Names of large numbers

How do you describe something so vast it defies ordinary counting? From atoms in a human body to grains of sand on a cosmic scale, we often encounter quantities so immense they need special names. While science leans on concise notation, our everyday language has developed elaborate and sometimes confusing systems to tackle these colossal figures. Large numbers are named using two primary systems, the 'short scale' and the 'long scale,' leading to significant numerical differences across regions. Beyond a trillion, named numbers are rarely used in practical science, which prefers the clarity and precision of scientific notation. The intellectual fascination with naming unimaginably vast numbers has a rich history, from ancient Greek mathematicians to playful modern coinages like the 'googol.'

Source: Wikipedia

AI Summary

Large numbers are named using two primary systems, the 'short scale' and the 'long scale,' leading to significant numerical differences across regions.
Beyond a trillion, named numbers are rarely used in practical science, which prefers the clarity and precision of scientific notation.
The intellectual fascination with naming unimaginably vast numbers has a rich history, from ancient Greek mathematicians to playful modern coinages like the 'googol.'

Naming the Unimaginable

For millennia, humans have felt the need to quantify the world around them—and sometimes, the numbers involved are truly staggering. While our early counting systems sufficed for everyday tasks, describing immense quantities required a new linguistic toolkit. This is where the fascinating world of large number names begins, bridging the gap between simple digits and the edge of infinity.

Short vs. Long: A Tale of Two Scales

The biggest source of confusion in naming large numbers stems from two different systems that have evolved across Europe: the 'short scale' and the 'long scale.' Think of them as different rhythmic approaches to grouping zeroes, and this difference dictates whether a 'billion' is a modest sum or an astronomical one.

In the short scale, a new name is assigned for every group of three zeroes. So, a million is 10^6, a billion is 10^9 (a thousand millions), a trillion is 10^12 (a thousand billions), and so on. This system is widely adopted in American English, modern British English, and many other parts of the world.

The mathematical pattern for the short scale, where 'n' corresponds to the Latin prefix used (e.g., n=1 for million, n=2 for billion, n=3 for trillion), clearly shows this triennial progression. Each step up the 'illion' ladder adds three more zeroes to the number.

\text{Value} = 10^{3n+3} \quad (\text{for n-illion, short scale})

The long scale, by contrast, assigns a new main name for every group of six zeroes. Here, a million is 10^6, but a billion is 10^12 (a million millions), and a trillion is 10^18 (a million billions). Intermediate values, like 10^9 (a thousand millions), often receive special names such as 'milliard'.

This system, where 'n' again relates to the Latin prefix, primarily groups numbers by powers of a million. It is still dominant in much of continental Europe, including French, German, and Spanish-speaking countries, and significantly impacts how large numbers are understood globally.

\text{Value} = 10^{6n} \quad (\text{for n-illion, long scale})

This difference creates more than just a linguistic curiosity. A 'billion' in the United States (10^9) is a thousand times smaller than a 'billion' in Germany (10^12). So, when you hear that an adult human body contains approximately 7.1 octillion atoms, that staggering figure only makes sense if you know it's being stated in the short scale!

When Words Fail: Scientific Notation

While these named numbers give us a sense of scale, for truly gargantuan quantities—the kind found in astronomy, physics, or particle science—words often fall short. The names become cumbersome, difficult to remember, and, as we've seen, potentially ambiguous across different language conventions.

This is where scientific notation shines. Instead of struggling with a 'quattuordecillion,' scientists simply express numbers as a coefficient multiplied by a power of ten, like 1.3 × 10^45 joules. It's unambiguous, universally understood, and far easier to say and write than a mouthful of Latin-derived prefixes.

N \times 10^a

When a number like 10^45 needs to be spoken, it's typically read as 'ten to the forty-fifth power' or simply 'ten to the forty-five.' This concise approach prioritizes clarity and precision over poetic naming, especially when dealing with magnitudes like the X-ray emission of a galaxy.

For certain quantities, specialized units or SI prefixes are used. We say 'femtosecond' rather than 'one quadrillionth of a second,' or measure cosmic distances in 'light-years' and 'parsecs.' These are carefully defined units designed to simplify the expression of incredibly large or small magnitudes within specific scientific domains.

