Orders of magnitude (numbers)

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


(0.000000000000000000000000000001; 1000−10; short scale: one nonillionth; long scale: one quintillionth)


(0.000000000000000000000000001; 1000−9; short scale: one octillionth; long scale: one quadrilliardth)


(0.000000000000000000000001; 1000−8; short scale: one septillionth; long scale: one quadrillionth)

ISO: yocto- (y)


(0.000000000000000000001; 1000−7; short scale: one sextillionth; long scale: one trilliardth)

ISO: zepto- (z)


(0.000000000000000001; 1000−6; short scale: one quintillionth; long scale: one trillionth)

ISO: atto- (a)


(0.000000000000001; 1000−5; short scale: one quadrillionth; long scale: one billiardth)

ISO: femto- (f)


(0.000000000001; 1000−4; short scale: one trillionth; long scale: one billionth)

ISO: pico- (p)


(0.000000001; 1000−3; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n)


(0.000001; 1000−2; long and short scales: one millionth)

ISO: micro- (μ)


(0.001; 1000−1; one thousandth)

ISO: milli- (m)


(0.01; one hundredth)

ISO: centi- (c)


(0.1; one tenth)

ISO: deci- (d)


(1; one)


(10; ten)

ISO: deca- (da)


(100; hundred)

ISO: hecto- (h)


(1000; thousand)

ISO: kilo- (k)


(10000; ten thousand or a myriad)


(100000; one hundred thousand or a lakh)


(1000000; 10002; long and short scales: one million)

ISO: mega- (M)


(10000000; a crore; long and short scales: ten million)


(100000000; long and short scales: one hundred million)


(1000000000; 10003; short scale: one billion; long scale: one thousand million, or one milliard)

ISO: giga- (G)


(10000000000; short scale: ten billion; long scale: ten thousand million, or ten milliard)


(100000000000; short scale: one hundred billion; long scale: hundred thousand million, or hundred milliard)


(1000000000000; 10004; short scale: one trillion; long scale: one billion)

ISO: tera- (T)


(1000000000000000; 10005; short scale: one quadrillion; long scale: one thousand billion, or one billiard)

ISO: peta- (P)


(1000000000000000000; 10006; short scale: one quintillion; long scale: one trillion)

ISO: exa- (E)


(1000000000000000000000; 10007; short scale: one sextillion; long scale: one thousand trillion, or one trilliard)

ISO: zetta- (Z)


(1000000000000000000000000; 10008; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)


(1000000000000000000000000000; 10009; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)


(1000000000000000000000000000000; 100010; short scale: one nonillion; long scale: one quintillion)


(1000000000000000000000000000000000; 100011; short scale: one decillion; long scale: one thousand quintillion, or one quintilliard)


(1000000000000000000000000000000000000; 100012; short scale: one undecillion; long scale: one sextillion)


(1000000000000000000000000000000000000000; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)

1042 to 10100

(1000000000000000000000000000000000000000000; 100014; short scale: one tredecillion; long scale: one septillion)

10100 (one googol) to 1010100 (one googolplex)

(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; 100033; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard)[40]

Larger than 1010100

(One googolplex; 10googol; short scale: googolplex; long scale: googolplex)

