Orders of magnitude (numbers)

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Orders of magnitude
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This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities.

[edit] Smaller than 10^-36

• Computing: The number 5Template:E is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value.
• Computing: The number 1.4Template:E is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.

[edit] 10^-36

(0.000 000 000 000 000 000 000 000 000 000 000 001)

[edit] 10^-33

(0.000 000 000 000 000 000 000 000 000 000 001)

[edit] 10^-30

(0.000 000 000 000 000 000 000 000 000 001)

[edit] 10^-27

(0.000 000 000 000 000 000 000 000 001), short scale: One octillionth, long scale: One quadrilliardth)

ISO: xonto- (x)

[edit] 10^-24

(0.000 000 000 000 000 000 000 001), short scale: One septillionth long scale: One quadrillionth)

ISO: yocto- (y)

• Chemistry: The mass of one carbon-12 atom is roughly 1.9926Template:E grams based on Avogadro's number.

[edit] 10^-21

(0.000 000 000 000 000 000 001, short scale: One sextillionth, long scale: One trilliardth)

ISO: zepto- (z)

[edit] 10^-18

(0.000 000 000 000 000 001, short scale: One quintillionth, long scale: One trillionth)

ISO: atto- (a)

[edit] 10^-15

(0.000 000 000 000 001, short scale: One quadrillionth, long scale: One billiardth)

ISO: femto- (f)

[edit] 10^-12

(0.000 000 000 001, short scale: One trillionth, long scale: One billionth)

ISO: pico- (p)

• Mathematics: Roughly the chances of getting heads 40 times in a row on a fair coin.

[edit] 10^-9

(0.000 000 001; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n)

• Mathematics - Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball Multistate Lottery, with a single ticket, under the rules as of 2006, are 146,107,962 to 1 against, for a probability of 7Template:E.
• 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 as of 2003, are 13,983,816 to 1 against, for a probability of 7Template:E.
• Physics: The time it takes light to travel 1 meter in a vacuum is approximately 3.3356Template:E seconds. The time it takes light to travel 1 Foot (length) in a vacuum is approximately 1.0167Template:E seconds.

[edit] 10^-6

(0.000 001; one millionth)

ISO: micro- (μ)

• Mathematics - Poker: The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5 × 10^-6
• Mathematics - Poker: The odds of being dealt a straight flush (other than a royal flush) in poker are 72,192 to 1 against, for a probability of 1.4 × 10^-5
• 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 × 10^-4

[edit] 10^-3

(0.001; one thousandth)

ISO: milli- (m)

• Mathematics - Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10^-3
• 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
• Mathematics - Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10^-3
• Physics: α = 0.007 297 352 533(27), the fine-structure constant

[edit] 10^-2

(0.01; one hundredth)

ISO: centi- (c)

• BioMed - HIV: About 1.2% of all 15–49 year-old humans were infected with HIV at the end of 2001^{[citation needed]}
• 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 kind 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 US Powerball Multistate Lottery, with a single ticket, under the rules as of 2006, are 36.61 to 1 against, for a probability of 0.027 (2.7%)
• Mathematics - Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 0.048 (4.8%).

[edit] 10^-1

(0.1; one tenth)

ISO: deci- (d)

• 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%)

[edit] 10⁰

(1; one)

• Mathematics: φ ≈ 1.6180339887, the golden ratio
• Mathematics: e ≈ 2.718281828459045, the base of the natural logarithm
• Mathematics: π ≈ 3.14159265358979, the ratio of a circle's circumference to its diameter
• BioMed: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously held in working memory
• Astronomy: 8 planets in the solar system

[edit] 10¹

(10; ten)

ISO: deca- (da)

• Human scale: there are 10 fingers on a pair of human hands
• Language: there are 26 letters in the Latin alphabet in the English language

[edit] 10²

(100; hundred)

ISO: hecto- (h)

• Computing: There are 128 characters in the ASCII character set.
• Geo: There were 192 member states of the United Nations as of 2006.

[edit] 10³

(1 000; thousand)

ISO: kilo- (k)

• Language: 2000–3000 letters on a typical typed page of text
• BioMed: the DNA of the simplest viruses has some 5000 base pairs.
• Language: There are about 6500 mutually unintelligible languages and dialects.

