Orders of magnitude (numbers) and Sexual Arousal: Difference between pages

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#REDIR [[Sexual arousal]]

{{Orders of magnitude}}

This list compares various sizes of positive [[number]]s, including counts of things, [[dimensionless number]]s and [[probability|probabilities]].

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[[#Smaller than 10-36|Smaller than 10^-36]]

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[[#10-36|10^-36]]

[[#10-33|10^-33]]

[[#10-30|10^-30]]

[[#10-27|10^-27]]

[[#10-24|10^-24]]

[[#10-21|10^-21]]

[[#10-18|10^-18]]

[[#10-15|10^-15]]

[[#10-12|10^-12]]

[[#10-9|10^-9]]

[[#10-6|10^-6]]

[[#10-3|10^-3]]

[[#10-2|10^-2]]

[[#10-1|10^-1]]

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[[#100|10⁰]]

[[#101|10¹]]

[[#102|10²]]

[[#103|10³]]

[[#104|10⁴]]

[[#105|10⁵]]

[[#106|10⁶]]

[[#109|10⁹]]

[[#1012|10¹²]]

[[#1015|10¹⁵]]

[[#1018|10¹⁸]]

[[#1021|10²¹]]

[[#1024|10²⁴]]

[[#1027|10²⁷]]

[[#1030|10³⁰]]

[[#1036|10³⁶]]

[[#1038|10³⁸]]

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[[#Larger than 1039|Larger than 10³⁹]]

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[[#top|Top of page]] &mdash; [[#See also|See also]] &mdash; [[#External links|External links]]

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== Smaller than 10^-36 ==

== 10^-36 ==

[[Planck's constant]]: Approximately 6.626 &times; 10^-34 J&middot;s

== 10^-33 ==

== 10^-30 ==

== 10^-27 ==

== 10^-24 ==

ISO: yocto - y

== 10^-21 ==

ISO: zepto - z

== 10^-18 ==

ISO: atto - a

== 10^-15 ==

ISO: femto - f

== 10^-12 ==

One trillionth (short scale), One billionth (long scale)

ISO: pico - p

* ''Math:'' Roughly the chances of getting heads 40 times in a row on a fair coin.

== 10^-9 ==

(0.000&nbsp;000&nbsp;001; [[long and short scales|short scale]]: one billionth; [[long and short scales|long scale]]: one milliardth)

ISO: nano - n

* ''Math - Lottery:'' The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball Multistate [[Lottery (U.S.)|Lottery]], with a single ticket, under the rules [[as of 2003|as at 2003]], are 120,526,770 to 1 against, for a probability of 8 &times; 10^-9.

* ''Math - 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|as at 2003]], are 13,983,816 to 1 against, for a probability of 7 &times; 10^-8.

== 10^-6 ==

(0.000&nbsp;001; one [[millionth]])

ISO: micro - prefix Greek letter mu

* ''Math - [[Poker]]:'' The odds of being dealt a [[royal flush]] in poker are 649,739 to 1 against, for a probability of 1.5 &times; 10^-6

* ''Math - 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 &times; 10^-5

* ''Math - 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 &times; 10^-4

== 10^-3 ==

(0.001; one [[thousandth]])

ISO: milli - m

* ''Math - Poker:'' The odds of being dealt a [[full house (poker)|full house]] in poker are 693 to 1 against, for a probability of 1.4 &times; 10^-3

* ''Math - Poker:'' The odds of being dealt a [[flush (poker)|flush]] in poker are 508 to 1 against, for a probability of 1.9 &times; 10^-3

* ''Math - Poker:'' The odds of being dealt a [[Straight (poker)|straight]] in poker are 254 to 1 against, for a probability of 4 &times; 10^-3

* ''Phys:'' &alpha; = 0.007 297 352 533(27), the [[fine structure constant]]

== 10^-2 ==

(0.01; one [[hundredth]])

* ''BioMed - HIV:'' About 1.2% of all 15&ndash;49 year-old humans were infected with [[HIV]] [[As of 2001|at the end of 2001]]

* ''Math - Lottery:'' The odds of winning any prize in the UK National [[Lottery]], with a single ticket, under the rules [[as of 2003|as at 2003]], are 54 to 1 against, for a probability of about 0.018 (1.8%)

* ''Math - 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%)

* ''Math - Lottery:'' The odds of winning any prize in the US Powerball Multistate [[Lottery (U.S.)|Lottery]], with a single ticket, under the rules [[as of 2003|as at 2003]], are 36.06 to 1 against, for a probability of 0.028 (2.8%)

* ''Math - Poker:'' The odds of being dealt [[two pair]] in poker are 20 to 1 against, for a probability of 0.048 (4.8%).

