This list contains selected positive

^{−360,783}.
* ''Computing:'' 2.2 is approximately equal to the smallest positive non-zero value that can be represented by an octuple-precision IEEE floating-point value.
:1 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.
:6.5 is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value.
:3.6 is approximately equal to the smallest positive non-zero value that can be represented by an 80-bit x86 double-extended IEEE floating-point value.
:1 is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value.
:4.9 is approximately equal to the smallest positive non-zero value that can be represented by a

^{−10};

^{−9};

^{−8}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one septillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one quadrillionth)
ISO:

^{−7}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one sextillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one trilliardth)
ISO: ^{−19}.

^{−6}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one quintillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one trillionth)
ISO:

^{−5}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one quadrillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one billiardth)
ISO:

^{−4}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one trillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one billionth)
ISO:

^{−3}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one billionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one milliardth)
ISO:

^{−2};

^{−1}; one thousandth)
ISO: ^{−3} (0.14%).
* ''Mathematics – Poker:'' The odds of being dealt a flush in poker are 507.8 to 1 against, for a probability of 1.9 × 10^{−3} (0.19%).
* ''Mathematics – Poker:'' The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10^{−3} (0.39%).
* ''Physics:'' ''α'' = , the

number
A number is a mathematical object
A mathematical object is an abstract concept arising in mathematics.
In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deduct ...

s in increasing order, including counts of things, dimensionless quantity
In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the International ...

and probabilities
Probability is the branch of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathe ...

. Each number is given a name in the short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

, which is used in English-speaking countries, as well as a name in the long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

, which is used in some of the countries that do not have English as their national language.
Smaller than (one googolth)

* ''Mathematics – random selections:'' Approximately is a rough first estimate of the probability that a typing "monkey
Monkey is a common name that may refer to certain groups or species of simian mammals of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of New World monkeys and Old World monkeys. Many monk ...

", or an English-illiterate typing robot, when placed in front of a typewriter, will type out William Shakespeare's play ''Hamlet
''The Tragedy of Hamlet, Prince of Denmark'', often shortened to ''Hamlet'' (), is a tragedy written by William Shakespeare
William Shakespeare (baptism, bapt. 26 April 1564 – 23 April 1616) was an English playwright, poet and acto ...

'' as its first set of inputs, on the precondition it typed the needed number of characters. However, demanding correct punctuation
Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, whether read silently or aloud. An ...

, capitalization
Capitalization (North American English
North American English (NAmE, NAE) is the most generalized variety (linguistics), variety of the English language as spoken in the United States and Canada. Because of their related histories and cultur ...

, and spacing, the probability falls to around 10double-precision
Double-precision floating-point format (sometimes called FP64 or float64) is a computer number format
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable compute ...

IEEE floating-point
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard
A technical standard is an established norm (social), norm or requirement for a repeatable technical task which is applied to a common and repeated use of rules, co ...

value.
:1 is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value.
10^{−100} to 10^{−30}

shuffling
Shuffling is a procedure used to randomization, randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut (cards), cut, to help ensure that the shuffler has not manipulated the outcome.
...

a standard 52-card deck
The standard 52-card deck of French-suited playing cards
French-suited playing cards or French-suited cards are playing cards, cards that use the French Suit (cards), suits of (clovers or clubs ), (tiles or diamonds ), (hearts ) ...

in any specific order is around 1.24 (or exactly )
* ''Computing:'' The number 1.4 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable comput ...

IEEE floating-point value.
10^{−30}

short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one nonillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one quintillionth)
* ''Mathematics:'' The probability in a game of bridge
A bridge is a Nonbuilding structure, structure built to Span (engineering), span a physical obstacle, such as a body of water, valley, or road, without closing the way underneath. It is constructed for the purpose of providing passage over the ...

of all four players getting a complete suit
A suit or lounge suit is a set of clothes comprising a suit jacket and trousers of identical textiles worn with a collared dress shirt, necktie, and dress shoes. It is considered informal wear in Western dress codes. The lounge suit originated ...

each is approximately .
10^{−27}

short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one octillionth; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one quadrilliardth)
10^{−24}

yocto-
''Yocto'' (symbol y) is a unit prefix A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use o ...

(y)
10^{−21}

zepto-
''Zepto''- (unit of measurement, unit symbol ''z''-) is a metric prefix, unit prefix in the metric system denoting a factor of 10−21 or .
Adopted in 1991, it is derived from the Latin "seven", since it is equal to 1000−7.
Examples of its us ...

(z)
* ''Mathematics:'' The probability of matching 20 numbers for 20 in a game of keno
Keno is a lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to ...

is approximately 2.83 × 10 10^{−18}

atto-
Atto (symbol a) is a unit prefixA unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of such p ...

(a)
* ''Mathematics:'' The probability of rolling snake eyes Snake eyes is a roll of two dice, with one pip on both dice.
Snake Eyes may also refer to:
Music
* ''Snake Eyes'' (album), a 2000 album by Killa Tay featuring a guest appearance by Spider Loc
* "Snake Eyes" (The Alan Parsons Project song), a 19 ...

10 times in a row on a pair of fair dice is about .
10^{−15}

femto-
''Femto-'' (symbol f) is a unit prefixA unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of ...

