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)[edit]

10−100 to 10−30[edit]


(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[edit]

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

10100 (one googol) to 10^{10^{100}} (one googolplex)[edit]

Larger than 10^{10^{100}} (one googolplex)[edit]

See also[edit]


  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. ^ The On-Line Encyclopedia of Integer Sequences
  6. ^ Plouffe's Inverter
  7. ^ Facebook Tops 1 Billion Active Users
  8. ^ a b "Earth microbes on the moon". Science@Nasa. 1 September 1998. Retrieved 2 November 2010. 
  9. ^ Xavier Gourdon (October 2004). "Computation of zeros of the Zeta function". Retrieved 2 November 2010. 
  10. ^ Alexander J. Yee & Shigeru Kondo (28 Dec 2013). "12.1 Trillion Digits of Pi". Retrieved 17 Feb 2014. 
  11. ^ 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. 
  12. ^ Berg, R. (1996). "The indigenous gastrointestinal microflora". Trends in Microbiology 4 (11): 430–5. doi:10.1016/0966-842X(96)10057-3. PMID 8950812. 
  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. ^ "60th Birthday of Microelectronics Industry". Semiconductor Industry Association. 13 December 2007. Retrieved 2 November 2010. 
  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. ^ "Scores of Zimbabwe farms 'seized'". BBC. 23 February 2009. Retrieved 14 March 2009. 
  19. ^ To see the Universe in a Grain of Taranaki Sand
  20. ^ [1]
  21. ^ Sudoku enumeration
  22. ^ "Star count: ANU astronomer makes best yet". The Australian National University. 17 July 2003. Retrieved 2 November 2010. 
  23. ^ How many atoms are in the human body?
  24. ^ 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 33863. PMID 9618454. 
  25. ^ (sequence A070177 in OEIS)
  26. ^ (sequence A035064 in OEIS)
  27. ^ John Tromp (2010). "John's Chess Playground". 
  28. ^ Planck collaboration (2013). "Planck 2013 results. XVI. Cosmological parameters". Submitted to Astronomy & Astrophysics. arXiv:1303.5076. 
  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. ^ a b 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[edit]