* ''Comp - Time:'' 0.01 [[seconds]] is equal to a [[jiffy]].

== 10^-1 ==

(0.1; one [[tenth]])

ISO: deci - d

* ''Math - Poker:'' The odds of being dealt only [[one pair (poker)|one pair]] in poker are about 5 to 2 against (2.37 to 1), for a probability of 0.42 (42%).

* ''Math - Poker:'' The odds of being dealt [[no pair]] in poker are nearly 1 to 2, for a probability of about 0.5 (50%)

== 10⁰ ==

(1; [[1 (number)|one]])

* ''Math:'' &phi; &asymp; 1.6180339887, the [[golden ratio]]

* ''Math:'' [[e (mathematical constant)|e]] &asymp; 2.718281828459, the base of the [[natural logarithm]]

* ''Math:'' [[pi|&pi;]] &asymp; 3.14159265358979, the ratio of a [[circle]]'s diameter to its circumference

* ''BioMed:'' [[The Magical Number Seven, Plus or Minus Two|7 &plusmn; 2]], in [[cognitive science]], [[George A. Miller]]'s estimate of the number of objects that can be simultaneously held in consciousness

* ''Astro:'' [[nine]] [[planet]]s in the [[solar system]]

== 10¹ ==

(10; [[10 (number)|ten]])

ISO: deca - da

* ''BioMed:'' there are 10 [[finger]]s on a pair of human [[hand]]s

* ''Sport:'' In Olympic basketball, the roster limit for a team is 12 (and they are limited to wearing numbers 4 through 15).

* ''Lang:'' there are 26 letters in the [[Latin alphabet]] in the [[English language]]

* ''Sport:'' In NCAA [[basketball]], players are not to wear digits above 5, and they are limited to one or two digits, making 42 distinct combinations (although 01, 02, 03, 04, and 05 typically aren't used). Since the roster limit is typically around 12, this doesn't present that much of a problem.

* ''Lit:'' [[42 (number)|42]], [[The Answer to Life, the Universe, and Everything]].

* ''Med:'' The human life expectancy, in developed nations, is in the range of 75 years.

== 10² ==

(100; [[100 (number)|hundred]])

ISO: hecto - h

* ''Sport:'' In North American professional sports, players typically wear uniform numbers from 1 to 99. In some sports, 0 and 00 are also allowed, making 101 different combinations.

* ''Pol:'' There are 100 Senators in the United States Senate.

* ''Pol:'' There are 120 members in the Israeli [[Parliament]] (The [[Knesset]]).

* ''Comp:'' There are 128 characters in the [[ASCII]] character set.

* ''Geo:'' There were 191 member states of the [[United Nations]] as of 2003.

* ''Science:'' 373.16 [[kelvin]]s (100 &deg;[[Degree Celsius|C]] is the [[boiling point]] of [[water]] ([[hydrogen|H]]<SUB>2</SUB>[[oxygen|O]]).

* ''Lit:'' 546 [[kelvin]]s (451 degrees [[Fahrenheit]]) is the ignition temperature of paper. Therefore, [[Ray Bradbury]] titled his dystopian novel about book burnings ''[[Fahrenheit 451]]''.

== 10³ ==

(1 000; [[1000 (number)|thousand]])

ISO: kilo - k

* ''Lang:'' 2000&ndash;3000 letters on a typical typed page of text

* ''BioMed:'' the [[DNA]] of the simplest [[virus]]es has some 5000 base pairs.