The Roots of Our 'Illions'

The familiar names like 'million,' 'billion,' and 'trillion' largely stem from combining Latin numerical roots with the suffix '-illion.' Each prefix—like 'bi' for two, 'tri' for three, 'quadra' for four—indicates the position or power of the number in its respective scale. This systematic approach allows for creating names for increasingly larger quantities.

The system of Latin-derived prefixes can theoretically extend far beyond what most standard dictionaries list. Mathematicians John Horton Conway and Richard K. Guy even devised a comprehensive system using Latin roots for units, tens, and hundreds, allowing for the construction of names for numbers like a 'centillion' (10^303 in the short scale).

Other Counting Systems

While the 'illion' systems prevail in many Western languages, other cultures have developed unique methods for naming large numbers. The Indian numbering system, for instance, uses names like 'lakh' (10^5, or one hundred thousand) and 'crore' (10^7, or ten million), defining values at different powers of ten than either the short or long scales.

And then there are the numbers we use informally—words like 'zillion,' 'gazillion,' or 'bazillion.' These aren't precise mathematical terms, of course, but they perfectly convey the idea of 'a very, very large, unspecified amount' without needing to commit to an exact, sometimes complicated, numerical value.

Historic Attempts to Name the Vast

Long before modern scientific notation, ancient thinkers grappled with naming the truly immense. Archimedes, the great Greek mathematician, famously tackled this in his work 'The Sand Reckoner.' He devised an ingenious system to name numbers large enough to count all the grains of sand in the known universe, ultimately estimating this at no more than 10^63.

Archimedes' system started by naming numbers up to a 'myriad myriad' (10^8) as 'first numbers.' He then used 10^8 as the 'unit of the second numbers,' creating a hierarchical structure to construct truly enormous numbers, demonstrating an early conceptual understanding of exponents and powers.

(10^8)^{(10^8)} = 10^{8 \cdot 10^8}

The very roots of our modern 'illion' names can be traced back to 15th-century Europe. Figures like Jehan Adam and Nicolas Chuquet, a French mathematician, documented and perhaps even helped standardize the use of terms like 'bymillion' and 'tryllion,' initially referring to powers of a million in what would become the long scale.

The Curious Case of the Googol

Not all large numbers are named by academic decree; some arise from pure imagination! The terms 'googol' and 'googolplex' were famously coined in 1940 by Edward Kasner's nine-year-old nephew, Milton Sirotta, when asked to think up a name for a very, very big number.

Milton defined a 'googol' as a 1 followed by one hundred zeroes. But he didn't stop there. He then proposed an even larger number: a 'googolplex,' which he originally described as a 1 followed by writing zeroes until you got tired. Kasner later refined this to be a precise, finite number: 1 followed by a googol zeroes.

\text{googol} = 10^{100}

The sheer scale of a googolplex is almost incomprehensible. Even if every atom in the observable universe were a zero, you couldn't write it out. It's a number that truly pushes the boundaries of our ability to visualize magnitude, yet it remains a finite, precisely defined entity.

\text{googolplex} = 10^{\text{googol}} = 10^{10^{100}}

These playfully named numbers have found a lasting place in popular culture, most notably inspiring the name of the tech giant Google, whose founders chose the name to reflect the immense amount of information their search engine would organize. Its corporate headquarters? The 'Googleplex,' of course.

The fascination doesn't end there. 'Googologists'—enthusiasts of large numbers—have proposed extensions like 'googolplexplex' (10^googolplex) and even 'giggol,' a number so vast it uses tetration, a hyper-operation far beyond simple exponentiation. These names, while not widely adopted, show our endless curiosity about the frontiers of quantity.

When the Numbers Get Real

While scientific notation reigns supreme for precise measurements, named large numbers sometimes appear in real-world contexts, particularly during periods of extreme hyperinflation. Hungary, for instance, once printed a 1 sextillion pengő banknote, a sum so vast it underscored the collapse of their currency.

More recently, in 2024, a Russian news outlet cited legal claims against Google totaling 2 undecillion rubles (2 × 10^36), a value so astronomically large that it was explicitly stated to be purely symbolic—far exceeding all financial assets in the world combined. Such numbers truly highlight the abstract nature of value when it reaches such heights.