[edit] 10⁴

(10 000; ten thousand)

• BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
• Language: There are 20,000–40,000 distinct Chinese characters, depending on how you count them
• BioMed: Each human being is estimated to have 30,000 to 40,000 genes
• Records: As of July 2004, the largest number of decimal places of π that have been recited from memory - > 42000
• Mathematics: 65537 is the largest known Fermat prime

[edit] 10⁵

(100 000; one hundred thousand)

• BioMed - Strands of hair on a head: The average human head has about 100,000–150,000 strands of hair
• Mathematics: 110,000 - The approximate number of entries on The On-Line Encyclopedia of Integer Sequences as of August 2005 [1]
• Language: 267,000 words in James Joyce's Ulysses
• Language - English words: The New Oxford Dictionary of English contains about 350,000 definitions for English words
• Mathematics: 365,596 solutions to n-Queens Problem for n = 14
• Language: 564,000 words in War and Peace
• Info: The FreeDB database has around 1 750 000 entries as of June 2005

[edit] 10⁶

(1 000 000; 1 million)

ISO: mega- (M)

• Geography/Computing - Geographic places: The NIMA GEOnet Names Server contains approximately 3.88 million named geographical features outside the United States, with 5.34 million names. The USGS Geographic Names Information System claims to have almost 2 million physical and cultural geographic features within the United States.
• BioMed - Species: The World Resources Institute claims that approximately 1.4 million species have been named, out of an unknown number of total species (estimates range between 2 and 100 million species).
• Mathematics - Chess: There are 2 279 184 solutions to n-Queens Problem for n = 15
• Mathematics - Playing cards: There are 2 598 960 different 5-card poker hands that can be dealt from a standard 52-card deck.
• Info - Web sites: as of July 2003, the Netcraft web survey estimates that there are 42 million distinct web sites
• Info - Books: The British Library claims that it holds over 150 million items. The Library of Congress claims that it holds approximately 119 million items. See The Gutenberg Galaxy
• Mathematics: 14,772,512 solutions to n-Queens Problem for n = 16
• Mathematics: 95,815,104 solutions to n-Queens Problem for n = 17
• Mathematics: 215,000,000 - The approximate number of mathematical constants collected on the Plouffe's Inverter as of August 2005 [2]
• Mathematics: 275,305,224 is the number of 5x5 normal magic squares, not counting rotations and reflections. This result was found in 1973 by Richard Schroeppel. It is the third 91768409-gonal number.
• Mathematics: 358,833,097 stellations of the rhombic triacontahedron
• Demographics: approx. 402,000,000 native speakers of English
• Astronomy - Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects

[edit] 10⁹

(1 000 000 000; short scale: 1 billion; long scale: 1 thousand million (old term: milliard)

ISO: giga- (G)

• Demographics - India: 1,096,000,000 - approximate population of India in 2007
• Demographics - China: 1,311,000,000 - approximate population of the People's Republic of China in 2007.
• Computing - Computational limit of a 32-bit CPU: 2 147 483 647 is equal to 2³¹−1, and as such is the largest number which can fit into a signed (two's complement) 32-bit integer on a computer, thus marking the upper computational limit of a 32-bit CPU such as Intel's Pentium-class computer chips.
• Mathematics: 2,147,483,647 is a Mersenne prime.
• BioMed - base pairs in the genome: approximately 3Template:E base pairs in the human genome
• Computing - IPv4: 4,294,967,296 (2³²) possible unique IP addresses.
• Computing: 4,294,967,296 - the number of bytes in 4 gibibytes; in computation, the 32-bit computers can directly access 2³² pieces of address space, this leads directly to the 4 gigabyte limit on main memory.
• Mathematics: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form <math>2^{2^n}+1</math> which is not a prime number.
• Demographics - world population: 6,587,890,000 - Estimated total mid-year population for the world in 2007 (April 10).
• Computing - web pages: approximately 8Template:E web pages indexed by Google as of 2004
• Astronomy - Observable galaxies: as of 2003 there are between 1Template:E and 8Template:E galaxies in the observable Universe
• BioMed - bacteria in the human body: there are roughly 10¹⁰ bacteria in the human oral cavity [3]
• Mathematics: 27,704,267,971 and 27,704,267,977 are sexy primes.
• BioMed - Neurons in the brain: approximately 10¹¹ neurons in the human brain
• Astronomy - stars in our galaxy: approximately 4Template:E stars in the Milky Way galaxy
• Mathematics: 258,584,046,368 is the number of domino tilings of a 10×10 checkerboard.

[edit] 10¹²

(1 000 000 000 000; short scale: 1 trillion; long scale: 1 billion)

ISO: tera- (T)

• BioMed - Bacteria on the human body: the surface of the human body houses roughly 10¹² bacteria [4]
• Mathematics: 1.1Template:E - The approximate number of known non-trivial zeros of Riemann zeta function as of August 2005 [5]
• Mathematics - Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000
• BioMed - Cells in the human body: the human body consists of roughly 10¹⁴ cells
• Computing - MAC-48: 281,474,976,710,656 (2⁴⁸) possible unique physical addresses.
• Mathematics: 953,467,954,114,363 is the largest known Motzkin prime.
• Computing - magnetic storage: 1TB largest 3.5inch hard disk as of 2007.