(f)
* ''Mathematics'': The Ramanujan constant, $e^\; =\; 262\backslash ,537\backslash ,412\backslash ,640\backslash ,768\backslash ,743.999\backslash ,999\backslash ,999\backslash ,999\backslash ,25\backslash ldots,$ is an almost integer
In recreational mathematics
Recreational mathematics is mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and c ...

, differing from the nearest integer by approximately .
10^{−12}

pico-
''Pico'' ( unit symbol p) is a unit prefix A unit prefix is a specifier or mnemonic that is prepended to units of measurement
A unit of measurement is a definite magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quant ...

(p)
* ''Mathematics:'' The probability in a game of bridge
A bridge is a Nonbuilding structure, structure built to Span (engineering), span a physical obstacle, such as a body of water, valley, or road, without closing the way underneath. It is constructed for the purpose of providing passage over the ...

of one player getting a complete suit is approximately ().
* ''Biology:'' Human visual sensitivity to light is approximately of its peak sensitivity at .
10^{−9}

nano-
Nano (symbol n) is a unit prefix A unit prefix is a specifier or mnemonic that is prepended to units of measurement
A unit of measurement is a definite magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity define ...

(n)
* ''Mathematics – Lottery:'' The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball
Powerball is an American lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. ...

lottery, with a single ticket, under the rules , are 292,201,338 to 1 against, for a probability of ().
* ''Mathematics – Lottery:'' The odds of winning the Grand Prize (matching all 6 numbers) in the Australian Powerball
Powerball is an American lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. ...

lottery, with a single ticket, under the rules , are 134,490,400 to 1 against, for a probability of ().
* ''Mathematics – Lottery:'' The odds of winning the Jackpot (matching the 6 main numbers) in the UK National Lottery, with a single ticket, under the rules , are 13,983,815 to 1 against, for a probability of ().
10^{−6}

long and short scales
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one millionth One millionth is equal to 0.000 001, or 1 x 10−6 in scientific notation
Scientific notation is a way of expressing numbers
A number is a mathematical object
A mathematical object is an abstract concept arising in mathematics.
In the usual ...

)
ISO: micro-
''Micro'' (Greek letter μ (Unicode, U+03BC) or the legacy symbol µ (U+00B5)) is a metric prefix, unit prefix in the metric system denoting a factor of 10−6 (one millionth). Confirmed in 1960, the prefix comes from the Ancient Greek, Greek (') ...

(μ)
* ''Mathematics – Poker
Poker is a family of card games in which Card player, players betting (poker), wager over which poker hand, hand is best according to that specific game's rules in ways similar List of poker hands, to these rankings. While the earliest known f ...

:'' The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5 ().
* ''Mathematics – Poker:'' The odds of being dealt a straight flush
In poker, players form sets of five playing cards, called ''hands'', according to the rules of the game. Each hand has a rank
Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or obj ...

(other than a royal flush) in poker are 72,192 to 1 against, for a probability of 1.4 (0.0014%).
* ''Mathematics – Poker:'' The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 (0.024%).
10^{−3}

milli-
''Milli'' (symbol m) is a unit prefix A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of ...

(m)
* ''Mathematics – Poker:'' The odds of being dealt a full house
''Full House'' is an American television Situation comedy, sitcom created by Jeff Franklin for American Broadcasting Company, ABC. The show chronicles the events of widowed father Danny Tanner who enlists his brother-in-law Jesse Katsopolis and ...

in poker are 693 to 1 against, for a probability of 1.4 × 10fine-structure constant
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

.
10^{−2}

hundredth
In arithmetic, a hundredth is a single part of something that has been divided equally into a hundred parts. For example, a hundredth of 675 is 6.75. In this manner it is used with the prefix "centi" such as in centimeter.
A hundredth is the mult ...

)
ISO: centi-
''Centi-'' (symbol c) is a metric prefix, unit prefix in the metric system denoting a factor of one hundredth. Proposed in 1793 and adopted in 1795, the prefix comes from the Latin , meaning "hundred" (cf. century, cent, percent, centennial). Sinc ...

(c)
* ''Mathematics – Lottery:'' The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%).
* ''Mathematics – Poker:'' The odds of being dealt a three of a kindThree of a kind may refer to:
* Three of a kind (poker), a type of poker hand
* Three of a Kind (1967 TV series), ''Three of a Kind'' (1967 TV series), a British comedy sketch and music show
* Three of a Kind (1981 TV series), ''Three of a Kind'' (1 ...

in poker are 46 to 1 against, for a probability of 0.021 (2.1%).
* ''Mathematics – Lottery:'' The odds of winning any prize in the Powerball
Powerball is an American lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. ...

, with a single ticket, under the rules as of 2015, are 24.87 to 1 against, for a probability of 0.0402 (4.02%).
* ''Mathematics – Poker:'' The odds of being dealt two pair
In poker
Poker is any of a number of card games in which players wager over which hand
A hand is a prehensile, multi- fingered appendage located at the end of the forearm
The forearm is the region of the upper limb between the Elb ...

in poker are 21 to 1 against, for a probability of 0.048 (4.8%).
10^{−1}

deci-
''Deci'' (symbol d) is a decimal
The decimal numeral system
A numeral system (or system of numeration) is a writing system
A writing system is a method of visually representing verbal communication
Communication (from Latin ''comm ...

