Orders of magnitude (numbers)

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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

1039 to 10100     Larger than 10100

Top of page — See also — External links

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Smaller than 10-36

  • Comp - IEEE floating-point number 5Template:E is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value.
  • Comp - IEEE floating-point number 1.4012985Template:E is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
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10-36

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10-33

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10-30

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10-27

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10-24

ISO: yocto - y

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10-21

ISO: zepto - z

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10-18

ISO: atto - a

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10-15

ISO: femto - f

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10-12

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

ISO: pico - p

  • Mathematics: Roughly the chances of getting heads 40 times in a row on a fair coin.
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10-9

(0.000 000 001; short scale: one billionth; long scale: one milliardth)

ISO: nano - n

  • Mathematics - 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 of 2003, are 120,526,770 to 1 against, for a probability of 8Template:E.
  • Mathematics - 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, are 13,983,816 to 1 against, for a probability of 7Template:E.
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10-6

(0.000 001; one millionth)

ISO: micro - μ

  • Mathematics - 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
  • Mathematics - 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
  • Mathematics - 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
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10-3

(0.001; one thousandth)

ISO: milli - m

  • Mathematics - Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10-3
  • Mathematics - Poker: The odds of being dealt a flush in poker are 508 to 1 against, for a probability of 1.9 × 10-3
  • Mathematics - 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

Meaning in words: 3 orders of magnitude smaller.

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10-2

(0.01; one hundredth)

ISO: centi - c

  • BioMed - HIV: About 1.2% of all 15–49 year-old humans were infected with HIV at the end of 2001
  • Mathematics - Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%)
  • Mathematics - 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%)
  • Mathematics - Lottery: The odds of winning any prize in the US Powerball Multistate Lottery, with a single ticket, under the rules as of 2003, are 36.06 to 1 against, for a probability of 0.028 (2.8%)
  • Mathematics - 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 jiffie.
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10-1

(0.1; one tenth)

ISO: deci - d

  • Mathematics - 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%).
  • Mathematics - Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5 (50%)
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100

(1; one)

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101

(10; ten)

ISO: deca - da

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102

(100; hundred)

ISO: hecto - h

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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.
  • Lang: There are about 6500 mutually unintelligible languages and dialects.

Meaning in words: 3 orders of magnitude greater.

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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
  • Mathematics: 65537 is a Fermat prime
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105

(100 000; one hundred thousand)

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106

(1 000 000; 1 million)

ISO: mega - M

  • Info: As of February 2006, there are approximately 1,000,000 articles in the English Wikipedia
  • 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).
  • Mathematics - Chess: There are 2 279 184 solutions to n-Queens Problem for n = 15
  • Mathematics - 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
  • Mathematics: 14,772,512 solutions to n-Queens Problem for n = 16
  • Mathematics: 95,815,104 solutions to n-Queens Problem for n = 17
  • Mathematics: 215,000,000 - The approximate number of mathematical constants collected on the Plouffe's Inverter as of August 2005 [2]
  • Mathematics: 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.
  • Geo: approx. 402,000,000 native speakers of English
  • Astro - Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects
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109

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

ISO: giga - G

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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 [4]
  • Mathematics: 1.1 * 1012 - The approximate number of known non-trivial zeros of Riemann zeta function as of August 2005 [5]
  • BioMed - Cells in the human body: the human body consists of roughly 1014 cells
  • Mathematics - Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000
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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 ([6] speaks of 1014), the overwhelming majority in the intestinal tract
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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 CPU: 9.22Template:E 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.
  • Mathematics - Rubik's Cube: There are 4.3Template:E different positions of a Rubik's Cube
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1021

(1 000 000 000 000 000 000 000; short scale: 1 sextillion; long scale: 1000 trillion)

ISO: zetta - Z

  • Geo - Grains of sand: all the world's beaches put together hold roughly 1023 grains of sand. [7]
  • 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. This estimate is based on galaxy counts and star estimates: [8]
  • Chem: there are roughly 6.022Template:E molecules in one mole of any substance (Avogadro's number)
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1024