Ultimately, the naming of large numbers reflects a deep human fascination—an intellectual curiosity that drives us to conceptualize and grasp the truly immense. Whether through ancient systems, modern conventions, or playful coinages, we continue to explore the outer limits of what can be counted and named.

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Names of large numbers

Depending on context (e.g. language, culture, region), some large numbers have names that allow for describing large quantities in a textual, not mathematical, form. For very large values, the text is generally shorter than a decimal numeric representation, although longer than scientific notation.

Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in the Americas. These naming procedures are 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.

Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as 10 with a numeric superscript. However, these somewhat rare names are considered acceptable for approximate statements. For example, the statement "There are approximately 7.1 octillion atoms in an adult human body" is understood to be in short scale of the table below (and is only accurate if referring to short scale rather than long scale).

The Indian numbering system uses the named numbers common between the long and short scales up to ten thousand. For larger values, it includes named numbers at each multiple of 100, including lakh (105) and crore (107).

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

Standard dictionary numbers

Names of large numbers

<table><thead><tr><th>x</th><th>Name (SS/LS, LS)</th><th>SS (103x+3)</th><th>LS (106x, 106x+3)</th><th>Appearance in different dictionaries</th></tr></thead><tbody><tr><td>AHD4</td><td>CED</td><td>COD</td><td>MW</td><td>OED</td><td>RHD2</td><td>SOED3</td><td>W3</td><td>HM</td></tr><tr><td>1</td><td>million</td><td>106</td><td>106</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td></td><td>milliard</td><td></td><td>109</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td></tr><tr><td>2</td><td>billion</td><td>109</td><td>1012</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>3</td><td>trillion</td><td>1012</td><td>1018</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>4</td><td>quadrillion</td><td>1015</td><td>1024</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>5</td><td>quintillion</td><td>1018</td><td>1030</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>6</td><td>sextillion</td><td>1021</td><td>1036</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>7</td><td>septillion</td><td>1024</td><td>1042</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>8</td><td>octillion</td><td>1027</td><td>1048</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>9</td><td>nonillion</td><td>1030</td><td>1054</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>10</td><td>decillion</td><td>1033</td><td>1060</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>11</td><td>undecillion</td><td>1036</td><td>1066</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>12</td><td>duodecillion</td><td>1039</td><td>1072</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>13</td><td>tredecillion</td><td>1042</td><td>1078</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>14</td><td>quattuordecillion</td><td>1045</td><td>1084</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>15</td><td>quindecillion</td><td>1048</td><td>1090</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>16</td><td>sexdecillion</td><td>1051</td><td>1096</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>17</td><td>septendecillion</td><td>1054</td><td>10102</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>18</td><td>octodecillion</td><td>1057</td><td>10108</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>19</td><td>novemdecillion</td><td>1060</td><td>10114</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td></tr><tr><td>20</td><td>vigintillion</td><td>1063</td><td>10120</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>100</td><td>centillion</td><td>10303</td><td>10600</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td></tr></tbody></table>

• Short scale: US, English Canada, modern British, Australia, and Eastern Europe • Long scale: French Canada, older British, Western & Central Europe

Apart from million, the words in this list ending with -illion are all derived by adding prefixes (bi-, tri-, etc., derived from Latin) to the stem -illion. Centillion appears to be the highest name ending in -illion that is included in these dictionaries. Trigintillion, often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern (unvigintillion, duovigintillion, duoquinquagintillion, etc.).

<table><thead><tr><th>Name</th><th>Value</th><th>Authorities</th></tr></thead><tbody><tr><td>AHD4</td><td>CED</td><td>COD</td><td>MW</td><td>OED</td><td>RHD2</td><td>SOED3</td><td>W3</td><td>HM</td></tr><tr><td>googol</td><td>10100</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>googolplex</td><td>10googol (1010100)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></tbody></table>

All of the dictionaries included googol and googolplex, generally crediting it to the Kasner and Newman book and to Kasner's nephew (see below). None include any higher names in the googol family (googolduplex, etc.). The Oxford English Dictionary comments that googol and googolplex are "not in formal mathematical use".