(d)
* ''Legal history'': 10% was widespread as the tax
A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity
In law
Law is a system
A system is a group of Interaction, interacting or interrelated elements that act accord ...

raised for income or produce in the ancient and medieval period; see tithe
A tithe (; from : ''teogoþa'' "tenth") is a one-tenth part of something, paid as a contribution to a religious organization or compulsory to government. Today, tithes are normally voluntary and paid in or s, whereas historically tithes were ...

.
* ''Mathematics:'' = ≈ 0.207879576.
* ''Mathematics – Poker:'' The odds of being dealt only one pair in poker are about 5 to 2 against (2.37 to 1), for a probability of 0.42 (42%).
* ''Mathematics – Poker:'' The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5 (50%).
10^{0}

one
1 (one, also called unit, and unity) is a number
A number is a mathematical object used to counting, count, measurement, measure, and nominal number, label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can ...

)
* ''Demography:'' The population of Monowi, an incorporated village in Nebraska
Nebraska () is a state
State may refer to:
Arts, entertainment, and media Literature
* ''State Magazine'', a monthly magazine published by the U.S. Department of State
* The State (newspaper), ''The State'' (newspaper), a daily newspaper ...

, United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

, was one in 2010.
* ''Religion:'' One is the number of gods in Judaism
Judaism is an Abrahamic religions, Abrahamic, monotheism, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion ...

, Christianity
Christianity is an Abrahamic
The Abrahamic religions, also referred to collectively as the world of Abrahamism and Semitic religions, are a group of Semitic-originated religion
Religion is a social system, social-cultural system of ...

, and Islam
Islam (; ar, اَلْإِسْلَامُ, al-’Islām, "submission o God
Oh God may refer to:
* An exclamation; similar to "oh no", "oh yes", "oh my", "aw goodness", "ah gosh", "ah gawd"; see interjection
An interjection is a word or ex ...

( monotheistic religions).
* ''Computing – Unicode
Unicode, formally the Unicode Standard, is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's wri ...

:'' One character is assigned to the Lisu Supplement Unicode block
A Unicode block is one of several contiguous ranges of numeric character codes (code point
In character encoding
In computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes t ...

, the fewest of any public-use Unicode block as of Unicode 14.0 (2021).
* ''Mathematics:'' ≈ , the ratio of the diagonal
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

of a square
In Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method ...

to its side length.
* ''Mathematics:'' φ ≈ , the golden ratio
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

.
* ''Mathematics:'' ≈ , the ratio of the diagonal
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

of a unit cube
300px, Unit cube
A unit cube, more formally a cube of side 1, is a cube
In geometry
Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the ...

.
* ''Mathematics:'' the number system understood by most computers, the binary
Binary may refer to:
Science and technology
Mathematics
* Binary number
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: ty ...

system, uses 2 digits: 0 and 1.
*''Mathematics:'' ≈ 2.236 067 9775, the correspondent to the diagonal of a rectangle whose side lengths are 1 and 2.
*''Mathematics:'' + 1 ≈ 2.414 213 562 373 095 049, The ratio of smaller of the two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice the larger quantity.
* ''Mathematics:'' e ≈ , the base of the natural logarithm
The natural logarithm of a number is its logarithm
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...

.
* ''Mathematics:'' the number system understood by ternary computer
A ternary computer (also called trinary computer) is a computer that uses ternary logic (three possible values) instead of the more popular Binary number, binary system ("Base 2") in its calculations.
Types of states
Ternary computing deals with th ...

s, the system, uses 3 digits: 0, 1, and 2.
* ''Religion:'' three manifestations of God in the Christian Trinity
The Christian
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus in Christianity, Jesus Christ. The words ''Christ (title), Christ'' and ''Christian ...

.
* ''Mathematics:'' ≈ , the ratio of a circle
A circle is a shape
A shape or figure is the form of an object or its external boundary, outline, or external surface
File:Water droplet lying on a damask.jpg, Water droplet lying on a damask. Surface tension is high enough to preven ...

's circumference to its diameter.
* ''Religion:'' the Four Noble Truths
In Buddhism
Buddhism (, ) is the Major religious groups#Largest religions, world's fourth-largest religion with over 520 million followers, or over 7% of the global population, known as Buddhists. Buddhism encompasses a variety of traditi ...

in Buddhism.
* ''Biology:'' 7 ± 2, in cognitive science
Cognitive science is the interdisciplinary
Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic discipline
An academic discipline or academic field is a subdivision of knowledge that is Educ ...

, George A. Miller's estimate of the number of objects that can be simultaneously held in human working memory
Working memory is a cognitive system with a limited capacity that can hold information temporarily. Working memory is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-te ...

.
* ''Music'': notes in a major
Major is a military rank
Military ranks are a system of hierarchical
A hierarchy (from the Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) in which the items are repre ...

or minor scale
In music theory
Music theory is the study of the practices and possibilities of music
Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General ...

