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Orders of magnitude (numbers)

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Orders of magnitude
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This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities.


Contents

Smaller than 10-36

10-36 10-33 10-30 10-27 10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1

100 101 102 103 104 105 106 109 1012 1015 1018 1021 1024 1027 1030 1036

Larger than 1036

Top of pageSee alsoExternal links


Smaller than 10-36

10-36

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 (American), One billionth (British)

ISO: pico - p

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

10-9

(0.000 000 001; short scale: one billionth; 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, with a single ticket, under the rules as at 2003, are 120,526,770 to 1 against, for a probability of 8 × 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 at 2003, are 13,983,816 to 1 against, for a probability of 7 × 10-8.

10-6

(0.000 001; 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 × 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 × 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 × 10-4

10-3

(0.001; one thousandth)

ISO: milli - m

  • Math - Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10-3
  • Math - Poker: The odds of being dealt a flush in poker are 508 to 1 against, for a probability of 1.9 × 10-3
  • Math - Poker: The odds of being dealt a straight in poker are 254 to 1 against, for a probability of 4 × 10-3
  • Phys: α = 0.007 297 352 533(27), the fine structure constant

10-2

(0.01; one hundredth)

  • BioMed - HIV: About 1.2% of all 15-49 year-old humans were infected with HIV 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 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, with a single ticket, under the rules 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%).

10-1

(0.1; one tenth)

ISO: deci - d

  • Math - 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%).
  • 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; one)

101

(10; ten)

ISO: deca - da

  • BioMed: there are 10 fingers on a pair of human hands
  • 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
  • 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, The Answer to Life, the Universe, and Everything.

102

(100; 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.
  • Comp: There are 128 characters in the ASCII character set.
  • Geo: There were 191 member states of the United Nations as of 2003.
  • Lit: 451 degrees Fahrenheit is the ignition temperature of paper. Therefore, Ray Bradbury titled his dystopian novel about book burnings Fahrenheit 451.

103

(1 000; thousand)

ISO: kilo - k

  • Lang: 2000-3000 letters on a typical typed page of text
  • BioMed: the DNA of the simplest viruses has some 5000 base pairs.

104

(10 000; ten thousand)

  • BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
  • Lang: There are 20,000 - 40,000 distinct Chinese characters, depending on how you count them
  • BioMed: Each human being is estimated to have 30,000 to 40,000 genes
  • Records: As of July 2004, the largest number of decimal places of π that have been recited from memory - > 42000

105

(100 000; one hundred thousand)

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 n-Queens Problem for n = 15
  • Math - 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 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 n-Queens Problem for n = 16
  • Math: 95,815,104 solutions to n-Queens Problem for n = 17
  • Geo: approx. 402,000,000 native speakers of English

109

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

ISO: giga - G

  • Astro - Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects
  • Comp - 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, thus marking the upper computational limit of a 32-bit CPU such as Intel's Pentium-class computer chips.
  • BioMed - Base pairs in the genome: approximately 3×109 base pairs in the human genome
  • Geo - Living human beings: approximately 6.3×109 human beings living as of mid 2003
  • Comp - Web pages: approximately 8 × 109 web pages indexed by Google as of 2004
  • Astro - Observable galaxies: between 1×1010 and 8×1010 galaxies in the observable (as of 2003) Universe
  • BioMed - Bacteria in the human body: there are roughly 1010 bacteria in the human oral cavity [1] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm)
  • BioMed - Neurons in the brain: approximately 1011 neurons in the human brain
  • Astro - Stars in our Galaxy: approximately 4 × 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 gigabytes; 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: 275,305,224 is the number of 5x5 magic squares, not counting rotations and reflections. This result was found in 1973 by Richard Schroeppel. It is the third 91768409-gonal number.

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 bacteria [2] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm)
  • BioMed - Cells in the human body: the human body consists of roughly 1014 cells
  • 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 ([3] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm) speaks of 1014)

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.
  • Math - Rubik's Cube: There are 4.3 × 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. [4] (http://astronomy.swin.edu.au/staff/gmackie/billions.html)
  • Astro - Stars: 70 sextillion, was recently given by Australian astronomers as the number of stars visible from Earth by Telescope. It could also be called 70 million trillion or 70 billion billion.
  • Astro - Stars in the observable universe: there are very approximately estimated to be 7 × 1022 stars in the observable universe, based on galaxy counts and star estimates: [5] (http://www.rednova.com/news/stories/1/2003/07/22/story004.html)
  • Chem: there are roughly 6.022 × 1023 molecules in one mole of any substance (Avogadro's number)

1024

ISO: yotta - Y

1027

  • BioMed - Atoms in the human body: the average human body contains roughly 7×1027 atoms, see [6] (http://education.jlab.org/qa/mathatom_04.html)

1030

1033

1036

Larger than 1036

  • Math: The Eddington-Dirac number is roughly 1040.
  • Geo: About 1047 molecules of water on Earth
  • Geo: Earth consists of roughly 1050 atoms
  • 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: 10100, a googol
  • Math - Hist: Asankhyeya is equal to 100140 in Ancient India
  • Math - Go: 10365, number of possible moves in the game of Go
  • Math: 107,816,229, order of magnitude of largest known prime number, as of February 2005. The exact value of that record prime is 225,964,951 - 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: 1080,000,000,000,000,000, largest named number in Archimedes' Sand Reckoner
  • Math: 10googol (<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 proof of Skewes
  • Math: <math>10^{\,\!10^{10^{1000}}}<math>, order of magnitude of another upper bound in a proof of Skewes
  • 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


External links

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