Orders of magnitude (numbers)

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The logarithmic scale can compactly represent the relationship among variously sized numbers.

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

Smaller than 10−100 (one googolth)

10−100 to 10−30

  • 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.

10−30

(Template:Gaps; 1000−10; short scale: one nonillionth; long scale: one quintillionth)

  • Mathematics: The probability in a game of bridge of all four players getting a complete suit is approximately Template:Val.[3]

10−27

(Template:Gaps; 1000−9; short scale: one octillionth; long scale: one quadrilliardth)

10−24

(Template:Gaps; 1000−8; short scale: one septillionth; long scale: one quadrillionth)

ISO: yocto- (y)

10−21

(Template:Gaps; 1000−7; short scale: one sextillionth; long scale: one trilliardth)

ISO: zepto- (z)

  • Mathematics: The probability of matching 20 numbers for 20 in a game of Keno is approximately 2.83 × 10−19.

10−18

(Template:Gaps; 1000−6; short scale: one quintillionth; long scale: one trillionth)

ISO: atto- (a)

  • Mathematics: The probability of rolling snake eyes 10 times in a row on a pair of fair dice is about Template:Val

10−15

(Template:Gaps; 1000−5; short scale: one quadrillionth; long scale: one billiardth)

ISO: femto- (f)

10−12

(Template:Gaps; 1000−4; short scale: one trillionth; long scale: one billionth)

ISO: pico- (p)

10−9

(Template:Gaps; 1000−3; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n)

10−6

(Template:Gaps; 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 (Template:Gaps).
  • 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 (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 × 10−4 (0.024%).

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 (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 = Template:Val, the fine-structure constant.

10−2

(0.01; one hundredth)

ISO: centi- (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 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%).

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%)
  • Legal history: 10% was widespread as the tax raised for income or produce in the ancient and medieval period, see tithe.

100

(1; one)

101

(10; ten)

ISO: deca- (da)

102

(100; hundred)

ISO: hecto- (h)

  • Demography: The population of Nassau Island, part of the Cook Islands, is around 100.
  • European history: Groupings of 100 homesteads was a common administrative unit in Northern Europe and Great Britain (see Hundred (county subdivision)).
  • Computing: There are 128 characters in the ASCII character set.
  • Phonology: The Taa language is estimated to have between 130 and 164 distinct phonemes.
  • Political Science: There were 193 member states of the United Nations as of 2011.

103

(Template:Gaps; thousand)

ISO: kilo- (k)

104

(Template:Gaps; ten thousand or a myriad)

  • BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
  • Demography: The population of Tuvalu was 10,544 in 2007.
  • Lexicography: 14,500 unique English words occur in the King James Version of the Bible
  • Language: There are 20,000–40,000 distinct Chinese characters.
  • BioMed: Each human being is estimated to have 30,000 to 40,000 genes
  • Mathematics: 65,537 is the largest known Fermat prime
  • Memory: Template:As of, the largest number of decimal places of π that have been recited from memory is 67,890

105

(Template:Gaps; one hundred thousand or a lakh)

106

(Template:Gaps; 10002; long and short scales: one million)

ISO: mega- (M)

  • Demography: The population of Riga, Latvia was 1,003,949 in 2004, according to Eurostat.
  • 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) Some scientists give 8.8 million species as an exact figure.
  • Genocide: Approximately 800,000–1,500,000 (1.5 Million) Armenians were killed in the Armenian Genocide.
  • Info: The freedb database of CD track listings has around 1,750,000 entries Template:As of
  • 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 11, 2020, Wikipedia contains approximately Template:Rounddown articles in the English language
  • Geography/Computing – Geographic places: The NIMA GEOnet Names Server contains approximately 3.88 million named geographic 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.
  • Genocide: Approximately 5,100,000–6,200,000 Jews were killed in the Holocaust.

107

(Template:Gaps; a crore; long and short scales: ten million)

108

(Template:Gaps; long and short scales: one hundred million)

109

(Template:Gaps; 10003; short scale: one billion; long scale: one thousand million, or one milliard)

ISO: giga- (G)

  • Internet: Approximately 1,000,000,000 active users were on Facebook as of October 2012.[7]
  • Demography: The population of Africa reached 1,000,000,000 sometime in 2009.
  • Demographics – India: 1,210,000,000 – approximate population of India in 2011
  • Demographics – China: 1,347,000,000 – approximate population of the People's Republic of China in 2011.
  • 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.
  • BioMed – base pairs in the genome: approximately 3Template:E base pairs in the human genome
  • Linguistics: 3,400,000,000 – the total number of speakers of Indo-European languages, of which 2,400,000,000 are native speakers; the other 1,000,000,000 speak Indo-European languages as a second language
  • 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: 7,000,000,000 – Estimated population for the world on 31 October 2011, the Day of Seven Billion.