== 10⁴ ==

(10 000; [[10000 (number)|ten thousand]])

* ''BioMed:'' Each neuron in the human brain is estimated to connect to 10,000 others

* ''Lang:'' There are 20,000&ndash;40,000 distinct [[Chinese character]]s, depending on how you count them

* ''BioMed:'' Each human being is estimated to have 30,000 to 40,000 [[gene]]s

* ''Records:'' As of July 2004, the largest number of decimal places of [[Pi|&pi;]] that have been recited from memory - &gt; 42000

* ''Math:'' 65537 is a [[Fermat prime]]

== 10⁵ ==

(100 000; one hundred thousand)

* ''BioMed - Hairs on a head:'' The average human head has about 100,000&ndash;150,000 [[hair|hairs]]

* ''Math:'' 110,000 - The approximate number of entries on The On-Line Encyclopedia of Integer Sequences [[as of 2005|as of August 2005]] [http://www.research.att.com/~njas/sequences/index.html]

* ''Lang:'' 267,000 words in [[James Joyce]]'s ''[[Ulysses (novel)|Ulysses]]''

* ''Geo:'' 338,200 population of the [[London Borough of Croydon]] in [[1998]]

* ''Lang - English words:'' The [[New Oxford Dictionary of English]] claims to contain 350,000 definitions for [[English language|English]] [[word]]s

* ''Math:'' 365,596 solutions to [[Eight queens puzzle|n-Queens Problem]] for n = 14

* ''Lang:'' 564,000 words in ''[[War and Peace]]''

* ''Info:'' As of [[June]] [[2005]], there are approximately 600,000 articles in the English [[Wikipedia]]

* ''Info:'' The [[FreeDB]] database has around [http://freedb.org/freedb_stats_server.php 1 750 000] entries as of [[June]] [[2005]]

== 10⁶ ==

(1 000 000; 1 [[million]])

ISO: mega - M

* ''Geo/Comp - 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.

* ''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).

* ''Math - Chess:'' There are 2 279 184 solutions to [[Eight queens puzzle|n-Queens Problem]] for n = 15

* ''Math - Playing cards:'' There are 2 598 960 different 5-card [[poker hand]]s that can be dealt from a standard 52-card deck.

* ''Info - Web sites:'' as of July [[2003]], the Netcraft web survey estimates that there are 42 million distinct web sites

* ''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 [[Gutenberg galaxy]]''

* ''Math:'' 14,772,512 solutions to [[Eight queens puzzle|n-Queens Problem]] for n = 16

* ''Math:'' 95,815,104 solutions to [[Eight queens puzzle|n-Queens Problem]] for n = 17

* ''Math:'' 215,000,000 - The approximate number of mathematical [[constant|constants]] collected on the Plouffe's Inverter [[as of 2005|as of August 2005]] [http://pi.lacim.uqam.ca/eng/]

* ''Math:'' 275,305,224 is the number of 5x5 [[magic square]]s, not counting rotations and reflections. This result was found in [[1973]] by [[Richard Schroeppel]]. It is the third 91768409[[-gonal number]].

* ''Geo:'' approx. 402,000,000 native speakers of [[English language|English]]

* ''Astro - Cataloged stars:'' The [[Guide Star Catalog II]] has entries on 998,402,801 distinct astronomical objects

== 10⁹ ==

(1 000 000 000; [[long and short scales|short scale]]: 1 billion; [[long and short scales|long scale]]: 1 [[milliard]])

ISO: giga - G

* ''Comp - Computational limit of a 32-bit [[Central processing unit|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 [[Central processing unit|CPU]] such as [[Intel]]'s [[Pentium]]-class [[computer chip]]s.

* ''BioMed - Base pairs in the genome:'' approximately 3&times;10⁹ [[base pair]]s in the human [[genome]]

* ''Comp - Web pages:'' approximately 8 &times; 10⁹ [[web page]]s indexed by [[Google]] [[as of 2004]]

* ''Astro - Observable galaxies:'' between 1&times;10¹⁰ and 8&times;10¹⁰ [[galaxy|galaxies]] in the observable ([[as of 2003]]) Universe

* ''BioMed - Bacteria in the human body:'' there are roughly 10¹⁰ bacteria in the human [[oral cavity]] [http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm]

* ''BioMed - Neurons in the brain:'' approximately 10¹¹ [[neuron]]s in the human [[brain]]

* ''Astro - Stars in our Galaxy:'' approximately 4 &times; 10¹¹ stars in the [[Milky Way galaxy]]

* ''Geo - India:'' 1,065,000,000 - Approximate population of [[India]] in [[2003]]

* ''Geo - China:'' 1,300,000,000 - Approximate population of the [[People's Republic of China]] in [[2004]].