.
* ''Astronomy:'' planets in the Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

.
* ''Religion:'' the Eightfold Path
The Noble Eightfold Path (Pali
Pali () is a Middle Indo-Aryan liturgical language native to the Indian subcontinent. It is widely studied because it is the language of the '' Pāli Canon'' or '' Tipiṭaka'' and is the sacred langua ...

in Buddhism.
* ''Literature:'' 9 circles of Hell
In religion
Religion is a - of designated and practices, , s, s, , , , , or , that relates humanity to , , and elements; however, there is no scholarly consensus over what precisely constitutes a religion.
Different religions may o ...

in the ''Inferno
Inferno may refer to:
* Hell, an afterlife place of suffering
* Conflagration, a large uncontrolled fire
Film
* ''L'Inferno'', a 1911 Italian film
* Inferno (1953 film), ''Inferno'' (1953 film), a film noir by Roy Ward Baker
* Inferno (1973 fi ...

'' by Dante Alighieri
Dante Alighieri (), probably baptized Durante di Alighiero degli Alighieri and often referred to simply as Dante (, also ; – 14 September 1321), was an Italian poet
A poet is a person who creates poetry
Poetry (derived from t ...

.
10^{1}

deca-
''Deca'' ( International spelling as used by the International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation
...

(da)
* ''Demography:'' The population of Pesnopoy, a village in Bulgaria
Bulgaria (; bg, България, Bǎlgariya), officially the Republic of Bulgaria ( bg, Република България, links=no, Republika Bǎlgariya, ), is a country in Southeast Europe. It is bordered by Romania to the north, Serbia ...

, was 10 in 2007.
* ''Human scale:'' There are 10 digit
Digit may refer to:
Mathematics and science
* Numerical digit, as used in mathematics or computer science
** Arabic numerals, the most common modern representation of numerical digits
* Digit (anatomy), one of several most distal parts of a limb ...

s on a pair of human hand
A hand is a prehensile, multi- fingered appendage located at the end of the forearm
The forearm is the region of the upper limb between the Elbow-joint, elbow and the wrist. The term forearm is used in anatomy to distinguish it from the arm, ...

s, and 10 toe
Toes are the digits (fingers) of the foot of a tetrapod. Animal
Animals (also called Metazoa) are multicellular eukaryotic organisms that form the Kingdom (biology), biological kingdom Animalia. With few exceptions, animals Heterotrop ...

s on a pair of human feet
The foot (plural: feet) is an anatomical
Anatomy (Greek ''anatomē'', 'dissection') is the branch of biology
Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemist ...

.
* ''Mathematics:'' The number system used in everyday life, the decimal
The decimal numeral system
A numeral system (or system of numeration) is a writing system
A writing system is a method of visually representing verbal communication
Communication (from Latin ''communicare'', meaning "to share") is t ...

system, has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
* ''Religion:'' the Ten Commandments
The Ten Commandments ( he, עֲשֶׂרֶת הַדִּבְּרוֹת, ''Aseret ha'Dibrot''), also known as the Decalogue, are a set of biblical
The Bible (from Koine Greek
Koine Greek (, , Greek approximately ;. , , , lit. " ...

in the Abrahamic religions
The Abrahamic religions, also referred to collectively as the world of Abrahamism and Semitic religions, are a group of Semitic
Semitic most commonly refers to the Semitic languages, a name used since the 1770s to refer to the language family ...

.
* ''Music:'' The number of notes (12) in a chromatic scale
The chromatic scale is a set of twelve pitches (more completely, pitch class
In , a pitch class (p.c. or pc) is a of all that are a whole number of s apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C sta ...

.
* ''Astrology:'' There are 12 zodiac signs, each one representing part of the annual path of the sun's movement across the night sky.
* ''Computing – Microsoft Windows
Microsoft Windows, commonly referred to as Windows, is a group of several proprietary
{{Short pages monitorone thousand billion, or one billiard)
ISO: peta- (P)
* ''Biology – Insects'': 1,000,000,000,000,000 to 10,000,000,000,000,000 (10^{15} to 10^{16}) – The estimated total number of ants on Earth alive at any one time (their Biomass (ecology), biomass is approximately equal to the total biomass of the human, human species).
* ''Computing:'' 9,007,199,254,740,992 (2^{53}) – number until which all integer values can exactly be represented in IEEE double precision floating-point format.
* ''Mathematics:'' 48,988,659,276,962,496 is the fifth taxicab number.
* ''Science Fiction'': In Isaac Asimov's Galactic Empire (Isaac Asimov), Galactic Empire, in what we call 22,500 CE there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited by humans in Asimov's "human galaxy" scenario, each with an average population of 2,000,000,000, thus yielding a total Galactic Empire population of approximately 50,000,000,000,000,000.
* ''Science Fiction'': There are approximately 10^{17} sentient beings in the ''Star Wars'' galaxy.
* ''Cryptography:'' There are 2^{56} = 72,057,594,037,927,936 different possible keys in the obsolete 56-bit Data Encryption Standard, DES symmetric cipher.

