Orders of magnitude (numbers)

Last updated

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

Contents

Smaller than 10−100 (one googolth)

Chimpanzee probably not typing Hamlet Chimpanzee seated at typewriter.jpg
Chimpanzee probably not typing Hamlet

10−100 to 10−30

1/52! chance of a specific shuffle Card shuffle.jpg
1/52! chance of a specific shuffle

10−30

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

ISO: quecto- (q)

10−27

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

ISO: ronto- (r)

10−24

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

ISO: yocto- (y)

10−21

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

ISO: zepto- (z)

10−18

Snake eyes Snake eyes dice.jpg
Snake eyes

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

ISO: atto- (a)

10−15

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

ISO: femto- (f)

10−12

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

ISO: pico- (p)

10−9

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

ISO: nano- (n)

10−6

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

ISO: micro- (μ)

Poker hands Poker Hands.png
Poker hands
Poker hands
HandChance
1. Royal flush0.00015%
2. Straight flush0.0014%
3. Four of a kind0.024%
4. Full house0.14%
5. Flush0.19%
6. Straight0.59%
7. Three of a kind2.1%
8. Two pairs4.8%
9. One pair42%
10. No pair50%

10−3

(0.001; 1000−1; one thousandth)

ISO: milli- (m)

10−2

(0.01; one hundredth)

ISO: centi- (c)

10−1

(0.1; one tenth)

ISO: deci- (d)

100

Eight planets of the Solar System Planets2013.svg
Eight planets of the Solar System

(1; one)

101

Ten digits on two human hands Two hand, ten fingers.jpg
Ten digits on two human hands

(10; ten)

ISO: deca- (da)

102

128 ASCII characters ASCII-Table-wide.svg
128 ASCII characters

(100; hundred)

ISO: hecto- (h)

103

Roman legion (precise size varies) Legion Task ORG.png
Roman legion (precise size varies)

(1000; thousand)

ISO: kilo- (k)

104

(10000; ten thousand or a myriad)

105

100,000-150,000 strands of human hair Woman with long brown hair, close-up view.jpg
100,000–150,000 strands of human hair

(100000; one hundred thousand or a lakh).

106

3,674,160 Pocket Cube positions Pocket cube scrambled.jpg
3,674,160 Pocket Cube positions

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

ISO: mega- (M)

107

12,988,816 domino tilings of a checkerboard Pavage domino.svg
12,988,816 domino tilings of a checkerboard

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

108

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

109

World population estimates World population v3.svg
World population estimates

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

ISO: giga- (G)

1010

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

1011

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

1012

10 stars in the Andromeda Galaxy Andromeda Galaxy (with h-alpha).jpg
10 stars in the Andromeda Galaxy

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

ISO: tera- (T)

1015

10 to 10 ants on Earth Ants eating01.jpg
10 to 10 ants on Earth

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

ISO: peta- (P)

1018

[?]4.33x10 Rubik's Cube positions Scrumbled Rubik's Cube.jpg
≈4.33×10 Rubik's Cube positions

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

ISO: exa- (E)

1021

[?]6.7x10 sudoku grids Sudoku Puzzle by L2G-20050714 solution standardized layout.svg
≈6.7×10 sudoku grids

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

ISO: zetta- (Z)

Visualisation of a mole of 1 mm cubes arranged into a cube with 84.4 km (52.4 mi) sides, overlaid on maps of South East England and London (top), and Long Island and New York City (bottom) Avogadro number cube visualisation.svg
Visualisation of a mole of 1 mm cubes arranged into a cube with 84.4 km (52.4 mi) sides, overlaid on maps of South East England and London (top), and Long Island and New York City (bottom)

1024

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

ISO: yotta- (Y)

1027

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

ISO: ronna- (R)

1030


5 x 10 bacterial cells on Earth E. coli Bacteria (7316101966).jpg
5 × 10 bacterial cells on Earth

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

ISO: quetta- (Q)

1033

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

1036

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

1039

(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)

4.52x10 legal chess positions ChessStartingPosition.jpg
4.52×10 legal chess positions

10100 (one googol) to 101000

(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard) [65]

[?]2.08x10 legal Go positions FloorGoban.JPG
≈2.08×10 legal Go positions

101000 to 1010100 (one googolplex)

Digit growth in the largest known prime Digits in largest prime found as a function of time.svg
Digit growth in the largest known prime

Larger than 1010100

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

See also

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<span class="mw-page-title-main">Logarithm</span> Mathematical function, inverse of an exponential function

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References

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  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. ↑ Calculated: 365! / 365365 ≈ 1.455×10−157
  4. ↑ Robert Matthews. "What are the odds of shuffling a deck of cards into the right order?". Science Focus. Retrieved December 10, 2018.
  5. ↑ www.BridgeHands.com, Sales. "Probabilities Miscellaneous: Bridge Odds". Archived from the original on 2009-10-03.
  6. ↑ Wilco, Daniel (16 March 2023). "The absurd odds of a perfect NCAA bracket". NCAA.com. Retrieved 16 April 2023.
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  14. ↑ "Kew report makes new tally for number of world's plants". BBC News. 2016-05-09. Retrieved 2020-11-27.
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  28. ↑ "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 (2009). "The human brain in numbers: a linearly scaled-up primate brain". Front. Hum. Neurosci. 3: 31. doi: 10.3389/neuro.09.031.2009 . PMC   2776484 . PMID   19915731.
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  32. ↑ "Prime Number Races" (PDF). granville.dvi. Retrieved 2024-01-04.
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  40. 1 2 Sloane, N. J. A. (ed.). "SequenceA186311(Least century 100k to 100k+99 with exactly n primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-16.
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  57. ↑ (sequence A070177 in the OEIS )
  58. ↑ (sequence A035064 in the OEIS )
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  66. ↑ Hanke, Steve; Krus, Nicholas. "Hyperinflation Table" (PDF). Retrieved 26 March 2021.
  67. ↑ "Richard Eldridge".
  68. ↑ Chris Caldwell, The Top Twenty: Elliptic Curve Primality Proof at The Prime Pages.
  69. ↑ Chris Caldwell, The Top Twenty: Sophie Germain (p) at The Prime Pages.
  70. ↑ Chris Caldwell, The Top Twenty: Twin at The Prime Pages.
  71. ↑ Chris Caldwell, The Top Twenty: Primorial at The Prime Pages.
  72. ↑ 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.
  73. ↑ Chris Caldwell, The Top Twenty: Palindrome at The Prime Pages.
  74. ↑ Gary Barnes, Riesel conjectures and proofs Archived 2021-04-12 at the Wayback Machine
  75. ↑ Chris Caldwell, The Top Twenty: Factorial primes Archived 2013-04-10 at the Wayback Machine at The Prime Pages.
  76. ↑ Chris Caldwell, The Top Twenty: Generalized Fermat Archived 2021-03-28 at the Wayback Machine at The Prime Pages.
  77. ↑ PRP records
  78. ↑ Chris Caldwell, The Top Twenty: Proth Archived 2020-11-24 at the Wayback Machine at The Prime Pages.
  79. 1 2 Chris Caldwell, The Top Twenty: Largest Known Primes at The Prime Pages.
  80. ↑ Chris Caldwell, Mersenne Primes: History, Theorems and Lists at The Prime Pages.
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  86. ↑ Kerr, Josh (7 December 2013). "Name the biggest number contest". Archived from the original on 20 March 2016. Retrieved 27 March 2014.
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