Usage of names of large numbers

Names of large numbers

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. The highest numerical value banknote ever printed was a note for 1 sextillion pengő (1021 or 1 milliárd bilpengő as printed) printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion (1014) Zimbabwean dollar note, which at the time of printing was worth about US$30. 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. A Kremlin spokesperson, Dmitry Peskov, stated that this value was symbolic.

Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of how large numbers are named. 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." When a number such as 1045 needs to be referred to in words, it is simply read out as "ten to the forty-fifth" or "ten to the forty-five". This is easier to say and less ambiguous than "quattuordecillion", which means something different in the long scale and the short scale.

When a number represents a quantity rather than a count, SI prefixes can be used—thus "femtosecond", not "one quadrillionth of a second"—although often powers of ten are used instead of some of the very high and very low prefixes. 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. To do this, he called the numbers up to a myriad myriad (108) "first numbers" and called 108 itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad myriad times, 108·108=1016. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad myriad times the unit of the 108-th numbers, i.e. ${\displaystyle (10^{8})^{(10^{8})}=10^{8\cdot 10^{8}},}$ and embedded this construction within another copy of itself to produce names for numbers up to ${\displaystyle ((10^{8})^{(10^{8})})^{(10^{8})}=10^{8\cdot 10^{16}}.}$ Archimedes then estimated the number of grains of sand that would be required to fill the known universe, and found that it was no more than "one thousand myriad of the eighth numbers" (1063).

Origins of the "standard dictionary numbers"

Names of large numbers

The words bymillion and trimillion were first recorded in 1475 in a manuscript of Jehan Adam. Subsequently, Nicolas Chuquet wrote a book Triparty en la science des nombres which was not published during Chuquet's lifetime. However, most of it was copied by Estienne de La Roche for a portion of his 1520 book, L'arismetique. Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment:

Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point tryllion Le quart quadrillion Le cinqe quyllion Le sixe sixlion Le sept.e septyllion Le huyte ottyllion Le neufe nonyllion et ainsi des ault's se plus oultre on vouloit preceder

(Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go).

Adam and Chuquet used the long scale of powers of a million; that is, Adam's bymillion (Chuquet's byllion) denoted 1012, and Adam's trimillion (Chuquet's tryllion) denoted 1018.

Googol family

Names of large numbers

The names googol and googolplex were invented by Edward Kasner's nephew Milton Sirotta and introduced in Kasner and Newman's 1940 book Mathematics and the Imagination in the following passage:

The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with one hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. 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. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. 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.

<table><thead><tr><th>Value</th><th>Name</th><th>Authority</th></tr></thead><tbody><tr><td>10100</td><td>googol</td><td>Kasner and Newman, dictionaries (see above)</td></tr><tr><td>10googol = 1010100</td><td>googolplex</td><td>Kasner and Newman, dictionaries (see above)</td></tr></tbody></table>

John Horton Conway and Richard K. Guy have suggested that N-plex be used as a name for 10N. This gives rise to the name googolplexplex for 10googolplex = 101010100, which is unofficially known as a googolplexian (or googolduplex) by some googologists. Conway and Guy have proposed that N-minex be used as a name for 10−N, giving rise to the name googolminex for the reciprocal of a googolplex, which is written as 10−(10100). None of these names are in wide use.

A googologist from Texas coined the term giggol for a tetrational number. Giggol is equal to ${\displaystyle {10\uparrow \uparrow 100}}$, or 10 tetrated to 100. If it is written in exponentiation, then it would be a power tower of 100 tens. It was coined by altering the vowel sound of "googol".

The names googol and googolplex inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.

Extensions of the standard dictionary numbers

Names of large numbers

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

Traditional British usage assigned new names for each power of one million (the long scale): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; and so on. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet.

Traditional American usage (which was also adapted from French usage but at a later date), Canadian, and modern British usage assign new names for each power of one thousand (the short scale). Thus, a billion is 1000 × 10002 = 109; a trillion is 1000 × 10003 = 1012; and so forth. Due to its dominance in the financial world (along with the US dollar), this was adopted for official United Nations documents.

Traditional French usage has varied; in 1948, France, which had originally popularized the short scale worldwide, reverted to the long scale.