1010

(Template:Gaps; short scale: ten billion; long scale: ten thousand million, or ten milliard)

1011

(Template:Gaps; short scale: one hundred billion; long scale: hundred thousand million, or hundred milliard)

1012

(Template:Gaps; 10004; short scale: one trillion; long scale: one billion)

ISO: tera- (T)

1015

(Template:Gaps; 10005; short scale: one quadrillion; long scale: one thousand billion, or one billiard)

ISO: peta- (P)

  • BioMed-Insects: 1,000,000,000,000,000 to 10,000,000,000,000,000 (1015 to 1016) – The estimated total number of ants on Earth alive at any one time (their biomass is approximately equal to the total biomass of the human race).[13]
  • Computing: 9,007,199,254,740,992 (253) – 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, 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.
  • Cryptography: There are 7.205759Template:E different possible keys in the obsolete 56 bit DES symmetric cipher.

1018

(Template:Gaps; 10006; short scale: one quintillion; long scale: one trillion)

ISO: exa- (E)

  • Computing – Manufacturing: An estimated 6Template:E transistors were produced worldwide in 2008.[14]
  • Computing – Computational limit of a 64-bit CPU: 9,223,372,036,854,775,807 (about 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 – Bases: 9,439,829,801,208,141,318 (≈9.44Template:E) is the 10th and largest number with more than one digit that can be written from base 2 to base 18 using only the digits 0 to 9.[15]
  • BioMed – Insects: It has been estimated that the insect population of the Earth is about 1019.[16]
  • 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 264−1 = 18,446,744,073,709,551,615 (≈1.84Template:E).
  • Mathematics – Legends: In the legend called the Tower of Brahma about a Hindu temple which contains a large room with three posts on one of which is 64 golden discs, the object of the mathematical game is for the Brahmins in the 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. It would take 264−1 = 18,446,744,073,709,551,615 (≈1.84Template:E) turns to complete the task (same number as the wheat and chessboard problem above).[17]
  • Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33Template:E) different positions of a 3x3x3 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 59,873,693,923,837,890,625 (9510, approximately 5.99Template:E) permutations.
  • Economics: Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent,[18] or a factor of 1020

1021

(Template:Gaps; 10007; short scale: one sextillion; long scale: one thousand trillion, or one trilliard)

ISO: zetta- (Z)

1024

(Template:Gaps; 10008; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)

1027

(Template:Gaps; 10009; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)

1030

(Template:Gaps; 100010; short scale: one nonillion; long scale: one quintillion)

  • BioMed – 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 × 1030[24]
  • Mathematics: The number of partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.[25]
  • Mathematics: 2108 = 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.[26]

1033

(Template:Gaps; 100011; short scale: one decillion; long scale: 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 7.24Template:E) different positions of Alexander's Star

1036

(Template:Gaps; 100012; short scale: one undecillion; long scale: one sextillion)

1039

(Template:Gaps; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)

1042 to 10100

(Template:Gaps; 100014; short scale: one tredecillion; long scale: one septillion)

  • Mathematics: 141×2141+1 = 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.93Template:E) is the second Cullen prime
  • Mathematics: There are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 (≈7.4Template:E) possible permutations for the Rubik's Revenge (4x4x4 Rubik's Cube).
  • Chess: 4.52Template:E is a proven upper bound for the number of legal chess positions.[27]
  • Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 (≈8.08Template:E) is the order of the Monster group.
  • Cryptography: 2192 = 6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896 (6.27710174Template:E), the total number of different possible keys in the AES 192-bit key space (symmetric cipher).
  • Cosmology: 8Template:E is roughly the number of Planck time intervals since the universe is theorised to have been created in the Big Bang 13.798 ± 0.037 billion years ago.[28]
  • Cosmology: 1Template:E 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 stadia to be what we call 2 light years.
  • 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 (≈8.07Template:E) – the number of ways to order the cards in a 52-card deck.
  • 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 (≈1.81Template:E) – The largest known prime factor found by ECM factorization Template:As of.[29]
  • 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 (≈2.83Template:E) possible permutations for the Professor's Cube (5x5x5 Rubik's Cube).
  • Cryptography: 2256 = 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 (1.15792089Template:E), the total number of different possible keys in the AES 256-bit key space (symmetric cipher).
  • Cosmology: Various sources estimate the total number of fundamental particles in the observable universe to be within the range of 1080 to 1085.[30][31] However, these estimates are generally regarded as guesswork.
  • Computing: 9.999 999Template:E is equal to the largest value that can be represented in the IEEE decimal32 floating-point format.
  • Mathematics: 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; 10100, a googol