* ''Geo - World population:'' 6,378,000,000 - Estimated total midyear population for the world in 2004.

* ''Math:'' 4,294,967,296 - smallest number of the form (2^(2^n)) that does not produce a [[prime number]] when 1 is added.

* ''Comp:'' 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.

* ''Comp:'' 4,294,967,296 - total number of [[CMYK]] colors possible when using 8 bit integers for each color component. However, virtually unlimited colors are possible by using floats from 0 to 1 as color components, so this limit is less important than it might seem.

* ''Math:'' 2,147,483,647 is a [[Mersenne prime]] and a [[Zsigmondy number]]

* ''Math:'' 4,294,967,297 is a [[Fermat number]] and [[semiprime]].

* ''Math:'' 27,704,267,971 and 27,704,267,977 are [[sexy prime]]s.

== 10¹² ==

(1 000 000 000 000; short scale: 1 trillion; long scale: 1 billion)

ISO: tera - T

* ''BioMed - Bacteria on the human body:'' the surface of the human body houses roughly 10¹² [[bacterium|bacteria]] [http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm]

* ''Math:'' 1.1 * 10¹² - The approximate number of known non-trivial zeros of [[Riemann zeta function]] [[as of 2005|as of August 2005]] [http://www.zetagrid.net/servlet/service/statistic]

* ''Math:'' 33,853,318,889,473 is a [[Pierpont prime]]

* ''BioMed - Cells in the human body:'' the human body consists of roughly 10¹⁴ [[cell (biology)|cell]]s

* ''Math - Known digits of [[pi]]:'' [[As of 2002]], the number of known digits of pi was 1 241 100 000 000

== 10¹⁵ ==

(1 000 000 000 000 000; short scale: 1 quadrillion; long scale: 1 billiard)

ISO: peta - P

* ''BioMed - Bacteria in the human body:'' there are roughly 10¹⁵ [[bacteria in the human body]] ([http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm] speaks of 10¹⁴), the overwhelming majority in the intestinal tract

== 10¹⁸ ==

(1 000 000 000 000 000 000; short scale: 1 quintillion; long scale: 1 trillion)

ISO: exa - E

* ''BioMed - Insects:'' It has been estimated that the insect population of the Earth comprises roughly 10¹⁸ insects.

* ''Comp - Computational limit of a 64-bit [[Central processing unit|CPU]]'': 9.22&times;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.

* ''Math - Rubik's Cube:'' There are 4.3&times;10¹⁹ different positions of a [[Rubik's Cube]]

== 10²¹ ==

(1 000 000 000 000 000 000 000; see [[names of large numbers]] for naming of this and larger numbers)

ISO: zetta - Z

* ''Geo - Grains of sand:'' all the world's beaches put together hold roughly 10²³ grains of sand. [http://astronomy.swin.edu.au/staff/gmackie/billions.html]

* ''Astro - Stars:'' 70 sextillion, was recently given by [[Australia]]n [[astronomer]]s as the number of [[star]]s visible from [[Earth]] by [[Telescope]]. It could also be called ''70 million trillion'' or ''70 billion billion''. This estimate is based on galaxy counts and star estimates: [http://www.rednova.com/news/stories/1/2003/07/22/story004.html]

* ''Math:'' 146,361,946,186,458,562,560,000 is the fifth [[unitary perfect number]].

* ''Chem:'' there are roughly 6.022&times;10²³ [[molecule]]s in one [[mole (unit)|mole]] of any substance ([[Avogadro's number]])

== 10²⁴ ==

ISO: yotta - Y

*''Computing: [[Yottabyte]] (YB) is 10²⁴ [[byte]]s.''

*''Math:'' 2,833,419,889,721,787,128,217,599 is a [[Woodall prime]].

== 10²⁷ ==

* ''BioMed - Atoms in the human body:'' the average human body contains roughly 7&times;10²⁷ atoms, see [http://education.jlab.org/qa/mathatom_04.html]

== 10³⁰ ==

== 10³³ ==

== 10³⁶ ==

* ''Math:'' 170,141,183,460,469,231,731,687,303,715,884,105,727 is a [[double Mersenne prime]]

== 10³⁸ ==

* ''Comp - Address range of [[IPv6]]'': 3.4&times;10³⁸ is equal to 2¹²⁸, and is the theoretical maximum number of internet addresses that can be allocated under the [[IPv6]] addressing system.