The term milliard is unambiguous and always means 109. It is seldom seen in American usage and rarely in British usage, but frequently in continental European usage. The term is sometimes attributed to French mathematician Jacques Peletier du Mans c. 1550 (for this reason, the long scale is also known as the Chuquet-Peletier system), but the Oxford English Dictionary states that the term derives from post-Classical Latin term milliartum, which became milliare and then milliart and finally our modern term.

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 terms "milliardo" in Italian, "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish, and "миллиард", milliard (transliterated) in Russian, are standard usage when discussing financial topics.

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. If the final root is multisyllabic and ends in a vowel, that vowel is removed; for example, centi + illion = centillion, not centiillion. Monosyllabic final roots ending in vowels only occur when the naming system does not apply, for very small numbers (million, billion, and sextillion), so they do not have defined behavior. The number "0" is skipped, i.e. it produces the empty string - 103 results in the root for units 3 followed by the root for hundreds 1. In this way, numbers up to 103·999+3 = 103000 (short scale) or 106·999 = 105994 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 9 or smaller. For larger n (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy. Today, sexdecillion and novemdecillion are standard dictionary numbers and, using the same reasoning as Conway and Guy did for the numbers up to nonillion, could probably be used to form acceptable prefixes. The Conway–Guy system for forming prefixes:

<table><thead><tr><th></th><th>Units</th><th>Tens</th><th>Hundreds</th></tr></thead><tbody><tr><td>0</td><td></td><td></td><td></td></tr><tr><td>1</td><td>Un</td><td>NDeci</td><td>NXCenti</td></tr><tr><td>2</td><td>Duo</td><td>MSViginti</td><td>NDucenti</td></tr><tr><td>3</td><td>TreS</td><td>NSTriginta</td><td>NSTrecenti</td></tr><tr><td>4</td><td>Quattuor</td><td>NSQuadraginta</td><td>NSQuadringenti</td></tr><tr><td>5</td><td>Quinqua3</td><td>NSQuinquaginta</td><td>NSQuingenti</td></tr><tr><td>6</td><td>SeSX</td><td>NSexaginta</td><td>NSescenti</td></tr><tr><td>7</td><td>SepteMN</td><td>NSeptuaginta</td><td>NSeptingenti</td></tr><tr><td>8</td><td>Octo</td><td>MXOctoginta</td><td>MXOctingenti</td></tr><tr><td>9</td><td>NoveMN</td><td>Nonaginta</td><td>Nongenti</td></tr></tbody></table>

• When preceding a component prefixed with S or X, a component suffixed with S - "tre" - suffixes with an s ("tres") and a component suffixed with SX - "se" - suffixes to match the prefix ("ses" or "sex"). • When preceding a component prefixed with M or N, a component suffixed with MN - "septe" and "nove" - suffixes to match the prefix ( "septem" and "novem" or "septen" and "noven"). • ^ Conway and Guy originally used "quinqua" but as a result of Miakinen's suggestion "quin" is mostly used.

The Conway–Guy system disagrees with some standard dictionary names, like "quindecillion", "sexdecillion", and "novemdecillion". Oliver Miakinen argued that since "quindecillion" is a widely accepted term, and the Latin for 15 is actually quindecim and not quinquadecim, the prefix "quinqua-" should be replaced with "quin-". This new prefix is more commonly used nowadays.

Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 106,000,258, Conway and Guy co-devised with Allan Wechsler the following set of consistent conventions that permit, in principle, the extension of this system indefinitely to provide English short-scale names for any integer whatsoever. The name of a number 103n+3, where n is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 103m+3, where m represents each group of comma-separated digits of n, with each but the last "-illion" trimmed to "-illi-", or, in the case of m = 0, either "-nilli-" or "-nillion". For example, 103,000,012, the 1,000,003rd "-illion" number, equals one "millinillitrillion"; 1033,002,010,111, the 11,000,670,036th "-illion" number, equals one "undecillinilliseptuagintasescentillisestrigintillion"; and 1029,629,629,633, the 9,876,543,210th "-illion" number, equals one "nonilliseseptuagintaoctingentillitresquadragintaquingentillideciducentillion".

The following table shows number names generated by the system described by Conway and Guy for the short and long scales. Note that since the scale begins at n=10, the short scale begins at 1033 and the long scale begins at 1060; below that, one is supposed to consult the dictionary.