[edit] 10¹⁵

(1 000 000 000 000 000; short scale: 1 quadrillion; long scale: 1 thousand billion (old term: billiard)

ISO: peta- (P)

• BioMed - Bacteria in the human body: there are roughly 10¹⁵ bacteria in the human body ([6] speaks of 10¹⁴), the overwhelming majority in the intestinal tract
• Mathematics: 48,988,659,276,962,496 is the fifth taxicab number.
• Mathematics: 53,060,477,521,960,000 is the number of domino tilings of a 12×12 checkerboard.

[edit] 10¹⁸

(1 000 000 000 000 000 000; short scale: 1 quintillion; long scale: 1 trillion)

ISO: exa- (E)

• BioMed - Insects: It has been estimated that the insect population of the Earth comprises roughly 10¹⁸ insects.
• Mathematics: 2,305,843,009,213,693,951 (2⁶¹-1) is a Mersenne prime
• Computing - Computational limit of a 64-bit CPU: 9.22Template:E is equal to 2⁶³-1, and as such is the largest number which can fit into a signed (two's complement) 64-bit integer on a computer.
• Mathematics - NCAA Basketball Tournament: There are 9,223,372,036,854,775,808 (2⁶³) possible ways to enter the bracket.
• Mathematics - Rubik's Cube: There are 4.3Template:E different positions of a Rubik's Cube
• Password strength - Usage of the 95-character set found on standard computer keyboards for a 10-character password yields a computationally intractable 95¹⁰ (approximately 6Template:E) permutations.

[edit] 10²¹

(1 000 000 000 000 000 000 000; short scale: 1 sextillion; long scale: 1,000 trillion)

ISO: zetta- (Z)

• Mathematics - Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7Template:E) 9×9 sudoku grids. [7]
• Astronomy - Stars: 70 sextillion = 7Template:E was estimated in 2003 by Australian astronomers as the number of stars within range of telescopes. This estimate is based on galaxy counts and star estimates: [8]
• Geo - Grains of sand: all the world's beaches put together hold roughly 10²³ grains of sand. [9]
• Mathematics: 112,202,208,776,036,178,000,000 is the number of domino tilings of a 14×14 checkerboard.
• Chemistry: there are roughly 6.022Template:E molecules in one mole of any substance (Avogadro's number)

[edit] 10²⁴

(1 000 000 000 000 000 000 000 000; short scale: 1 septillion; long scale: 1 quadrillion)

ISO: yotta- (Y)

• Computing: Yottabyte (YB) is 10²⁴ bytes.
• Mathematics: 146,361,946,186,458,562,560,000 (≈1.5Template:E) is the fifth unitary perfect number.
• Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8Template:E) is a Woodall prime.

[edit] 10²⁷

(1 000 000 000 000 000 000 000 000 000 ; short scale: 1 octillion; long scale: 1,000 quadrillion)

ISO: xona- (X)

• BioMed - Atoms in the human body: the average human body contains roughly 7Template:E atoms, see [10]
• Mathematics - Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas Hold'em is approximately 2.117Template:E, see Poker probability (Texas hold 'em).

[edit] 10³⁰

(1 000 000 000 000 000 000 000 000 000 000; short scale: 1 nonillion; long scale: 1 quintillion)

• BioMed: number of bacterial cells on Earth
• Mathematics: 2,444,888,770,250,892,795,802,079,170,816 is the number of domino tilings of a 16×16 checkerboard.
• Mathematics: The partition of 1000 is 24,061,467,864,032,622,473,692,149,727,991.

[edit] 10³³

(1 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 decillion; long scale: 1,000 quintillion)

• Mathematics: 1,298,074,214,633,706,835,075,030,044,377,087 (≈1.3Template:E) is a Carol prime

[edit] 10³⁶

(1 000 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 undecillion; long scale: 1 sextillion)

• Computing: The address range of IPv6 (2¹²⁸) is approximately equal to 3.4Template:E, and is the theoretical maximum number of Internet addresses that can be allocated under the IPv6 addressing system.
• Computing: The IEEE floating-point number 3.4028235Template:E is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.
• Mathematics: 548,943,583,215,388,338,077,567,813,208,427,340,288 is the number of domino tilings of an 18×18 checkerboard.

[edit] 10³⁹

(1 000 000 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 duodecillion; long scale: 1,000 sextillion)

• Mathematics: 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7Template:E) is a double Mersenne prime
• Cosmology: The Eddington-Dirac number is roughly 10⁴⁰.
• Physics: <math>e^2/Gm^2 \,</math>, the ratio of the electrical to the gravitational forces between two protons, is roughly 10⁴⁰.

[edit] 10⁴² to 10¹⁰⁰

See names of large numbers for the names of these and larger numbers.

• Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4Template:E) is a Pierpont prime
• Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9Template:E) is a Cullen prime
• Mathematics: 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 (≈3.6Template:E) is a prime Bell number
• Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 is order of Monster group
• Cosmology: 8Template:E is roughly the number of Planck time intervals since the universe is theorized to have been created in the Big Bang 13.7 ± 0.2 billion years ago
• Mathematics: 709,601,635,082,267,320,966,424,084,955,776,789,770,864,725,643,996,885,415,676,682,297 (≈7Template:E) - The largest known prime factor found by ECM factorization as of August 2005 [11]
• Mathematics - Cards: 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8Template:E) - the number of ways to order the cards in a 52-card deck.
• Mathematics: 475,420,437,734,698,220,747,368,027,166,749,382,927,701,417,016,557,193,662,268,716,376,935,476,241 (≈4.8Template:E) is a Fibonacci prime
• Cosmology: various sources estimate the total number of fundamental particles in the observable universe in the range 10⁸⁰ to 10⁸⁵. However, these estimates are generally regarded as guesswork.
• Mathematics: 10¹⁰⁰, a googol

[edit] Larger than 10¹⁰⁰

• Board games: 4.8231Template:E, number of ways to arrange the tiles in English Scrabble (100! / 9! / 2! / 2! / 4! / 12! / 2! / 3! / 2! / 9! / 1! / 1! / 4! / 2! / 6! / 8! / 2! / 1! / 6! / 4! / 6! / 4! / 2! / 2! / 1! / 2! / 1! / 2!).
• Chess: Shannon number, 10¹²⁰, an estimation of the game-tree complexity of chess.
• Physics: 8Template:E, 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 - History: Asankhyeya is equal to 10¹⁴⁰ in ancient India.
• Xiangqi: 10¹⁵⁰, an estimation of the game-tree complexity of xiangqi.
• Physics: 4Template:E, approximate number of Planck volumes in the observable universe.
• Computing: 1.7976931348623157Template:E is approximately equal to the largest value that can be represented by a double-precision IEEE floating-point number.
• Go: 10³⁶⁵, an estimation of the game-tree complexity in the game of Go.^{[citation needed]}
• Mathematics: 2638⁴⁴⁰⁵ + 4405²⁶³⁸ is a 15071-digit Leyland prime; the largest which has been proven as of 2007.
• Mathematics: 137211941292195 · 2¹⁷¹⁹⁶⁰ − 1 is a 51780-digit Sophie Germain prime; the largest known as of 2007.
• Mathematics: 2003663613 · 2¹⁹⁵⁰⁰⁰ ± 1 are 58711-digit twin primes; the largest known as of 2007.
• Mathematics: 34790! – 1 is a 142891-digit factorial prime; the largest known as of 2007.
• Mathematics: 10¹⁵⁰⁰⁰⁶ + 7426247×10⁷⁵⁰⁰⁰ + 1 is a 150007-digit happy prime. It is also a palindromic prime.
• Mathematics: 392113# + 1 is a 169966-digit primorial prime; the largest known as of 2007.
• Mathematics: approximately 7.76 · 10²⁰⁶⁵⁴⁴ cattle in the smallest herd which satisfies the conditions of the Archimedes' cattle problem.
• Mathematics: 2^32,582,657 − 1 is a 9,808,358-digit Mersenne prime; the largest known prime as of September 2006.
• Mathematics: 2^32,582,656 × (2^32,582,657 − 1) is a 19,616,714-digit perfect number, the largest known as of 2007.
• Mathematics: (2^32,582,657 − 1)² is a 19,616,715-digit semiprime, the largest known as of 2007.
• Mathematics - History: 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner.
• Mathematics: 10^googol (<math>10^{10^{100}}</math>), a googolplex.
• Mathematics: <math>10^{\,\!10^{10^{34}}}</math>, order of magnitude of an upper bound that occurred in a proof of Skewes.
• Mathematics: <math>10^{\,\!10^{10^{1000}}}</math>, order of magnitude of another upper bound in a proof of Skewes.
• Mathematics: Moser's number should appear somewhere in this section, but is difficult to calculate.
• Mathematics: Graham's number, probably the largest number seriously used in a mathematical proof; representation in powers of 10 would be impractical (the number of digits in the exponent far exceeds the number of particles in the observable universe).

Note: To correctly interpret the last few entries, keep in mind that exponentiation is performed from right to left. For example,

<math>10^{\,\!10^{100}} \mbox{ means } 10^{\,\!(10^{100})}</math>

[edit] See also

• Large numbers
• List of numbers
• Planck units
• Mathematical constant
• Encyclopediac size comparisons on Wikipedia
• Long Scales
• Short Scales

[edit] External links

• Seth Lloyd's paper Computational capacity of the universe provides a number of interesting dimensionless quantities.fr:Ordre de grandeur (nombre)

ko:수의 비교 it:Ordini di grandezza (numeri) ja:数量の比較 (無次元数) sl:Red velikosti (števila) zh:数量级 (数)