Names of Large Numbers

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This is the third installment in the large numbers series. In the previous post, we  discussed about googol, a number which is 10^{100}

.  In this post, we discuss other large numbers and their names.

A Googol

Aside  from googol, names were given to other large numbers. The number 10^{googol}  or 10^{10^{100}}, for example, was named googolplex.  Some of the names of large numbers are shown in the table below.

It can be noted that there are two type of naming systems for large numbers –the short scale and the long scale. As we can see, one billion in the long scale is 10^{12} while it is only 10^9 in the short scale.

Names of Large Numbers

Name

Short Scale

Long Scale


Million

106

106

Milliard

109

Billion

109

1012

Billiard

1015

Trillion

1012

1018

Quadrillion

1015

1024

Quintillion

1018

1030

Sextillion

1021

1036

Septillion

1024

1042

Octillion

1027

1048

Nonillion

1030

1054

Decillion

1033

1060

Undecillion

1036

1066

Duodecillion

1039

1072

Tredecillion

1042

1078

Quattuordecillion

1045

1084

Quindecillion (Quinquadecillion)

1048

1090

Sexdecillion (Sedecillion)

1051

1096

Septendecillion

1054

10102

Octodecillion

1057

10108

Novemdecillion (Novendecillion)

1060

10114

Vigintillion

1063

10120

Centillion

10303

10600

Many countries use the short-scale including the United States, while Great Britain was a popular supporter of the long scale naming system.  In 1974, however, the British government adapted the short scale system, although until now, there are still organizations in Britain that use the long scale system.

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6 thoughts on “Names of Large Numbers

  1. Short scale / long scale???

    No it’s much cruder than that. Some Americans misunderstood the words for big numbers and re-defined them themselves – much as other English and European words have been misunderstood and re-defined.
    While the US invented the Trillion dollar national debt back in the 1980s, they didn’t invent a new word that coincidentally was called the trillion, just got the proper word wrong.

    That though is a normal event when languages or dialects diverge.

    With no proper billions (10 to the 12)of our own, we Brits found ourselves in the 1970s and 1980s talking about US billions (10 to the 9).
    Nowadays the Slavs and continental Europeans who kept on to their Milliards and billiards much longer are finding it easier to adapt than explain to their American bankers what a billion really is (“I want a 500 milliard bail-out please” doesn’t sound right).

    Indeed – that the rest of civilisation has found it easier to change our own numbering system than get Americans to recognise they have made a mistake tells you a great deal about the modern world :)

    PS – I’m enjoying all your blogs Guillermo. Thanks

      • No – it goes back much further than English – someone will tell us I guess.
        But the words Milliard and billiard (and old billion) have the same name and meaning in almost every European language, not just English.
        French, Portuguese, Polish, Russian I can guarantee, but I’m pretty sure most other languages too.

  2. Hate to burst the “English invented everything” bubble (and I am English!!) but …

    Billion is a French word that was invented in the C15, while million can trace French and Italian ancestry. According to dictionary.com byllion originally meant a million million, but in France this was changed to hundred thousand million, drifted across the Atlantic and never was corrected while the rest of Europe used the original meaning.

    • “but in France this was changed to hundred thousand million,” I think this isn’t quite right.
      I once talked house prices with a French girlfriend and she said all house prices in Paris were quoted in a unit but she couldn’t tell me what it was. James Bond counted his money in old french Francs for the same reason. In 1960 France devalued by a factor of 100 and a lot of numbers and money amounts got confused thereafter. Much the same happened in Poland after 1995 when a Milliard Zloties could mean a billion or 100 thousand new zloties (4 zeroes were removed in the revaluation).

      I can’t believe the US followed a French pattern as late as teh 1960s. Surely they just felt that since they had invented 10 to the power of 9 in an economic sense (if not the mathematical or economic sense), they could invent the names too.

      A favourite quote:
      There are 10^11 stars in the galaxy. That used to be a huge number. But it’s only a hundred billion. It’s less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.
      Richard Feynman
      US educator & physicist (1918 – 1988)
      (I guess 400 billion is a closer estimate now – they call it inflation. The economic number I’m told is $1,327 billion – interpret the comma and the billion either the continental way or the US way)

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