<table><thead><tr><th>Base -illion (short scale)</th><th>Base -illion (long scale)</th><th>Value</th><th>US, Canada, and modern British (short scale)</th><th>Traditional British (long scale)</th><th>Traditional European (Peletier long scale)</th></tr></thead><tbody><tr><td>1</td><td>1</td><td>106</td><td>million</td><td>million</td><td>million</td></tr><tr><td>2</td><td>1</td><td>109</td><td>billion</td><td>thousand million</td><td>milliard</td></tr><tr><td>3</td><td>2</td><td>1012</td><td>trillion</td><td>billion</td><td>billion</td></tr><tr><td>4</td><td>2</td><td>1015</td><td>quadrillion</td><td>thousand billion</td><td>billiard</td></tr><tr><td>5</td><td>3</td><td>1018</td><td>quintillion</td><td>trillion</td><td>trillion</td></tr><tr><td>6</td><td>3</td><td>1021</td><td>sextillion</td><td>thousand trillion</td><td>trilliard</td></tr><tr><td>7</td><td>4</td><td>1024</td><td>septillion</td><td>quadrillion</td><td>quadrillion</td></tr><tr><td>8</td><td>4</td><td>1027</td><td>octillion</td><td>thousand quadrillion</td><td>quadrilliard</td></tr><tr><td>9</td><td>5</td><td>1030</td><td>nonillion</td><td>quintillion</td><td>quintillion</td></tr><tr><td>10</td><td>5</td><td>1033</td><td>decillion</td><td>thousand quintillion</td><td>quintilliard</td></tr><tr><td>11</td><td>6</td><td>1036</td><td>undecillion</td><td>sextillion</td><td>sextillion</td></tr><tr><td>12</td><td>6</td><td>1039</td><td>duodecillion</td><td>thousand sextillion</td><td>sextilliard</td></tr><tr><td>13</td><td>7</td><td>1042</td><td>tredecillion</td><td>septillion</td><td>septillion</td></tr><tr><td>14</td><td>7</td><td>1045</td><td>quattuordecillion</td><td>thousand septillion</td><td>septilliard</td></tr><tr><td>15</td><td>8</td><td>1048</td><td>quindecillion</td><td>octillion</td><td>octillion</td></tr><tr><td>16</td><td>8</td><td>1051</td><td>sedecillion</td><td>thousand octillion</td><td>octilliard</td></tr><tr><td>17</td><td>9</td><td>1054</td><td>septendecillion</td><td>nonillion</td><td>nonillion</td></tr><tr><td>18</td><td>9</td><td>1057</td><td>octodecillion</td><td>thousand nonillion</td><td>nonilliard</td></tr><tr><td>19</td><td>10</td><td>1060</td><td>novendecillion</td><td>decillion</td><td>decillion</td></tr><tr><td>20</td><td>10</td><td>1063</td><td>vigintillion</td><td>thousand decillion</td><td>decilliard</td></tr><tr><td>21</td><td>11</td><td>1066</td><td>unvigintillion</td><td>undecillion</td><td>undecillion</td></tr><tr><td>22</td><td>11</td><td>1069</td><td>duovigintillion</td><td>thousand undecillion</td><td>undecilliard</td></tr><tr><td>23</td><td>12</td><td>1072</td><td>tresvigintillion</td><td>duodecillion</td><td>duodecillion</td></tr><tr><td>24</td><td>12</td><td>1075</td><td>quattuorvigintillion</td><td>thousand duodecillion</td><td>duodecilliard</td></tr><tr><td>25</td><td>13</td><td>1078</td><td>quinvigintillion</td><td>tredecillion</td><td>tredecillion</td></tr><tr><td>26</td><td>13</td><td>1081</td><td>sesvigintillion</td><td>thousand tredecillion</td><td>tredecilliard</td></tr><tr><td>27</td><td>14</td><td>1084</td><td>septemvigintillion</td><td>quattuordecillion</td><td>quattuordecillion</td></tr><tr><td>28</td><td>14</td><td>1087</td><td>octovigintillion</td><td>thousand quattuordecillion</td><td>quattuordecilliard</td></tr><tr><td>29</td><td>15</td><td>1090</td><td>novemvigintillion</td><td>quindecillion</td><td>quindecillion</td></tr><tr><td>30</td><td>15</td><td>1093</td><td>trigintillion</td><td>thousand quindecillion</td><td>quindecilliard</td></tr><tr><td>31</td><td>16</td><td>1096</td><td>untrigintillion</td><td>sedecillion</td><td>sedecillion</td></tr><tr><td>32</td><td>16</td><td>1099</td><td>duotrigintillion</td><td>thousand sedecillion</td><td>sedecilliard</td></tr><tr><td>33</td><td>17</td><td>10102</td><td>trestrigintillion</td><td>septendecillion</td><td>septendecillion</td></tr><tr><td>34</td><td>17</td><td>10105</td><td>quattuortrigintillion</td><td>thousand septendecillion</td><td>septendecilliard</td></tr><tr><td>35</td><td>18</td><td>10108</td><td>quintrigintillion</td><td>octodecillion</td><td>octodecillion</td></tr><tr><td>36</td><td>18</td><td>10111</td><td>sestrigintillion</td><td>thousand