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

ISO: yotta - Y

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1027

(1 000 000 000 000 000 000 000 000 000; short scale: 1 octillion; long scale: 1000 quadrillion)

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1030

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

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1033

(1 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 decillion; long scale: 1000 quintillion)

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1036

(1 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 decillion; long scale: 1000 quintillion)

  • Comp - Address range of IPv6 (2128) is approximately equal to 3.4Template:E, and is the theoretical maximum number of internet addresses that can be allocated under the IPv6 addressing system.
  • Comp - IEEE floating-point number 3.4028235Template:E is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.
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1039 to 10100

See names of large numbers for the names of these and larger numbers.

  • Mathematics: 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7Template:E) is a double Mersenne prime
  • Cosmology: The Eddington-Dirac number is roughly 1040.
  • Physics: <math>e^2/Gm^2 \,</math>, the ratio of the electrical to the gravitational forces between two protons, is roughly 1040.
  • Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4Template:E) is a Pierpont prime
  • Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9Template:E) is a Cullen prime
  • Geo: About 1047 molecules of water on Earth
  • Geo: Earth consists of roughly 1050 atoms
  • Mathematics: 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 (≈3.6Template:E) is a Bell prime
  • Cosmology: 8Template:E is roughly the number of Plank time intervals since the universe is theorized to have been created in the Big Bang 13.7 ± 0.2 billion years ago
  • Mathematics: 709,601,635,082,267,320,966,424,084,955,776,789,770,864,725,643,996,885,415,676,682,297 (≈7Template:E) - The largest known prime factor found by ECM factorization as of August 2005 [10]
  • Mathematics - Cards: 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8Template:E) - the number of ways to order the cards in a 52-card deck.
  • Mathematics: 475,420,437,734,698,220,747,368,027,166,749,382,927,701,417,016,557,193,662,268,716,376,935,476,241 (≈4.8Template:E) is a Fibonacci prime
  • 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
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Larger than 10100

  • Chess: Shannon number, 10120, an estimation of the game-tree complexity of chess
  • Mathematics - Hist: Asankhyeya is equal to 10140 in Ancient India
  • Xiangqi: 10150, an estimation of the game-tree complexity of xiangqi
  • Physics: 4Template:E, approximate number of Plank volumes in the observable universe.
  • Comp - IEEE floating-point number 1.7976931348623157Template:E is approximately equal to the largest value that can be represented by a double-precision IEEE floating-point value.
  • Mathematics - Go: 10365, number of possible moves in the game of Go
  • Mathematics: 7068555 · 2121301 − 1 is a Sophie Germain prime
  • Mathematics: 16869987339975 · 2171960 − 1 is a Chen prime
  • Mathematics: 16869987339975 · 2171960 ± 1 are twin primes
  • Mathematics: 34790!–1 is a factorial prime
  • Mathematics: 392113#+1 is a primorial prime
  • Mathematics: 109,152,051, order of magnitude of the largest known prime, as of December 2005. The exact value of that record prime is 230,402,457−1. 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.
  • Mathematics - Hist: 1080,000,000,000,000,000, largest named number in Archimedes' Sand Reckoner
  • Mathematics: 10googol (<math>10^{10^{100}}</math>), a googolplex
  • Mathematics: <math>10^{\,\!10^{10^{34}}}</math>, order of magnitude of an upper bound that occurred in a proof of Skewes
  • Mathematics: <math>10^{\,\!10^{10^{1000}}}</math>, order of magnitude of another upper bound in a proof of Skewes
  • Mathematics: Moser's number should appear somewhere in this section, but is difficult to calculate
  • Mathematics: 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>
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See also

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External links

it:Ordini di grandezza (numeri) ja:数量の比較 (数値) ko:수의 비교 sl:Red velikosti (števila)

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