Orders of magnitude (numbers)

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Orders of magnitude
area
angular velocity
charge
currency
data
density
energy
frequency
length
magnetic flux density
mass
numbers
power
pressure
specific energy density
specific heat capacity
speed
temperature
time
volume
Conversion of units
physical unit
SI
SI base unit
SI derived unit
SI prefix
Planck units

This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national language.

[edit] Smaller than 10^-36

• Computing: The number 5×10^-324 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 1.4×10^-45 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; 1000^-12; short scale: one undecillionth, long scale: one sextillionth)

[edit] 10^-33

(0.000 000 000 000 000 000 000 000 000 000 001; 1000^-11; short scale: one decillionth, long scale: one quintilliardth)

[edit] 10^-30

(0.000 000 000 000 000 000 000 000 000 001; 1000^-10; short scale: one nonillionth, long scale: one quintillionth)

[edit] 10^-27

(0.000 000 000 000 000 000 000 000 001; 1000^-9; short scale: one octillionth, long scale: one quadrilliardth)

[edit] 10^-24

(0.000 000 000 000 000 000 000 001; 1000^-8; short scale: one septillionth long scale: one quadrillionth)

ISO: yocto- (y)

• Chemistry: The mass of one carbon-12 atom is roughly 1.9926×10^-23 grams based on Avogadro's number.

[edit] 10^-21

(0.000 000 000 000 000 000 001; 1000^-7; short scale: one sextillionth, long scale: one trilliardth)

ISO: zepto- (z)

[edit] 10^-18

(0.000 000 000 000 000 001; 1000^-6; short scale: one quintillionth, long scale: one trillionth)

ISO: atto- (a)

[edit] 10^-15

(0.000 000 000 000 001; 1000^-5; short scale: one quadrillionth, long scale: one billiardth)

ISO: femto- (f)

[edit] 10^-12

(0.000 000 000 001; 1000^-4; 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; 1000^-3; 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 7×10^-9.
• 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 7×10^-8.
• Physics: The time it takes light to travel 1 meter in a vacuum is approximately 3.3356×10^-9 seconds. The time it takes light to travel 1 Foot (length) in a vacuum is approximately 1.0167×10^-9 seconds.

[edit] 10^-6

(0.000 001; 1000^-2; long and short scales: 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; 1000^-1; 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, and 10 toes on a pair of human feet.
• 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 or a myriad)

• 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 one counts 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 or a lakh)

• 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; 1000²; long and short scales: one million)

ISO: mega- (M)

• 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)
• Info - Web sites: as of early 2008, the Wikipedia contains approximately 2,192,000 articles in the English language
• 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.
• 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
• Mathematics: 14,772,512 solutions to n-Queens Problem for n = 16
• Info - Web sites: as of July 2003, the Netcraft web survey estimates that there are 42 million distinct web sites
• Mathematics: 95,815,104 solutions to n-Queens Problem for n = 17
• 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: 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; 1000³; short scale: one billion; long scale: one milliard or 1000 million)

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 3×10⁹ 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 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 8×10⁹ web pages indexed by Google as of 2004
• Astronomy - Observable galaxies: as of 2003 there are between 1×10¹⁰ and 8×10¹⁰ 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 4×10¹¹ 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; 1000⁴; short scale: one trillion; long scale: one billion)

ISO: tera- (T)

• BioMed - Bacteria on the human body: the surface of the human body houses roughly 10¹² bacteria.[4]
• Mathematics: 1.1×10¹² - 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.
• Marine biology: 3,500,000,000,000 - estimated population of fish in the ocean.
• 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; 1000⁵; short scale: one quadrillion; long scale: one billiard or 1000 billion)

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; 1000⁶; short scale: one quintillion; long scale: one 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: 9.22×10¹⁸ 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 4.3×10¹⁹ 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 6×10¹⁹) permutations.

[edit] 10²¹

(1 000 000 000 000 000 000 000; 1000⁷; short scale: one sextillion; long scale: one trilliard or 1000 trillion)

ISO: zetta- (Z)

• Mathematics - Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×10²¹) 9×9 sudoku grids. [7]
• Astronomy - Stars: 70 sextillion = 7×10²² estimated number of stars within range of telescopes (as of 2003), see mass of the observable universe. [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.
• Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×10²³) is the fifth unitary perfect number.
• Chemistry: there are roughly 6.022×10²³ molecules in one mole of any substance (Avogadro's number)

[edit] 10²⁴

(1 000 000 000 000 000 000 000 000; 1000⁸; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)

• Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8×10²⁴) is a Woodall prime.

[edit] 10²⁷

(1 000 000 000 000 000 000 000 000 000; 1000⁹; short scale: one octillion; long scale: one quadrilliard or 1000 quadrillion)

• BioMed - Atoms in the human body: the average human body contains roughly 7×10²⁷ 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 2.117×10²⁸, see Poker probability (Texas hold 'em).

[edit] 10³⁰

(1 000 000 000 000 000 000 000 000 000 000; 1000¹⁰; short scale: one nonillion; long scale: one 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; 1000¹¹; short scale: one decillion; long scale: one quintilliard or 1000 quintillion)

• Mathematics: 1,298,074,214,633,706,835,075,030,044,377,087 (≈1.3×10³³) is a Carol prime

[edit] 10³⁶

(1 000 000 000 000 000 000 000 000 000 000 000 000; 1000¹²; short scale: one undecillion; long scale: one sextillion)

• Computing: The address range of IPv6 (2¹²⁸) is approximately equal to 3.4×10³⁸, and is the theoretical maximum number of Internet addresses that can be allocated under the IPv6 addressing system.
• Computing: The IEEE floating-point number 3.4028235×10³⁸ is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.
• Computing: The total number of different Universally Unique Identifiers (UUIDs) that can be generated is about 3.4×10³⁸.
• 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; 1000¹³; short scale: one duodecillion; long scale: one sextilliard or 1000 sextillion)

• Mathematics: 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×10³⁸) is a double Mersenne prime
• Cosmology: The Eddington-Dirac number is roughly 10⁴⁰.
• Physics: , the ratio of the electrical to the gravitational forces between two protons, is roughly 10⁴⁰.

[edit] 10⁴²

(1 000 000 000 000 000 000 000 000 000 000 000 000 000 000; 1000¹⁴; short scale: one tredecillion; long scale: one septillion)

• Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4×10⁴³) is a Pierpont prime
• Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9×10⁴⁴) is a Cullen prime

[edit] 10⁴⁵ to 10¹⁰⁰

(1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000; 1000¹⁵; long scale: one septilliard or 1000 septillion

• Mathematics: 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 (≈3.6×10⁵³) 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: 8×10⁶⁰ 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 (≈7×10⁶⁵) - 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 (≈8×10⁶⁷) - 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 (≈4.8×10⁷¹) 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: 4.8231×10¹¹⁵, 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: 8×10¹²⁰, 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: 4×10¹⁸⁵, approximate number of Planck volumes in the observable universe.
• Computing: 1.7976931348623157×10³⁰⁸ 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 (), a googolplex.
• Mathematics: , order of magnitude of an upper bound that occurred in a proof of Skewes.
• Mathematics: , 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,

[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.