octodecillion</td><td>octodecilliard</td></tr><tr><td>37</td><td>19</td><td>10114</td><td>septentrigintillion</td><td>novendecillion</td><td>novendecillion</td></tr><tr><td>38</td><td>19</td><td>10117</td><td>octotrigintillion</td><td>thousand novendecillion</td><td>novendecilliard</td></tr><tr><td>39</td><td>20</td><td>10120</td><td>noventrigintillion</td><td>vigintillion</td><td>vigintillion</td></tr><tr><td>40</td><td>20</td><td>10123</td><td>quadragintillion</td><td>thousand vigintillion</td><td>vigintilliard</td></tr><tr><td>50</td><td>25</td><td>10153</td><td>quinquagintillion</td><td>thousand quinvigintillion</td><td>quinvigintilliard</td></tr><tr><td>60</td><td>30</td><td>10183</td><td>sexagintillion</td><td>thousand trigintillion</td><td>trigintilliard</td></tr><tr><td>70</td><td>35</td><td>10213</td><td>septuagintillion</td><td>thousand quintrigintillion</td><td>quintrigintilliard</td></tr><tr><td>80</td><td>40</td><td>10243</td><td>octogintillion</td><td>thousand quadragintillion</td><td>quadragintilliard</td></tr><tr><td>90</td><td>45</td><td>10273</td><td>nonagintillion</td><td>thousand quinquadragintillion</td><td>quinquadragintilliard</td></tr><tr><td>100</td><td>50</td><td>10303</td><td>centillion</td><td>thousand quinquagintillion</td><td>quinquagintilliard</td></tr><tr><td>101</td><td>51</td><td>10306</td><td>uncentillion</td><td>unquinquagintillion</td><td>unquinquagintillion</td></tr><tr><td>110</td><td>55</td><td>10333</td><td>decicentillion</td><td>thousand quinquinquagintillion</td><td>quinquinquagintilliard</td></tr><tr><td>111</td><td>56</td><td>10336</td><td>undecicentillion</td><td>sesquinquagintillion</td><td>sesquinquagintillion</td></tr><tr><td>120</td><td>60</td><td>10363</td><td>viginticentillion</td><td>thousand sexagintillion</td><td>sexagintilliard</td></tr><tr><td>121</td><td>61</td><td>10366</td><td>unviginticentillion</td><td>unsexagintillion</td><td>unsexagintillion</td></tr><tr><td>130</td><td>65</td><td>10393</td><td>trigintacentillion</td><td>thousand quinsexagintillion</td><td>quinsexagintilliard</td></tr><tr><td>140</td><td>70</td><td>10423</td><td>quadragintacentillion</td><td>thousand septuagintillion</td><td>septuagintilliard</td></tr><tr><td>150</td><td>75</td><td>10453</td><td>quinquagintacentillion</td><td>thousand quinseptuagintillion</td><td>quinseptuagintilliard</td></tr><tr><td>160</td><td>80</td><td>10483</td><td>sexagintacentillion</td><td>thousand octogintillion</td><td>octogintilliard</td></tr><tr><td>170</td><td>85</td><td>10513</td><td>septuagintacentillion</td><td>thousand quinoctogintillion</td><td>quinoctogintilliard</td></tr><tr><td>180</td><td>90</td><td>10543</td><td>octogintacentillion</td><td>thousand nonagintillion</td><td>nonagintilliard</td></tr><tr><td>190</td><td>95</td><td>10573</td><td>nonagintacentillion</td><td>thousand quinnonagintillion</td><td>quinnonagintilliard</td></tr><tr><td>200</td><td>100</td><td>10603</td><td>ducentillion</td><td>thousand centillion</td><td>centilliard</td></tr><tr><td>300</td><td>150</td><td>10903</td><td>trecentillion</td><td>thousand quinquagintacentillion</td><td>quinquagintacentilliard</td></tr><tr><td>400</td><td>200</td><td>101203</td><td>quadringentillion</td><td>thousand ducentillion</td><td>ducentilliard</td></tr><tr><td>500</td><td>250</td><td>101503</td><td>quingentillion</td><td>thousand quinquagintaducentillion</td><td>quinquagintaducentilliard</td></tr><tr><td>600</td><td>300</td><td>101803</td><td>sescentillion</td><td>thousand trecentillion</td><td>trecentilliard</td></tr><tr><td>700</td><td>350</td><td>102103</td><td>septingentillion</td><td>thousand quinquagintatrecentillion</td><td>quinquagintatrecentilliard</td></tr><tr><td>800</td><td>400</td><td>102403</td><td>octingentillion</td><td>thousand quadringentillion</td><td>quadringentilliard</td></tr><tr><td>900</td><td>450</td><td>102703</td><td>nongentillion</td><td>thousand quinquagintaquadringentillion</td><td>quinquagintaquadringentilliard</td></tr><tr><td>1000</td><td>500</td><td>103003</td><td>millinillion</td><td>thousand quingentillion</td><td>quingentilliard</td></tr></tbody></table>