^{6}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one quintillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one trillion)
ISO: exa- (E)
* ''Mathematics:'' Goldbach's conjecture has been Goldbach's conjecture#Verified results, verified for all ''n'' ≤ 4 by a project which computed all prime numbers up to that limit.
* ''Computing – Manufacturing:'' An estimated 6 transistors were produced worldwide in 2008.
* ''Computing – Computational limit of a 64-bit Central processing unit, CPU'': 9,223,372,036,854,775,807 (about 9.22) is equal to 2^{63}−1, and as such is the largest number which can fit into a signed (two's complement) 64-bit integer on a computer.
* ''Mathematics – NCAA Men's Division I Basketball Championship, NCAA Basketball Tournament:'' There are 9,223,372,036,854,775,808 (2^{63}) possible ways to enter the Bracketology, bracket.
* ''Mathematics – Radix, Bases:'' 9,439,829,801,208,141,318 (≈9.44) is the 10th and (by conjecture) largest number with more than one digit that can be written from base 2 to base 18 using only the digits 0 to 9, meaning the digits for 10 to 17 are not needed in bases above 10.
* ''Biology – Insects:'' It has been estimated that the insect population of the Earth is about 10^{19}.
* ''Mathematics – Answer to the wheat and chessboard problem:'' When doubling the grains of wheat on each successive square of a chessboard, beginning with one grain of wheat on the first square, the final number of grains of wheat on all 64 squares of the chessboard when added up is 2^{64}−1 = 18,446,744,073,709,551,615 (≈1.84).
* ''Mathematics – Legends:'' The Tower of Brahma legend tells about a Hindu temple containing a large room with three posts, on one of which are 64 golden discs, and the object of the mathematical game is for the Brahmins in this temple to move all of the discs to another pole so that they are in the same order, never placing a larger disc above a smaller disc, moving only one at a time. Using the simplest algorithm for moving the disks, it would take 2^{64}−1 = 18,446,744,073,709,551,615 (≈1.84) turns to complete the task (the same number as the wheat and chessboard problem above).
* ''Computing – IPv6:'' 18,446,744,073,709,551,616 (2^{64}; ≈1.84) possible unique /64 subnetworks.
* ''Mathematics – Rubik's Cube:'' There are 43,252,003,274,489,856,000 (≈4.33) different positions of a 3×3×3 Rubik's Cube.
* ''Password strength:'' Usage of the 95-character set found on standard computer keyboards for a 10-character password yields a computationally intractability (complexity), intractable 59,873,693,923,837,890,625 (95^{10}, approximately 5.99) permutations.
* ''Economics:'' Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent, or a factor of 10^{20}.

^{7}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one sextillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one thousand trillion, or one trilliard)
ISO: zetta- (Z)
* ''Geo – Grains of sand:'' All the world's beaches combined have been estimated to hold roughly 10^{21} grains of sand.
* ''Computing – Manufacturing:'' Intel predicted that there would be 1.2 transistors in the world by 2015 and Forbes estimated that 2.9 transistors had been shipped up to 2014.
* ''Mathematics – Sudoku:'' There are 6,670,903,752,021,072,936,960 (≈6.7) 9×9 sudoku grids.
* ''Astronomy – Stars:'' 70 sextillion = 7, the estimated number of stars within range of telescopes (as of 2003).
* ''Astronomy – Stars:'' in the range of 10^{23} to 10^{24} stars in the observable universe.
* ''Mathematics:'' 146,361,946,186,458,562,560,000 (≈1.5) is the fifth unitary perfect number.
* ''Mathematics:'' 357,686,312,646,216,567,629,137 (≈3.6) is the largest left-truncatable prime.
* ''Chemistry – Physics:'' The Avogadro constant () is the number of constituents (e.g. atoms or molecules) in one mole (unit), mole of a substance, defined for convenience as expressing the order of magnitude separating the molecular from the macroscopic scale.

^{8}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one septillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one quadrillion)
ISO: yotta- (Y)
* ''Mathematics:'' 2,833,419,889,721,787,128,217,599 (≈2.8) is the fifth Woodall prime.
* ''Mathematics:'' 3,608,528,850,368,400,786,036,725 (≈3.6) is the largest polydivisible number.
* ''Mathematics:'' 2^{86} = 77,371,252,455,336,267,181,195,264 is the largest known power of two not containing the digit '0' in its decimal representation.

^{9}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one octillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one thousand quadrillion, or one quadrilliard)
* ''Biology – Atoms in the human body:'' the average human body contains roughly 7 atoms.
* ''Mathematics – Poker:'' the number of unique combinations of hands and shared cards in a 10-player game of Texas hold 'em is approximately 2.117.

^{10}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one nonillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one quintillion)
* ''Biology – Bacterial cells on Earth:'' The number of bacterial cells on Earth is estimated at around 5,000,000,000,000,000,000,000,000,000,000, or 5 × 10^{30}.
* ''Mathematics:'' 5,000,000,000,000,000,000,000,000,000,027 is the largest v:quasi-minimal prime, quasi-minimal prime.
* ''Mathematics:'' The number of partition of a set, partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.
* ''Mathematics:'' 3^{68} = 278,128,389,443,693,511,257,285,776,231,761 is the largest known power of three not containing the digit '0' in its decimal representation.
* ''Mathematics:'' 2^{108} = 324,518,553,658,426,726,783,156,020,576,256 is the largest known power of two not containing the digit '9' in its decimal representation.

^{11}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one decillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one thousand quintillion, or one quintilliard)
* ''Mathematics – Alexander's Star:'' There are 72,431,714,252,715,638,411,621,302,272,000,000 (about 7.24) different positions of Alexander's Star.

