Millions, Billions and Other Large Numbers
In the modern world, we regularly encounter the words million and billion, and businesses, governments, astronomers and journalists often think in the millions, billions or even trillions. However, the word million has been around in English only since the late fourteenth century. The word billion was not introduced in the French language until the fifteenth century and didn’t find its way into English until the end of the seventeenth century, which is fairly late in the history of counting. What words were used before this time to talk about large numbers? This article looks at how we started using million and billion and how the meaning of billion has changed.
Before the Words Million and Billion
In fact, the largest number with a single-word name in ancient Greek was 10,000. It was called murios and borrowed into Late Latin as myrias. From myrias we get the English word myriad meaning “an extremely large number or amount”. The ancients also had the “myriad myriad” (10,000 × 10,000) or one hundred million. Larger numbers were described in more roundabout ways or by using mathematical notation; indeed, one million is expressed in Latin as decies centena milia or 10 × 100 × 1,000, and Archimedes (3rd century BCE) had to establish his own system of mathematical notation in order to systematically express numbers larger than the “myriad”. He explains this system in The Sand Reckoner, a treatise that sets out to quantify all the grains of sand in the universe in order to challenge the idea that such a quantity was too large to be counted.
What Exactly Is a Billion?
For those who were taught numbers before the 1970s, the answer to this question may well have been different depending on where you received your schooling. While it is accepted in English today that one billion equals 109, it is important to be aware, especially when reading older texts, that in the United Kingdom billion hasn’t always meant 109. Until the 1970s, when the United Kingdom officially adopted the American definition of billion, this word represented 1012 in British English.
This difference resulted from the emergence of two competing systems for naming large numbers. A fifteenth-century mathematician, Nicolas Chuquet, established one system by combining Latin numerical prefixes (bi-, tri-, etc.) with the suffix -illion to form powers of one million. In this system, a billion equals one million times one million (or one million squared, 1012) and a trillion equals one million cubed (1018). This is known as the long scale, which was used in the United Kingdom until they followed the United States in 1974 by officially adopting the short scale, a system born in France in the seventeenth century and popular in the French-speaking world until midway through the nineteenth century. The short scale uses the same names (billion, trillion, quadrillion, etc.) but assigns different values to them, with one billion equalling a thousand million, one trillion equalling a thousand billion, and so forth, the logic being that the prefix attached to -illion represents n in the formula 103(n+1). For example, quadrillion, with the prefix quadri- meaning “four” is equal to 103(4+1) or more simply 1015. The short scale is used today throughout the English-speaking world, whereas the French language has settled on the long scale, so that an English billion is translated in French as un milliard and a French billion (also called mille milliards or “one thousand milliards” in English) is translated in English as a trillion. The differences between the long scale and the short scale are summarized in this table:
|Number||Short Scale||Long Scale||SI* Prefix||SI Symbol|
|106||one million||one million||mega-||M|
|109||one billion||one thousand million or a milliard||giga-||G|
|1012||one trillion||one billion||tera-||T|
|1015||one quadrillion||one thousand billion||peta-||P|
|1018||one quintillion||one trillion||exa-||E|
|1021||one sextillion||one thousand trillion||zetta-||Z|
|1024||one septillion||one quadrillion||yotta-||Y|
|1027||one octillion||one thousand quadrillion|
|1030||one nonillion||one quintillion|
* SI refers to the International System (of Units), a system of measurement widely used in science and international trade.
People often wonder if there is a correct or best way to abbreviate million and billion when writing about figures.
The most commonly seen short forms for thousand, million, billion and trillion in North America and the United Kingdom, respectively, are outlined in the table below.
|Number||North America||United Kingdom||Rarer Forms|
|thousand||K||k or K||thsnd(.), M|
|million||M||m||mil(.), mill(.), mln(.), MM|
|billion||B||bn||bil(.), bill(.), bln(.)|
|trillion||T||tn||tril(.), trill(.), trn(.), tln(.)|
Notice that M appears twice in the table above, to represent both thousand and million. Some (especially older) finance texts use M for thousand and MM for million, which can be a source of confusion as M is now widely used to denote million in North America.
Of the style guides that address spacing in this context, most (AP Stylebook, Chicago Manual of Style, Canadian Style, The Economist Style Guide) say to leave no space (100bn, for example), although it is also common in books and newspaper articles to see the abbreviation preceded by a space.
Since there is no universally accepted way of abbreviating these words, the best practice is to be consistent with whatever system of short forms you choose and to ensure that the meanings of your chosen short forms are clear to your audience—for example by establishing at some point in the text that M stands for million, and so forth. Most style guides agree that it is best to spell out these words in full where possible, and to use the abbreviations where spacing is limited (e.g. in headlines and tables) or when figures are repeated often. The Guardian and The Telegraph spell out thousand, million, etc. in full when referring to people and animals and use the abbreviated forms only when discussing inanimate objects or in financial contexts. Scientific texts, on the other hand, avoid appellations like million, billion and trillion and instead use scientific notation when writing about very large and very small numbers. Scientific notation represents numbers in powers of ten, so that 650 billion can be written as 650 × 109 or as 6.50 × 1011.
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