Unit prefixes

Names of large numbers

The following table lists the unit prefixes for powers of 1000 and 1024 according to the International System of Quantities (ISQ).

<table><thead><tr><th>Decimal</th><th>Binary</th></tr></thead><tbody><tr><td>Value</td><td>SI</td><td>Value</td><td>IEC</td></tr><tr><td>1000 (103)</td><td>k</td><td>kilo</td><td>1024 (210)</td><td>Ki</td><td>kibi</td></tr><tr><td>10002 (106)</td><td>M</td><td>mega</td><td>10242 (220)</td><td>Mi</td><td>mebi</td></tr><tr><td>10003 (109)</td><td>G</td><td>giga</td><td>10243 (230)</td><td>Gi</td><td>gibi</td></tr><tr><td>10004 (1012)</td><td>T</td><td>tera</td><td>10244 (240)</td><td>Ti</td><td>tebi</td></tr><tr><td>10005 (1015)</td><td>P</td><td>peta</td><td>10245 (250)</td><td>Pi</td><td>pebi</td></tr><tr><td>10006 (1018)</td><td>E</td><td>exa</td><td>10246 (260)</td><td>Ei</td><td>exbi</td></tr><tr><td>10007 (1021)</td><td>Z</td><td>zetta</td><td>10247 (270)</td><td>Zi</td><td>zebi</td></tr><tr><td>10008 (1024)</td><td>Y</td><td>yotta</td><td>10248 (280)</td><td>Yi</td><td>yobi</td></tr><tr><td>10009 (1027)</td><td>R</td><td>ronna</td><td>10249 (290)</td><td>Ri</td><td>robi</td></tr><tr><td>100010 (1030)</td><td>Q</td><td>quetta</td><td>102410 (2100)</td><td>Qi</td><td>quebi</td></tr></tbody></table>

Other named large numbers used in mathematics, physics and chemistry

Names of large numbers

• Avogadro number – Number of particles in one mole, 6.02214076×1023 • Eddington number – Number of protons in the observable universe, about 1.57×1079 • Shannon number – Lower bound on the game-tree complexity of chess, about 10120 • Skewes's number – Large upper bound related to the prime-counting function, about 10101034 • Moser's number • Graham's number – Upper bound on the answer to a problem in Ramsey theory • TREE(3) • SSCG(3) • Rayo's number – Claimed to be the largest named number