Long and short scales

In both scales, names are given to orders of magnitude at increments of 1000. Both systems use the same names for magnitudes less than 109. Differences arise from the use of identical names for larger magnitudes. For the same magnitude name (n-illion), the value is 103n+3 in the short scale but 106n in the long scale for positive integers n. In some languages, the long scale uses additional names for the intermediate multipliers, replacing the ending -ion with -iard; for example, the next multiplier after million is milliard (109); after a billion it is billiard (1015). Hence, a long scale n-illiard equals 106n+3. The following table shows the size of first few short and long scale magnitudes. Notice how billion and trillion are in both scales but have different sizes. ==Comparison==

The following tables show the corresponding names and values of the two scales. Note that instead of using an intermediate long scale word (illiard), a quantity is sometimes specified in terms of the smaller illion word. For example, "thousand billion" instead of "billiard". The different sizes of the same name of the two scales can be described as: ==Avoiding confusion==

One way to avoid confusion between the two scales is to use positional notation. For example, 1,000,000,000,000 rather than 1 trillion (short scale) or 1 billion (long scale). This method becomes unwieldy for very large numbers. Another way is to combine unambiguous words: ten, hundred, thousand, and million. For example: one thousand million and one million million, though this also becomes unwieldy with longer numbers. Methods that are better at longer numbers include: • Scientific notation (for example 1.2), or its engineering notation variant (for example 12), or the computing variant E notation (for example 1.2e10). This is the most common practice among scientists and mathematicians, but can be cumbersome in spoken word. • SI metric prefixes. For example, giga for 109 and tera for 1012 can give gigawatt (109 W) and terawatt (1012 W). ==History==

Although this situation has been developing since the 1200s, the first recorded use of the terms short scale () and long scale () was by the French mathematician Geneviève Guitel in 1975. whereas the United States used the short scale, and it is used for all official purposes. The British usage and American usage are now identical. 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, Spanish billón, German Billion, Dutch biljoen, Danish billion, Swedish biljon, Finnish biljoona, Slovenian bilijon, Polish bilion, and European Portuguese word bilião (with a different spelling to the Brazilian Portuguese variant, but in Brazil referring to short scale) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 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 Welsh word biliwn all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 British English word billion (109 in the short scale). The term billion originally meant 1012 when introduced. The word milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is not found 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, unlike the term billion, it is internationally unambiguous and phonetically distinct from million. Likewise, many long scale countries use the word billiard (or similar) for one thousand long scale billions (i.e., 1015), and the word trilliard (or similar) for one thousand long scale trillions (i.e., 1021), etc. ;Timeline ==Current usage==

Short scale users English-speaking Most English-language countries and regions use the short scale with 109 being billion. For example: • 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. Dutch-speaking Most Dutch-language countries and regions use the long scale with 109 = . French-speaking Most French-language countries and regions use the long scale with 109 = , for example: (, ). There are ambiguities for numbers above 1012. • (, ) • (French: , ; German: , ; Italian: , ; Romansh: , ) Using both Some countries use either the short or long scales, depending on the internal language being used or the context. Using neither The following countries use naming systems for large numbers that are not etymologically related to the short and long scales: By continent The long and short scales are both present on most continents, with usage dependent on the language used. For example: Notes on current usage Short scale Long scale Both long and short scale Neither long nor short scale ==See also==