# Names of large numbers

Names of large numbers are the words English and other languages use for powers of ten beyond a thousand, such as million, billion, and trillion. In English these names are coined from the Latin names for small numbers n by adding the ending -illion, a pattern suggested by the word million; billion and trillion come from the Latin prefixes bi- (n = 2) and tri- (n = 3).<sup>[1](https://ibiblio.org/units/large.html)</sup> The same word can mean different values depending on the naming scale in use, which is the central complication in the subject.

| Key fact | Detail |
|---|---|
| Naming rule (short scale) | The name coined from Latin number n applies to \( 10^{3n+3} \); billion (n = 2) is \( 10^{9} \), trillion (n = 3) is \( 10^{12} \)<sup>[1](https://ibiblio.org/units/large.html)</sup> |
| Short vs long scale | 10<sup>9</sup> is billion (short) or milliard (long); 10<sup>12</sup> is trillion (short) or billion (long); 10<sup>18</sup> is quintillion (short) or trillion (long)<sup>[2](https://pages.stern.nyu.edu/~gsimon/C220103Page/ClassNotes/DecimalPoint.pdf)</sup> |
| Zero-count formula | In the short scale a name for n has \( 3(n+1) \) zeros, so trillion (n = 3) has 12 zeros<sup>[3](https://num8ers.com/large-numbers-names/)</sup> |
| Earliest trace | Byllion appears in Nicolas Chuquet's unpublished *Le Triparty en la Science des Nombres* (1484), copied by De la Roche in 1520; trillion entered English in the 1680s<sup>[4](https://www.etymonline.com/word/trillion)</sup> |
| SI alternative | The SI provides prefixes for decimal multiples and submultiples from \( 10^{24} \) to \( 10^{-24} \)<sup>[5](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)</sup> |
| Indian system | 100,000 (1 lakh) = \( 10^{5} \) = 100,000; 10 million (1 crore) = \( 10^{7} \) = 10,000,000<sup>[3](https://num8ers.com/large-numbers-names/)</sup> |
| Historical depth | India had names for numbers well beyond a billion before the 3rd century; the ancient Greeks had no name above ten thousand and the Romans none above a hundred thousand<sup>[4](https://www.etymonline.com/word/trillion)</sup> |

## The -illion system and the two scales

The English names follow a single construction: take the Latin name for a small number n and add -illion. In the American, or short scale, system the resulting name applies to \( 10^{3n+3} \), so billion is \( 10^{9} \) and trillion is \( 10^{12} \).<sup>[1](https://ibiblio.org/units/large.html)</sup> A quick way to recover the value is to count zeros: a short-scale name for n has \( 3(n+1) \) zeros, which is why trillion, with n = 3, has \( 3 \times 4 = 12 \) zeros.<sup>[3](https://num8ers.com/large-numbers-names/)</sup>

The long scale, used in other European countries, groups powers of ten in multiples of 6 rather than 3, so the name coined from n applies to \( 10^{6n} \).<sup>[3](https://num8ers.com/large-numbers-names/)</sup> The two scales diverge after a million, and the divergent words are the source of most confusion:

| Value | Short scale | Long scale |
|---|---|---|
| \( 10^{6} \) | million | million |
| \( 10^{9} \) | billion | milliard |
| \( 10^{12} \) | trillion | billion |
| \( 10^{15} \) | quadrillion | billiard |
| \( 10^{18} \) | quintillion | trillion |

<sup>[2](https://pages.stern.nyu.edu/~gsimon/C220103Page/ClassNotes/DecimalPoint.pdf)</sup>

The long scale is closer to the etymology, since a long-scale billion (\( 10^{12} \)) really is a million millions, matching the bi- prefix; the short-scale billion (\( 10^{9} \)) does not. The U.S. sense is nonetheless reported as increasingly common in British technical writing.<sup>[4](https://www.etymonline.com/word/trillion)</sup>

## History

The -illion words trace to France. The word later borrowed as trillion comes from French billion, originally byllion in Nicolas Chuquet's unpublished manuscript *Le Triparty en la Science des Nombres* of 1484, which was copied by De la Roche in 1520; the English word trillion is attested from the 1680s.<sup>[4](https://www.etymonline.com/word/trillion)</sup>