See also


  1. Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. p. 53. ISBN 0-7167-1088-9.
  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. http://www.guinnessworldrecords.com/world-records/most-pi-places-memorised
  6. The On-Line Encyclopedia of Integer Sequences
  7. Plouffe's Inverter
  8. Christof Baron (2015). "Facebook users worldwide 2016 | Statista". Statista. statista.com.
  9. 1 2 "Earth microbes on the moon". Science@Nasa. 1 September 1998. Retrieved 2 November 2010.
  10. "there was, to our knowledge, no actual, direct estimate of numbers of cells or of neurons in the entire human brain to be cited until 2009. A reasonable approximation was provided by Williams and Herrup (1988), from the compilation of partial numbers in the literature. These authors estimated the number of neurons in the human brain at about 85 billion [...] With more recent estimates of 21–26 billion neurons in the cerebral cortex (Pelvig et al., 2008 ) and 101 billion neurons in the cerebellum (Andersen et al., 1992 ), however, the total number of neurons in the human brain would increase to over 120 billion neurons." Herculano-Houzel, Suzana. "The human brain in numbers: a linearly scaled-up primate brain". Front. Hum. Neurosci. 3. doi:10.3389/neuro.09.031.2009.
  11. Kapitsa, Sergei P (1996). "The phenomenological theory of world population growth". Physics-Uspekhi. 39 (1): 57–71. (citing the range of 80 to 150 billion); see world population.
  12. Elizabeth Howell, How Many Stars Are in the Milky Way?, Space.com, 21 May 2014 (citing estimates from 100 to 400 billion).
  13. "While estimates among different experts vary, an acceptable range is between 100 billion and 200 billion galaxies, Mario Livio, an astrophysicist at the Space Telescope Science Institute in Baltimore, told Space.com." Elizabeth Howell,, How Many Galaxies Are There?, Space.com, 1 April 1, 2014.
  14. Xavier Gourdon (October 2004). "Computation of zeros of the Zeta function". Retrieved 2 November 2010.
  15. Alexander J. Yee & Shigeru Kondo (28 Dec 2013). "12.1 Trillion Digits of Pi". Retrieved 17 Feb 2014.
  16. Savage, D. C. (1977). "Microbial Ecology of the Gastrointestinal Tract". Annual Review of Microbiology. 31: 107–33. doi:10.1146/annurev.mi.31.100177.000543. PMID 334036.
  17. Berg, R. (1996). "The indigenous gastrointestinal microflora". Trends in Microbiology. 4 (11): 430–5. doi:10.1016/0966-842X(96)10057-3. PMID 8950812.
  18. Koch, Christof. Biophysics of computation: information processing in single neurons. Oxford university press, 2004.
  19. Bert Holldobler and E.O. Wilson The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies New York:2009 W.W. Norton Page 5
  20. "60th Birthday of Microelectronics Industry". Semiconductor Industry Association. 13 December 2007. Retrieved 2 November 2010.
  21. Sequence A131646 in The On-Line Encyclopedia of Integer Sequences
  22. "Frequently Asked Questions on Entomology". Entomological Society of America.
  23. Ivan Moscovich, 1000 playthinks: puzzles, paradoxes, illusions & games, Workman Pub., 2001 ISBN 0-7611-1826-8.
  24. "Scores of Zimbabwe farms 'seized'". BBC. 23 February 2009. Retrieved 14 March 2009.
  25. To see the Universe in a Grain of Taranaki Sand
  26. "How Many Transistors Have Ever Shipped? - Forbes". Retrieved 1 September 2015.
  27. Sudoku enumeration
  28. "Star count: ANU astronomer makes best yet". The Australian National University. 17 July 2003. Archived from the original on July 24, 2005. Retrieved 2 November 2010.
  29. "Astronomers count the stars". BBC News. July 22, 2003. Retrieved 2006-07-18. "trillions-of-earths-could-be-orbiting-300-sextillion-stars" van Dokkum, Pieter G.; Charlie Conroy (2010). "A substantial population of low-mass stars in luminous elliptical galaxies". Nature. 468 (7326): 940–942. arXiv:1009.5992Freely accessible. Bibcode:2010Natur.468..940V. doi:10.1038/nature09578. PMID 21124316. "How many stars?"; see mass of the observable universe
  30. How many atoms are in the human body?
  31. William B. Whitman; David C. Coleman; William J. Wiebe (1998). "Prokaryotes: The unseen majority". Proceedings of the National Academy of Sciences of the United States of America. 95 (12): 6578–6583. doi:10.1073/pnas.95.12.6578. PMC 33863Freely accessible. PMID 9618454.
  32. (sequence A070177 in the OEIS)
  33. (sequence A035064 in the OEIS)
  34. John Tromp (2010). "John's Chess Playground".
  35. Planck Collaboration (2015). "Planck 2015 results. XIII. Cosmological parameters (See Table 4 on page 31 of pfd).". arXiv:1502.01589Freely accessible.
  36. Paul Zimmermann, "50 largest factors found by ECM".
  37. Matthew Champion, "Re: How many atoms make up the universe?", 1998
  38. WMAP- Content of the Universe. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01.
  39. "Names of large and small numbers". bmanolov.free.fr. Miscellaneous pages by Borislav Manolov.
  40. http://www.richardeldridge.com
  41. Chris Caldwell, The Top Twenty: Elliptic Curve Primality Proof at The Prime Pages.
  42. Chris Caldwell, The Top Twenty: Twin Primes at The Prime Pages.
  43. Chris Caldwell, The Top Twenty: Sophie Germain (p) at The Prime Pages.
  44. Chris Caldwell, The Top Twenty: Palindrome at The Prime Pages.
  45. PrimeGrid's Primorial Prime Search
  46. Chris Caldwell, The Top Twenty: Factorial primes at The Prime Pages.
  47. 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.
  48. Chris Caldwell, The Top Twenty: Generalized Fermat at The Prime Pages.
  49. Chris Caldwell, The Top Twenty: Proth at The Prime Pages.
  50. 1 2 Chris Caldwell, The Top Twenty: Largest Known Primes at The Prime Pages.
  51. Chris Caldwell, Mersenne Primes: History, Theorems and Lists at The Prime Pages.
  52. Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.

External links

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