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 1033 1036 1039
1042 to 10100     Larger than 10100 Top of page — See also — External links

[edit] Smaller than 10^-36

• Computing: The number 5×10^-324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value.
• Computing: The number 1.4×10^-45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.

[edit] 10^-36

(0.000 000 000 000 000 000 000 000 000 000 000 001)

[edit] 10^-33

(0.000 000 000 000 000 000 000 000 000 000 001)

[edit] 10^-30

(0.000 000 000 000 000 000 000 000 000 001)

[edit] 10^-27

(0.000 000 000 000 000 000 000 000 001)

[edit] 10^-24

(0.000 000 000 000 000 000 000 001)

ISO: yocto - y

[edit] 10^-21

(0.000 000 000 000 000 000 001, short scale: One sextillionth, long scale: One trilliardth)

ISO: zepto - z

[edit] 10^-18

(0.000 000 000 000 000 001, short scale: One quintillionth, long scale: One trillionth)

ISO: atto - a

[edit] 10^-15

(0.000 000 000 000 001, short scale: One quadrillionth, long scale: One billiardth)

ISO: femto - f

[edit] 10^-12

(0.000 000 000 001, short scale: One trillionth, long scale: One billionth)

ISO: pico - p

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

[edit] 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 2006, are 146,107,962 to 1 against, for a probability of 7×10^-9.
• 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 7×10^-8.

[edit] 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

[edit] 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 507.8 to 1 against, for a probability of 1.9 × 10^-3
• Mathematics - Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10^-3
• Physics: α = 0.007 297 352 533(27), the fine structure constant

[edit] 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^{[citation needed]}
• 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 2006, are 36.61 to 1 against, for a probability of 0.027 (2.7%)
• Mathematics - Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 0.048 (4.8%).

[edit] 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%)

[edit] 10⁰

(1; one)

• Mathematics: φ ≈ 1.6180339887, the golden ratio
• Mathematics: e ≈ 2.718281828459045, the base of the natural logarithm
• Mathematics: π ≈ 3.14159265358979, the ratio of a circle's circumference to its diameter
• BioMed: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously held in working memory
• Astronomy: 8 planets in the solar system

[edit] 10¹

(10; ten)

ISO: deca - da

• Human scale: there are 10 fingers on a pair of human hands
• Language: there are 26 letters in the Latin alphabet in the English language

[edit] 10²

(100; hundred)

ISO: hecto - h

• Computing: There are 128 characters in the ASCII character set.
• Geo: There were 192 member states of the United Nations as of 2006.

[edit] 10³

(1 000; thousand)

ISO: kilo - k

• Language: 2000–3000 letters on a typical typed page of text
• BioMed: the DNA of the simplest viruses has some 5000 base pairs.
• Language: There are about 6500 mutually unintelligible languages and dialects.

[edit] 10⁴

(10 000; ten thousand)

• BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
• Language: 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 the largest known Fermat prime

[edit] 10⁵

(100 000; one hundred thousand)

• BioMed - Strands of hair on a head: The average human head has about 100,000–150,000 strands of hair
• Mathematics: 110,000 - The approximate number of entries on The On-Line Encyclopedia of Integer Sequences as of August 2005 [1]
• Language: 267,000 words in James Joyce's Ulysses
• Language - English words: The New Oxford Dictionary of English contains about 350,000 definitions for English words
• Mathematics: 365,596 solutions to n-Queens Problem for n = 14
• Language: 564,000 words in War and Peace
• Info: The FreeDB database has around 1 750 000 entries as of June 2005

[edit] 10⁶

(1 000 000; 1 million)

ISO: mega - M

• Info: Currently there are 1,723,413 articles and 4,043,358 registered users in the English Wikipedia
• Geography/Computing - 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 The 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 normal magic squares, not counting rotations and reflections. This result was found in 1973 by Richard Schroeppel. It is the third 91768409-gonal number.
• Demographics: approx. 402,000,000 native speakers of English
• Astronomy - Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects

[edit] 10⁹

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

ISO: giga - G

• Computing - 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
• Computing - IPv4: 4,294,967,296 (2³²) possible unique IP addresses.
• Computing - Web pages: approximately 8×10⁹ web pages indexed by Google as of 2004
• Astronomy - Observable galaxies: as of 2003 there are between 1×10¹⁰ and 8×10¹⁰ galaxies in the observable Universe
• BioMed - Bacteria in the human body: there are roughly 10¹⁰ bacteria in the human oral cavity [3]
• BioMed - Neurons in the brain: approximately 10¹¹ neurons in the human brain
• Astronomy - Stars in our Galaxy: approximately 4×10¹¹ stars in the Milky Way galaxy
• Demographics - India: 1,065,000,000 - Approximate population of India in 2003
• Demographics - China: 1,300,000,000 - Approximate population of the People's Republic of China in 2004.
• Demographics - World population: 6,378,000,000 - Estimated total mid-year population for the world in 2004.
• Computing: 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.
• Mathematics: 2,147,483,647 is a Mersenne prime.
• Mathematics: 2,464,195,387 is a semiprime.
• Mathematics: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form which is not a prime number.
• Mathematics: 27,704,267,971 and 27,704,267,977 are sexy primes.

[edit] 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
• Computing - MAC-48: 281,474,976,710,656 (2⁴⁸) possible unique physical addresses.

[edit] 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
• Mathematics: 48,988,659,276,962,496 is the fifth Taxicab number.

