Names of large numbers

For very large values, the text is generally shorter than a decimal numeric representation although longer than scientific notation.

[1] English also has words, such as zillion, that are used informally to mean large but unspecified amounts.

Some names of large numbers, such as million, billion, and trillion, have real referents in human experience, and are encountered in many contexts, particularly in finance and economics.

At times, the names of large numbers have been forced into common usage as a result of hyperinflation.

[13] In global economics, the name of a significantly larger number was used in 2024, when the Russian news outlet RBK stated that the sum of legal claims against Google in Russia totalled 2 undecillion (2×1036) rubles, or US $20 decillion (US $2×1034); a value worth more than all financial assets in the world combined.

Even well-established names like sextillion are rarely used, since in the context of science, including astronomy, where such large numbers often occur, they are nearly always written using scientific notation.

In this notation, powers of ten are expressed as 10 with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is 1.3×1045 joules."

In some cases, specialized units are used, such as the astronomer's parsec and light year or the particle physicist's barn.

Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one way people try to conceptualize and understand them.

One of the earliest examples of this is The Sand Reckoner, in which Archimedes gave a system for naming large numbers.

One motivation for such a pursuit is that attributed to the inventor of the word googol, who was certain that any finite number "had to have a name".

[citation needed] Most names proposed for large numbers belong to systematic schemes which are extensible.

[citation needed] The words bymillion and trimillion were first recorded in 1475 in a manuscript of Jehan Adam.

At the same time that he suggested "googol" he gave a name for a still larger number: "googolplex".

A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out.

This is a description of what would happen if one tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance.

The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it.John Horton Conway and Richard K. Guy[17] have suggested that N-plex be used as a name for 10N.

[citation needed] This section illustrates several systems for naming large numbers, and shows how they can be extended past vigintillion.

Due to its dominance in the financial world (and by the US dollar), this was adopted for official United Nations documents.

Concerning names ending in -illiard for numbers 106n+3, milliard is certainly in widespread use in languages other than English, but the degree of actual use of the larger terms is questionable.

The naming procedure for large numbers is based on taking the number n occurring in 103n+3 (short scale) or 106n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion.

[17] The following table shows number names generated by the system described by Conway and Guy for the short and long scales.

[18] The International System of Quantities (ISQ) defines a series of prefixes denoting integer powers of 1024 between 10241 and 10248.