== Larger than 10³⁹ ==

* ''Cosmology:'' The [[Eddington-Dirac number]] is roughly 10⁴⁰.

* ''Physics'': <math>e^2/Gm^2 \,</math>, the ratio of the [[electromagnetic force|electrical]] to the [[gravitational]] [[force]]s between two [[protons]], is roughly 10⁴⁰.

* ''Math:'' 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 is a [[Cullen prime]]

* ''Geo:'' About 10⁴⁷ molecules of [[water]] on [[Earth]]

* ''Geo:'' Earth consists of roughly 10⁵⁰ atoms

* ''Math:'' 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 is a [[Bell prime]]

* ''Math:'' 10⁶⁶ - The magnitude of the largest known [[prime factor]] found by [[Lenstra elliptic curve factorization|ECM]] factorization [[as of 2005|as of August 2005]] [http://www.loria.fr/~zimmerma/records/p66]

* ''Astro - Fundamental particles in the observable universe:'' various sources estimate the total number of fundamental particles in the [[observable universe]] in the range 10⁸⁰ to 10⁸⁵. However, these estimates are best regarded as guesswork.

* ''Math:'' [[1 E100|10¹⁰⁰]], a [[googol]]

* ''Chess:'' [[Shannon number]], 10¹²⁰, an estimation of the [[game-tree complexity]] of chess

* ''Math - Hist:'' [[Asankhyeya]] is equal to 100¹⁴⁰ in [[Ancient India]]

* ''Xiangqi:'' 10¹⁵⁰, an estimation of the game-tree complexity of xiangqi

* ''Math - Go:'' 10³⁶⁵, number of possible moves in the game of [[Go (board game)|Go]]

* ''Math:'' 7068555 &middot; 2¹²¹³⁰¹ &minus; 1 is a [[Sophie Germain prime]]

* ''Math:'' 16869987339975 &middot; 2¹⁷¹⁹⁶⁰ &minus; 1 is a [[Chen prime]]

* ''Math:'' 16869987339975 &middot; 2¹⁷¹⁹⁶⁰ &plusmn; 1 are [[twin prime]]s

* ''Math:'' 34790!-1 is a [[factorial prime]]

* ''Math:'' 392113#+1 is a [[primorial prime]]

* ''Math:'' 10^7,816,229, order of magnitude of largest known [[prime number]], [[As of 2005|as of February 2005]]. The exact value of that record prime is 2^25,964,951 - 1. Proving prime numbers with a thousand to several tens of thousands of decimal digits, depending on special form, can be done in minutes on modern computers.

* ''Math - Hist:'' 10^{80,000,000,000,000,000}, largest named number in [[Archimedes]]' ''[[The Sand Reckoner|Sand Reckoner]]''

* ''Math:'' 10^googol (<math>10^{10^{100}}</math>), a [[googolplex]]

* ''Math:'' <math>10^{\,\!10^{10^{34}}}</math>, order of magnitude of an upper bound that occurred in a [[Skewes' number|proof of Skewes]]

* ''Math:'' <math>10^{\,\!10^{10^{1000}}}</math>, order of magnitude of another upper bound in a proof of Skewes

* ''Math:'' ''[[Moser's number]]'' should appear somewhere in this section, but is difficult to calculate

* ''Math:'' [[Graham's number]], probably the largest number seriously used in a [[mathematical proof]], can be written as <math>f^{64}(4)</math>; representation in powers of 10 would be impractical, for the definition of the number see the main article about it

''Note:'' To correctly interpret the last few entries, keep in mind that exponentiation is performed from right to left. For example,

: <math>10^{\,\!10^{100}} \mbox{ means } 10^{\,\!(10^{100})}</math>

==See also==

* [[Large number]]

* [[List of numbers]]

* [[Planck units]]

* [[Mathematical constant]]

* [[Wikipedia:size comparisons]]

== External links ==

* Seth Lloyd's paper [http://arxiv.org/abs/quant-ph/0110141 ''Computational capacity of the universe''] provides a number of interesting dimensionless quantities

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[[Category:Orders of magnitude]]

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