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Long and short scales AI simulator
(@Long and short scales_simulator)
Hub AI
Long and short scales AI simulator
(@Long and short scales_simulator)
Long and short scales
The long and short scales are two powers of ten number naming systems that are consistent with each other for smaller numbers, but are contradictory for larger numbers. Other numbering systems, particularly in East Asia and South Asia, have large number naming that differs from both the long and the short scales. Such numbering systems include the Indian numbering system and Chinese, Japanese, and Korean numerals. Much of the remainder of the world has adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking. Use of the short scale is found in most English-speaking and Arabic-speaking countries, most Eurasian post-communist countries, and Brazil.
For powers of ten less than 9 (one, ten, hundred, thousand, and million), the short and long scales are identical; but, for larger powers of ten, the two systems differ in confusing ways. For identical names, the long scale grows by multiples of one million (106), whereas the short scale grows by multiples of one thousand (103). For example, the short scale billion is one thousand million (109), whereas in the long scale, billion is one million million (1012), making the word 'billion' a false friend between long- and short-scale languages. The long scale system includes additional names for interleaved values, typically replacing the word-ending '-ion' with '-iard'.
To avoid confusion, the International System of Units (SI) recommends using the metric prefixes to indicate magnitude. For example, giga- is always 109, which is 'billion' in short scale but 'milliard' in long scale.
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.
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".
Long and short scales
The long and short scales are two powers of ten number naming systems that are consistent with each other for smaller numbers, but are contradictory for larger numbers. Other numbering systems, particularly in East Asia and South Asia, have large number naming that differs from both the long and the short scales. Such numbering systems include the Indian numbering system and Chinese, Japanese, and Korean numerals. Much of the remainder of the world has adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking. Use of the short scale is found in most English-speaking and Arabic-speaking countries, most Eurasian post-communist countries, and Brazil.
For powers of ten less than 9 (one, ten, hundred, thousand, and million), the short and long scales are identical; but, for larger powers of ten, the two systems differ in confusing ways. For identical names, the long scale grows by multiples of one million (106), whereas the short scale grows by multiples of one thousand (103). For example, the short scale billion is one thousand million (109), whereas in the long scale, billion is one million million (1012), making the word 'billion' a false friend between long- and short-scale languages. The long scale system includes additional names for interleaved values, typically replacing the word-ending '-ion' with '-iard'.
To avoid confusion, the International System of Units (SI) recommends using the metric prefixes to indicate magnitude. For example, giga- is always 109, which is 'billion' in short scale but 'milliard' in long scale.
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.
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".