10100 (one googol) to (one googolplex)

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Larger than (one googolplex)

See also

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References

  1. {{#invoke:citation/CS1|citation |CitationClass=book }}
  2. There are around 130,000 letters and 199,749 total characters in Hamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64199749 ≈ 10360,783.
  3. Bridge hands
  4. P. L. Walraven and H. J. Lebeek. "Foveal Sensitivity of the Human Eye in the Near Infrared". J. Opt. Soc. Am. 53, 765–766 (1963).
  5. The On-Line Encyclopedia of Integer Sequences
  6. Plouffe's Inverter
  7. Facebook Tops 1 Billion Active Users
  8. 8.0 8.1 Template:Cite web
  9. Template:Cite web
  10. Template:Cite web
  11. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  12. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  13. Bert Holldobler and E.O. Wilson The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies New York:2009 W.W. Norton Page 5
  14. Template:Cite web
  15. Sequence A131646 in The On-Line Encyclopedia of Integer Sequences
  16. "Frequently Asked Questions on Entomology". Entomological Society of America.
  17. Ivan Moscovich, 1000 playthinks: puzzles, paradoxes, illusions & games, Workman Pub., 2001 ISBN 0-7611-1826-8.
  18. Template:Cite news
  19. To see the Universe in a Grain of Taranaki Sand
  20. [1]
  21. Sudoku enumeration
  22. Template:Cite web
  23. How many atoms are in the human body?
  24. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  25. (sequence A070177 in OEIS)
  26. (sequence A035064 in OEIS)
  27. Template:Cite web
  28. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  29. Paul Zimmermann, "50 largest factors found by ECM".
  30. Matthew Champion, "Re: How many atoms make up the universe?", 1998
  31. WMAP- Content of the Universe. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01.
  32. http://www.richardeldridge.com
  33. Chris Caldwell, The Top Twenty: Elliptic Curve Primality Proof at The Prime Pages.
  34. Chris Caldwell, The Top Twenty: Twin Primes at The Prime Pages.
  35. Chris Caldwell, The Top Twenty: Sophie Germain (p) at The Prime Pages.
  36. Chris Caldwell, The Top Twenty: Palindrome at The Prime Pages.
  37. PrimeGrid's Primorial Prime Search
  38. Chris Caldwell, The Top Twenty: Factorial primes at The Prime Pages.
  39. From the third paragraph of the story: "Each book contains 410 pages; each page, 40 lines; each line, about 80 black letters." That makes 410 x 40 x 80 = 1,312,000 characters. The fifth paragraph tells us that "there are 25 orthographic symbols" including spaces and punctuation. The magnitude of the resulting number is found by taking logarithms. However, this calculation only gives a lower bound on the number of books as it does not take into account variations in the titles – the narrator does not specify a limit on the number of characters on the spine. For further discussion of this, see Bloch, William Goldbloom. The Unimaginable Mathematics of Borges' Library of Babel. Oxford University Press: Oxford, 2008.
  40. Chris Caldwell, The Top Twenty: Generalized Fermat at The Prime Pages.
  41. Chris Caldwell, The Top Twenty: Proth at The Prime Pages.
  42. 42.0 42.1 Chris Caldwell, The Top Twenty: Largest Known Primes at The Prime Pages.
  43. Chris Caldwell, Mersenne Primes: History, Theorems and Lists at The Prime Pages.
  44. Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.
  45. American Scientist January–February 2009 Books-a-Million by Brian Hayes Book Review of The Unimaginable Mathematics of Borges’ Library of Babel by William Goldbloom Bloch:
  46. Bloch, William Goldbloom The Unimaginable Mathematics of Borges’ Library of Babel (2008) Oxford University Press

External links

Template:Orders of magnitude wide