debt levels
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (). For more detailed explanations for some of these calculations, see Approximations of π.
Orders of magnitude
World-Wide Debt, Equity and Equity-related issuance reached record-breaking levels in 2003 with over $5 trillion in proceeds raised, surpassing 2001’s record of $4.4 trillion. The $5 trillion of borrowings represented 14% of the GDP flow during the year (4.938/36.3) (see world economy).
Debt issuance reported by Thomson Financial () ($ billions and number of isses).
Dollar amounts are debt owed by each sector (amounts borrowed by each sector)