Named large numbers are far older outside Europe. In the West, -illion-style names were used mainly by mathematicians until the 16th century, but India had names, rooted in its own numbering tradition, for numbers well beyond a billion before the 3rd century.<sup>[4](https://www.etymonline.com/word/trillion)</sup> [Ancient Greek](https://www.edgepedia.org/ancient-greek) had no name for a number greater than ten thousand, and Latin none higher than a hundred thousand.<sup>[4](https://www.etymonline.com/word/trillion)</sup>

## The Indian numbering system

India, Pakistan, Bangladesh, and Nepal use a distinct grouping system built on the words lakh and crore: 100,000 (1 lakh) equals \( 10^{5} \) (100,000) and 10 million (1 crore) equals \( 10^{7} \) (10,000,000).<sup>[3](https://num8ers.com/large-numbers-names/)</sup>

## SI prefixes and scientific notation

For measurement, the SI replaces number names with prefixes attached to units. The current system provides decimal multiples and submultiples from \( 10^{24} \) to \( 10^{-24} \).<sup>[5](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)</sup> Prefix symbols can neither stand alone nor be attached to the number 1, and the kilogram is the only coherent SI unit whose name and symbol include a prefix, a historical accident.<sup>[5](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)</sup> Style guides recommend choosing a prefix so the numerical value falls between 0.1 and 1000, as in 62 kW rather than 62,000 W, and using only one prefix at a time.<sup>[6](https://www.ashrae.org/technical-resources/publications-library/ashrae-handbook/the-si-guide)</sup>

[Scientific notation](https://www.edgepedia.org/scientific-notation) handles the same need for counts and pure numbers: a number is written as a factor times a power of ten, so 3,560,000 becomes \( 3.56 \times 10^{6} \).<sup>[7](https://www.nlr.gov/comm-standards/editorial/scientific-notation)</sup> Large-number names survive mainly in popular science and news writing for general audiences, while scientific journals use \( 10^{n} \) notation, in part because the names are ambiguous across scales.<sup>[8](https://library.fridoverweij.com/docs/arithmetic/scientific_notation.html)</sup><sup> • </sup><sup>[3](https://num8ers.com/large-numbers-names/)</sup>

## Why the scales matter

The practical consequence of the two scales is that a number written in words can differ by a factor of 1000 between traditions: a European reading "billion" in an older British text understands \( 10^{12} \), while an American reader understands \( 10^{9} \).<sup>[2](https://pages.stern.nyu.edu/~gsimon/C220103Page/ClassNotes/DecimalPoint.pdf)</sup> Both systems group digits in threes, mirroring comma placement, but assign names at different intervals, short scale every three powers of ten and long scale every six.<sup>[3](https://num8ers.com/large-numbers-names/)</sup> For unambiguous work, scientific notation and SI prefixes avoid the problem entirely, which is why technical writing favors them.<sup>[7](https://www.nlr.gov/comm-standards/editorial/scientific-notation)</sup>

## References

1. [Large Numbers, ibiblio.org (Russ Rowlett, University of North Carolina)](https://ibiblio.org/units/large.html)
2. [Get It Right: decimal point and number names, NYU Stern class notes](https://pages.stern.nyu.edu/~gsimon/C220103Page/ClassNotes/DecimalPoint.pdf)
3. [Large Number Names Chart: What Comes After Trillion?, NUM8ERS](https://num8ers.com/large-numbers-names/)
4. [Trillion, Etymology, Origin & Meaning, Online Etymology Dictionary](https://www.etymonline.com/word/trillion)
5. [NIST Special Publication 330, Section 3: SI prefixes](https://www.nist.gov/pml/special-publication-330/sp-330-section-3)
6. [The SI Guide, ASHRAE Handbook](https://www.ashrae.org/technical-resources/publications-library/ashrae-handbook/the-si-guide)
7. [Scientific notation, Communication Standards, NLR](https://www.nlr.gov/comm-standards/editorial/scientific-notation)
8. [Arithmetic: Scientific notation, Frido Verweij library docs](https://library.fridoverweij.com/docs/arithmetic/scientific_notation.html)

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*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Numbers and algebra › Arithmetic and number systems › Integer sequences and partitions › Special and named integers › Named large numbers and number naming systems*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*

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