[edit] 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.
• Mathematics: 2,305,843,009,213,693,951 (2⁶¹-1) is a Mersenne prime
• Computing - Computational limit of a 64-bit CPU: 9.22×10¹⁸ 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.
• Mathematics - Rubik's Cube: There are 4.3×10¹⁹ different positions of a Rubik's Cube
• Mathematics - NCAA Basketball Tournament: There are 9,223,372,036,854,775,808 (2⁶³) possible ways to enter the bracket.

[edit] 10²¹

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

ISO: zetta - Z

• Mathematics - Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×10²¹) 9×9 sudoku grids. [7]
• Geo - Grains of sand: all the world's beaches put together hold roughly 10²³ grains of sand. [8]
• Astronomy - 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: [9]
• Chemistry: there are roughly 6.022×10²³ molecules in one mole of any substance (Avogadro's number)

[edit] 10²⁴

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

ISO: yotta - Y

• Computing: Yottabyte (YB) is 10²⁴ bytes.
• Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×10²⁴) is the fifth unitary perfect number.
• Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8×10²⁵) is a Woodall prime.

[edit] 10²⁷

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

• BioMed - Atoms in the human body: the average human body contains roughly 7×10²⁷ atoms, see [10]
• Mathematics - Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas Hold'em is approximately 2.117×10²⁸, see Poker probability (Texas hold 'em).

[edit] 10³⁰

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

• BioMed: number of bacterial cells on Earth
• Mathematics: The partition of 1000 is 24,061,467,864,032,622,473,692,149,727,991.

[edit] 10³³

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

• Mathematics: 1,298,074,214,633,706,835,075,030,044,377,087 (≈1.3×10³⁴) is a Carol prime

[edit] 10³⁶

(1 000 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 undecillion; long scale: 1 sextillion)

• Computing: The address range of IPv6 (2¹²⁸) is approximately equal to 3.4×10³⁸, and is the theoretical maximum number of internet addresses that can be allocated under the IPv6 addressing system.
• Computing: The IEEE floating-point number 3.4028235×10³⁸ is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.

[edit] 10³⁹

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

• The amount of money you would have if you put ¢1 in a savings account, at the start of year 1AD in which you recieved 5% untaxed interest at the end of each year: $30,517,196,578,016,400,000,000,000,000,000,000,000,000
• Mathematics: 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×10³⁹) is a double Mersenne prime
• Cosmology: The Eddington-Dirac number is roughly 10⁴⁰.
• Physics: , the ratio of the electrical to the gravitational forces between two protons, is roughly 10⁴⁰.

[edit] 10⁴² to 10¹⁰⁰

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

• Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4×10⁴⁴) is a Pierpont prime
• Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9×10⁴⁵) 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 (≈3.6×10⁵⁴) is a prime Bell number
• Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 is order of Monster simple group
• Cosmology: 8×10⁶⁰ is roughly the number of Planck 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 (≈7×10⁶⁶) - The largest known prime factor found by ECM factorization as of August 2005 [11]
• 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 (≈8×10⁶⁷) - 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 (≈4.8×10⁷²) is a Fibonacci prime
• Cosmology: various sources estimate the total number of fundamental particles in the observable universe in the range 10⁸⁰ to 10⁸⁵. However, these estimates are generally regarded as guesswork.
• Mathematics: 10¹⁰⁰, a googol

[edit] Larger than 10¹⁰⁰

• Chess: Shannon number, 10¹²⁰, an estimation of the game-tree complexity of chess.
• Physics: 8×10¹²⁰, ratio of the mass-energy in the observable universe to the energy of a photon with a wavelength the size of the observable universe.
• Mathematics - History: Asankhyeya is equal to 10¹⁴⁰ in ancient India.
• Xiangqi: 10¹⁵⁰, an estimation of the game-tree complexity of xiangqi.
• Physics: 4×10¹⁸⁵, approximate number of Planck volumes in the observable universe.
• Computing: 1.7976931348623157×10³⁰⁸ is approximately equal to the largest value that can be represented by a double-precision IEEE floating-point number.
• Go: 10³⁶⁵, an estimation of the game-tree complexity in the game of Go.^{[citation needed]}
• Mathematics: 137211941292195 · 2¹⁷¹⁹⁶⁰ − 1 is a 51780-digit Sophie Germain prime; the largest known as of 2007.
• Mathematics: 2003663613 · 2¹⁹⁵⁰⁰⁰ ± 1 are 58711-digit twin primes; the largest known as of 2007.
• Mathematics: 34790! – 1 is a 142891-digit factorial prime; the largest known as of 2007.
• Mathematics: 392113# + 1 is a 169966-digit primorial prime; the largest known as of 2007.
• Mathematics: 2^32,582,657 − 1 is a 9,808,358-digit Mersenne prime; the largest known prime as of September 2006.
• Mathematics - History: 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner.
• Mathematics: 10^googol (), a googolplex.
• Mathematics: , order of magnitude of an upper bound that occurred in a proof of Skewes.
• Mathematics: , 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 f⁶⁴(4); representation in powers of 10 would be impractical (the number of digits in the exponent far exceeds the number of particles in the observable universe).

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

[edit] See also

• Large number
• List of numbers
• Planck units
• Mathematical constant
• Encyclopediac size comparisons on Wikipedia

[edit] External links

• Seth Lloyd's paper Computational capacity of the universe provides a number of interesting dimensionless quantities.