^{12}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one undecillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one sextillion)
* ''Physics'': ''Coulomb's constant, k_{e} Elementary charge, e^{2} / Gravitational constant, Gm ^{2}'', the ratio of the electromagnetic force, electromagnetic to the gravitational forces between two protons, is roughly 10^{36}.
* ''Mathematics:'' 2^{27-1}-1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7) is the largest known double Mersenne prime.
* ''Computing:'' 2^{128} = 340,282,366,920,938,463,463,374,607,431,768,211,456 (≈3.40282367), the theoretical maximum number of Internet addresses that can be allocated under the IPv6 addressing system, one more than the largest value that can be represented by a single-precision IEEE floating-point value, the total number of different Universally Unique Identifiers (UUIDs) that can be generated.
* ''Cryptography:'' 2^{128} = 340,282,366,920,938,463,463,374,607,431,768,211,456 (≈3.40282367), the total number of different possible keys in the Advanced Encryption Standard, AES 128-bit key space (cryptography), key space (symmetric cipher).

^{13}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one duodecillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one thousand sextillion, or one sextilliard)
* ''Cosmology:'' The Eddington–Dirac number is roughly 10^{40}.
* ''Mathematics:'' Primorial, 97# × 2^{5} × 3^{3} × 5 × 7 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800 (≈6.97) is the least common multiple of every integer from 1 to 100.

^{14}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: one tredecillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: one septillion)
* ''Mathematics:'' 141×2^{141}+1 = 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.93) is the second Cullen prime.
* ''Mathematics:'' There are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 (≈7.4) possible permutations for the Rubik's Revenge (4×4×4 Rubik's Cube).
* ''Chess'': 4.52 is a proven upper bound for the number of legal chess positions.
* ''Geo'': 1.33 is the estimated number of atoms in Earth.
* ''Mathematics:'' 2^{168} = 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856 is the largest known power of two which is not Pandigital number, pandigital: There is no digit '2' in its decimal representation.
* ''Mathematics:'' 3^{106} = 375,710,212,613,636,260,325,580,163,599,137,907,799,836,383,538,729 is the largest known power of three which is not pandigital: There is no digit '4'.
* ''Mathematics:'' 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 (≈8.08) is the Order (group theory), order of the monster group.
* ''Cryptography:'' 2^{192} = 6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896 (6.27710174), the total number of different possible keys in the Advanced Encryption Standard, AES 192-bit key space (cryptography), key space (symmetric cipher).
* ''Cosmology:'' 8 is roughly the number of Planck time intervals since the universe is theorised to have been created in the Big Bang 13.799 ± 0.021 1000000000 (number), billion years ago.
* ''Cosmology:'' 1 is Archimedes' estimate in ''The Sand Reckoner'' of the total number of grains of sand that could fit into the entire cosmos, the diameter of which he estimated in stadion (unit), stadia to be what we call 2 light-years.
* ''Mathematics – Cards:'' 52factorial, ! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8.07) – the number of ways to order the Playing card, cards in a 52-card deck.
* ''Mathematics:'' There are ≈1.01×10^{68} possible combinations for the Megaminx.
* ''Mathematics:'' 1,808,422,353,177,349,564,546,512,035,512,530,001,279,481,259,854,248,860,454,348,989,451,026,887 (≈1.81) – The largest known prime factor found by Lenstra elliptic-curve factorization, ECM factorization .
* ''Mathematics:'' There are 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 (≈2.83) possible permutations for the Professor's Cube (5×5×5 Rubik's Cube).
* ''Cryptography:'' 2^{256} = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 (≈1.15792089), the total number of different possible keys in the Advanced Encryption Standard, AES 256-bit key space (cryptography), key space (symmetric cipher).
* ''Cosmology:'' Various sources estimate the total number of fundamental particles in the observable universe to be within the range of 10^{80} to 10^{85}.WMAP- Content of the Universe

. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01. However, these estimates are generally regarded as guesswork. (Compare the Eddington number, the estimated total number of protons in the observable universe.) * ''Computing:'' 9.999 999 is equal to the largest value that can be represented in the IEEE decimal32 floating-point format. * ''Computing:'' 69! (roughly 1.7112245), is the highest factorial value that can be represented on a calculator with two digits for powers of ten without overflow. * ''Mathematics:'' One googol, 1, 1 followed by one hundred zeros, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: ten duotrigintillion; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: ten thousand sexdecillion, or ten sexdecillard)
* ''Mathematics:'' There are 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 887 168 573 442 107 637 760 000 000 000 000 000 000 000 000 (≈1.57) distinguishable permutations of the V-Cube 6 (6×6×6 Rubik's Cube).
* ''Chess:'' Shannon number, 10^{120}, a lower bound of the game-tree complexity of chess.
* ''Physics:'' 10^{120}, Cosmological constant problem, discrepancy between the observed value of the cosmological constant and a naive estimate based on Quantum Field Theory and the Planck energy.
* ''Physics:'' 8, ratio of the mass-energy in the observable universe to the energy of a photon with a wavelength the size of the observable universe.
* ''Mathematics:'' 19 568 584 333 460 072 587 245 340 037 736 278 982 017 213 829 337 604 336 734 362 294 738 647 777 395 483 196 097 971 852 999 259 921 329 236 506 842 360 439 300 (≈1.96) is the period of Fermat pseudoprime, primary pretenders.
* ''History – Religion:'' Asaṃkhyeya is a Buddhism, Buddhist name for the number 10^{140}. It is listed in the Avatamsaka Sutra and metaphorically means "innumerable" in the Sanskrit language of History of India, ancient India.
* ''Xiangqi:'' 10^{150}, an estimation of the game-tree complexity of xiangqi.
* ''Mathematics:'' There are 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692 043 434 567 152 132 912 323 232 706 135 469 180 065 278 712 755 853 360 682 328 551 719 137 311 299 993 600 000 000 000 000 000 000 000 000 000 000 000 (≈1.95) distinguishable permutations of the V-Cube 7 (7×7×7 Rubik's Cube).
* ''Go:'' There are 208 168 199 381 979 984 699 478 633 344 862 770 286 522 453 884 530 548 425 639 456 820 927 419 612 738 015 378 525 648 451 698 519 643 907 259 916 015 628 128 546 089 888 314 427 129 715 319 317 557 736 620 397 247 064 840 935 (≈2.08) legal positions in the game of Go. See Go and mathematics.
* ''Economics:'' The annualized rate of the Hungarian pengő#Hyperinflation, hyperinflation in Hungary in 1946 was estimated to be 2.9%. It was the most extreme case of hyperinflation ever recorded.
* ''Board games:'' 3.457, number of ways to arrange the tiles in English-language Scrabble, English Scrabble on a standard 15-by-15 Scrabble board.
* ''Physics:'' 10^{186}, approximate number of Planck volumes in the observable universe.
* ''Shogi:'' 10^{226}, an estimation of the game-tree complexity of shogi.
* ''Physics:'' 7, approximate spacetime volume of the history of the observable universe in Planck units.
* ''Computing:'' 1.797 693 134 862 315 807 is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
* ''Computing:'' (10 – 10^{−15}) is equal to the largest value that can be represented in the IEEE decimal64 floating-point format.
* ''Mathematics:'' Primorial, 997# × 31# × 2^{5} × 3^{4} × 5^{4} × 7 = 7 128 865 274 665 093 053 166 384 155 714 272 920 668 358 861 885 893 040 452 001 991 154 324 087 581 111 499 476 444 151 913 871 586 911 717 817 019 575 256 512 980 264 067 621 009 251 465 871 004 305 131 072 686 268 143 200 196 609 974 862 745 937 188 343 705 015 434 452 523 739 745 298 963 145 674 982 128 236 956 232 823 794 011 068 809 262 317 708 861 979 540 791 247 754 558 049 326 475 737 829 923 352 751 796 735 248 042 463 638 051 137 034 331 214 781 746 850 878 453 485 678 021 888 075 373 249 921 995 672 056 932 029 099 390 891 687 487 672 697 950 931 603 520 000 (≈7.13) is the least common multiple of every integer from 1 to 1000.

^{−33}) is equal to the largest value that can be represented in the IEEE decimal128 floating-point format.
* ''Computing:'' 10^{10,000} − 1 is equal to the largest value that can be represented in Windows Phone's calculator.
* ''Mathematics:'' 2638^{4405} + 4405^{2638} is a 15,071-digit Leyland number, Leyland prime; the largest which has been proven .
* ''Mathematics:'' 3,756,801,695,685 × 2^{666,669} ± 1 are 200,700-digit twin primes; the largest known .
* ''Mathematics:'' 18,543,637,900,515 × 2^{666,667} − 1 is a 200,701-digit Sophie Germain prime; the largest known .
* ''Mathematics:'' approximately 7.76 × 10^{206,544} cattle in the smallest herd which satisfies the conditions of Archimedes's cattle problem.
* ''Mathematics:'' 10^{474,500} + 999 × 10^{237,249} + 1 is a 474,501-digit palindromic prime, the largest known .
* ''Mathematics:'' 2,996,863,034,895 × 2^{1,290,000}±1 are 388,342-digit twin primes; the largest known .
* ''Mathematics:'' 1,098,133# – 1 is a 476,311-digit primorial prime; the largest known .
* ''Mathematics:'' 208,003! − 1 is a 1,015,843-digit factorial prime; the largest known .
* ''Mathematics – Literature:'' Jorge Luis Borges' Library of Babel contains at least 25^{1,312,000} ≈ 1.956 × 10^{1,834,097} books (this is a lower bound).
* ''Mathematics:'' 4 × 72^{1,119,849} − 1 is the smallest prime of the form 4×72^{''n''}−1
* ''Mathematics:'' (2^{15,135,397}+1)/3 is a 4,556,209-digit Wagstaff prime, Wagstaff probable prime, the largest known .
* ''Mathematics:'' 1,059,094^{1,048,576} + 1 is a 6,317,602-digit Generalized Fermat prime, the largest known .
* ''Mathematics:'' (10^{8,177,207}−1)/9 is a 8,177,207-digit probable prime, the largest known .
* ''Mathematics:'' 10,223 × 2^{31,172,165} + 1 is a 9,383,761-digit Proth prime, the largest known Proth prime and non-Mersenne prime .
* ''Mathematics:'' 2^{82,589,933} − 1 is a 24,862,048-digit Mersenne prime; the largest known prime of any kind .Chris Caldwell

The Top Twenty: Largest Known Primes

at The Prime Pages. * ''Mathematics:'' 2^{82,589,932} × (2^{82,589,933} − 1) is a 49,724,095-digit perfect number, the largest known as of 2020.
* ''Mathematics – History:'' 10^{8×1016}, largest named number in Archimedes' ''The Sand Reckoner, Sand Reckoner''.
* ''Mathematics:'' 10^{googol} ($10^$), a googolplex. A number 1 followed by 1 googol zeros. Carl Sagan has estimated that 1 googolplex, fully written out, would not fit in the observable universe because of its size, while also noting that one could also write the number as 10^{10100}.

