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What differentiates the long and short numbering scales

There are numerous systems for naming and annotating long numbers and the most popular of these are known as long scale and short scale . The long scale is based on powers of one million , while the short scale is based on powers of one thousand .

For example, one million (1 followed by six zeros) on the short scale is understood as 1000 × 1000 1 , while on the long scale it is understood as 1000000 1 . Similarly, a trillion would be represented as 1000 × 1000 2 and would be equal to 1000 × 1000000 1 (billion) on the long scale.

General description

For whole numbers less than one billion (<10 9 ), the two scales are identical but diverge from this figure:

  • Short scale : each new name in the numerical scale above one million (10 6 ) is a thousand times greater than the previous one . Thus, one trillion is one billion (10 9 ), one trillion is one trillion (10 12 ), etc.
  • Long scale : each new name in the numerical scale above one million (10 6 ) is 1 million times greater than the previous one . Thus, one trillion is 1 million million (10 12 ), one trillion is 1 million trillion (10 18 ), etc.

Example: 10 9 is 1 trillion on the short scale or 1 trillion on the long scale. 10 12 are one trillion on the short scale or 1 trillion on the long scale.

 

Comparative table between long scale and short scale
Scientific notationPositional notationShort scaleLong scale
10 01OneOne
10 110TenTen
10 2100HundredHundred
10 31 000One thousandOne thousand
10 61 000 000 000Million (1000 × 1000 1 )Million (1000000 1 )
10 91 000 000 000 000Billion (1000 × 1000 2 )Billion or billion (1000 × 1000000 1 )
10 121 000 000 000 000 000Trillion (1000 × 1000 3 )Billion (1000000 2 )
10 151 000 000 000 000 000 000Quadrillion (1000 × 1000 4 )Thousand billions (1000 × 1000000 2 )
10 181 000 000 000 000 000 000 000Quintillón (1000 × 1000 5 )Trillion (1000000 3 )
10 211 000 000 000 000 000 000 000 000Sextillion (1000 × 1000 6 )One thousand trillion (1000 × 1000000 3 )
10 241 000 000 000 000 000 000 000 000 000Septillion (1000 × 1000 7 )Quadrillion (1000000 5 )

Use by countries

The long scale is the most used in continental Europe and in most countries of South and Central America, with exceptions such as Puerto Rico or Brazil.

The short scale is used in most English and Arabic speaking countries. Also in many other countries, for example Brazil and Russia.

Japan, China, India and other Southeast Asian countries use a different nomenclature system. In Africa there are many countries that use the short scale and there are also many that use the long scale.

 

The decimal separator

In addition to the long scale and the short scale, a decimal separator different from that of other countries is used in many countries that are culturally or geographically related .

 

The three most used decimal separators are the period, the comma and the momayyez (comma at half height «.»):

  • The point is used in most English-speaking countries, in Mexico, China, Egypt and other African countries. Ex: 1.5
  • The comma is used in South America, Europe, Russia, Central Asia and many countries in Africa. Ex: 1,5
  • The momayyez is used in the countries of Arabia, Iran and in general in the countries of the Arab world. Ex: 10.5

In the International System of Units, the period and comma are admitted , as in the ISO 80000-1 standards . From the Association of Academies of the Spanish Language, both are also admitted, but the adoption of the point with the aim of standardization is recommended.

Neither a period nor a comma are allowed in any of these norms as separators between other numbers that are not between the whole part and the decimals. To separate the thousands and other figures it is recommended not to use any symbol , or to leave a space between figures to improve the reading if necessary in very long numbers: for example 10 000.5 (ten thousand and five tenths).

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