^{googol}; short scale
The long and short scales are two of several naming systems for integer powers of ten
480px, Visualisation of powers of 10 from one to 1 billion.
A power of 10 is any of the integer
An integer (from the Latin
Latin (, or , ) is a cla ...

: googolplex; long scale
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...

: googolplex)
* ''Mathematics – Literature:'' The number of different ways in which the books in Jorge Luis Borges' The Library of Babel, Library of Babel can be arranged is approximately $10^$, the factorial of the number of books in the Library of Babel.
* ''Cosmology:'' In Chaotic Inflation theory, chaotic inflation theory, proposed by physicist Andrei Linde, our universe is one of many other universes with different physical constants that originated as part of our local section of the Multiverse#Bubble theory, multiverse, owing to a vacuum that had not decayed to its ground state. According to Linde and Vanchurin, the total number of these universes is about $10^$.
* ''Mathematics:'' $10^$, order of magnitude of an upper bound that occurred in a Skewes' number, proof of Skewes (this was later estimated to be closer to 1.397 × 10^{316}).
*''Cosmology:'' The estimated number of Planck time, Planck time units for quantum fluctuations and quantum tunnelling, tunnelling to generate a new Big Bang is estimated to be $10^$.
* ''Mathematics:'' $10^$, a number in Names of large numbers#The googol family, the googol family called a googolplexplex, googolplexian, or googolduplex. 1 followed by a googolplex zeros, or 10^{googolplex}
* ''Mathematics:'' $10^$, order of magnitude of another upper bound in a proof of Stanley Skewes, Skewes.
* ''Mathematics:'' Steinhaus' Steinhaus–Moser notation#Mega, mega lies between 10[4]257 and 10[4]258 (where ''a''[''n'']''b'' is hyperoperation).
* ''Mathematics:'' Moser's number, "2 in a mega-gon" in Steinhaus–Moser notation, is approximately equal to 10[10[4]257]10, the last four digits are ...1056.
* ''Mathematics:'' Graham's number, the last ten digits of which are ...2464195387, equals 3[3[3[...3[3[3[6]3+2]3+2]3...]3+2]3+2]3 with 64 levels of brackets. Arises as an upper bound solution to a problem in Ramsey theory. Representation in powers of 10 would be impractical (the number of 10s in the power tower $10^$ would be virtually indistinguishable from the number itself).
* ''Mathematics:'' Kruskal's tree theorem, TREE(3): appears in relation to a theorem on trees in graph theory. Representation of the number is difficult, but one weak lower bound is ''A''^{''A''(187196)}(1), where A(n) is a version of the Ackermann function.
* ''Mathematics:'' Friedman's SSCG function, SSCG(3): appears in relation to the Robertson–Seymour theorem. Known to be greater than both TREE(3) and the TREE function nested inside itself TREE(3) times with TREE(3) at the bottom.
* ''Mathematics:'' Transcendental integers: a set of numbers defined in 2000 by Harvey Friedman, appears in proof theory.H. Friedman

Enormous integers in real life

(accessed 2021-02-06)

''Computational capacity of the universe''

provides a number of interesting dimensionless quantities.

* {{DEFAULTSORT:Orders Of Magnitude (Numbers) Orders of magnitude, Numbers

10^{18}

10^{21}

10^{24}

10^{27}

10^{30}

10^{33}

10^{36}

10^{39}

10^{42} to 10^{100}

. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01. However, these estimates are generally regarded as guesswork. (Compare the Eddington number, the estimated total number of protons in the observable universe.) * ''Computing:'' 9.999 999 is equal to the largest value that can be represented in the IEEE decimal32 floating-point format. * ''Computing:'' 69! (roughly 1.7112245), is the highest factorial value that can be represented on a calculator with two digits for powers of ten without overflow. * ''Mathematics:'' One googol, 1, 1 followed by one hundred zeros, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

10^{100} (one googol) to 10^{1000}

10^{1000} to 10^{10100} (one googolplex)

The Top Twenty: Largest Known Primes

at The Prime Pages. * ''Mathematics:'' 2

Larger than 10^{10100}

Enormous integers in real life

(accessed 2021-02-06)

See also

* Conway chained arrow notation * Wikipedia:Size comparisons, Encyclopedic size comparisons on Wikipedia * Fast-growing hierarchy * Large numbers * List of numbers * Mathematical constant * Names of large numbers * Names of small numbers * Power of 10References

External links

* Seth Lloyd's pape''Computational capacity of the universe''

provides a number of interesting dimensionless quantities.

* {{DEFAULTSORT:Orders Of Magnitude (Numbers) Orders of magnitude, Numbers