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Orders of magnitude (numbers)

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

Smaller than 10-36

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

10-36

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

10-33

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

10-30

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

10-27

(0.000 000 000 000 000 000 000 000 001), short scale: One octillionth, long scale: One quadrilliardth)

ISO: xonto- (x)

10-24

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

ISO: yocto- (y)

10-21

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

ISO: zepto- (z)

10-18

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

ISO: atto- (a)

10-15

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

ISO: femto- (f)

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.

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.
  • 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.
  • Physics: The time it takes light to travel 1 meter in a vacuum is approximately 3.3356 seconds. The time it takes light to travel 1 Foot (length) in a vacuum is approximately 1.0167 seconds.

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

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

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 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%).

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%)

100

(1; one)

101

(10; ten)

ISO: deca- (da)

102

(100; hundred)

ISO: hecto- (h)

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.

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 one counts 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

105

(100 000; one hundred thousand)

106

(1 000 000; 1 million)

ISO: mega- (M)

109

(1 000 000 000; short scale: 1 billion; long scale: 1 thousand million (old term: milliard)

ISO: giga- (G)

  • Demographics - India: 1,096,000,000 - approximate population of India in 2007
  • Demographics - China: 1,311,000,000 - approximate population of the People's Republic of China in 2007.
  • 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.
  • Mathematics: 2,147,483,647 is a Mersenne prime.
  • BioMed - base pairs in the genome: approximately 3 base pairs in the human genome
  • Computing - IPv4: 4,294,967,296 (232) possible unique IP addresses.
  • 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: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form 2^{2^n}+1 which is not a prime number.
  • Demographics - world population: 6,587,890,000 - Estimated total mid-year population for the world in 2007 (April 10).
  • Computing - web pages: approximately 8 web pages indexed by Google as of 2004
  • Astronomy - Observable galaxies: as of 2003 there are between 1 and 8 galaxies in the observable Universe
  • BioMed - bacteria in the human body: there are roughly 1010 bacteria in the human oral cavity
  • Mathematics: 27,704,267,971 and 27,704,267,977 are sexy primes.
  • BioMed - Neurons in the brain: approximately 1011 neurons in the human brain
  • Astronomy - stars in our galaxy: approximately 4 stars in the Milky Way galaxy
  • Mathematics: 258,584,046,368 is the number of domino tilings of a 10×10 checkerboard.

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
  • Mathematics: 1.1 - The approximate number of known non-trivial zeros of Riemann zeta function as of August 2005
  • Mathematics - Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000
  • BioMed - Cells in the human body: the human body consists of roughly 1014 cells
  • Computing - MAC-48: 281,474,976,710,656 (248) possible unique physical addresses.
  • Mathematics: 953,467,954,114,363 is the largest known Motzkin prime.
  • Computing - magnetic storage: 1TB largest 3.5inch hard disk as of 2007.

1015

(1 000 000 000 000 000; short scale: 1 quadrillion; long scale: 1,000 billion, or sometimes 1 billiard)

ISO: peta- (P)

  • BioMed - Bacteria in the human body: there are roughly 1015 bacteria in the human body ( speaks of 1014), the overwhelming majority in the intestinal tract
  • Mathematics: 48,988,659,276,962,496 is the fifth taxicab number.
  • Mathematics: 53,060,477,521,960,000 is the number of domino tilings of a 12×12 checkerboard.

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 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 - NCAA Basketball Tournament: There are 9,223,372,036,854,775,808 (263) possible ways to enter the bracket.
  • Mathematics - Rubik's Cube: There are 4.3 different positions of a Rubik's Cube
  • Password strength - Usage of the 95-character set found on standard computer keyboards for a 10-character password yields a computationally intractable 9510 (approximately 6) permutations.

1021

(1 000 000 000 000 000 000 000; short scale: 1 sextillion; long scale: 1,000 trillion or 1 trilliard)

ISO: zetta- (Z)

  • Mathematics - Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7) 9×9 sudoku grids.
  • Astronomy - Stars: 70 sextillion = 7 estimated number of stars within range of telescopes (as of 2003).
  • Geo - Grains of sand: all the world's beaches put together hold roughly 1023 grains of sand.
  • Mathematics: 112,202,208,776,036,178,000,000 is the number of domino tilings of a 14×14 checkerboard.
  • Mathematics: 146,361,946,186,458,562,560,000 (≈1.5) is the fifth unitary perfect number.
  • Chemistry: there are roughly 6.022 molecules in one mole of any substance (Avogadro's number)

1024

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

ISO: yotta- (Y)

  • Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8) is a Woodall prime.

1027

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

ISO: xona- (X)

  • BioMed - Atoms in the human body: the average human body contains roughly 7 atoms, see
  • 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, see Poker probability (Texas hold 'em).

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: 2,444,888,770,250,892,795,802,079,170,816 is the number of domino tilings of a 16×16 checkerboard.
  • Mathematics: The partition of 1000 is 24,061,467,864,032,622,473,692,149,727,991.

1033

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

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

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, 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 is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.
  • Computing: The total number of different Universally Unique Identifiers (UUIDs) that can be generated is about 3.4.
  • Mathematics: 548,943,583,215,388,338,077,567,813,208,427,340,288 is the number of domino tilings of an 18×18 checkerboard.

1039

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

1042

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

  • Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4) is a Pierpont prime
  • Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9) is a Cullen prime

1045 to 10100

  • Mathematics: 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 (≈3.6) 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 group
  • Cosmology: 8 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) - The largest known prime factor found by ECM factorization as of August 2005
  • 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) - 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) 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

Larger than 10100

  • Board games: 4.8231, number of ways to arrange the tiles in English Scrabble (100! / 9! / 2! / 2! / 4! / 12! / 2! / 3! / 2! / 9! / 1! / 1! / 4! / 2! / 6! / 8! / 2! / 1! / 6! / 4! / 6! / 4! / 2! / 2! / 1! / 2! / 1! / 2!).
  • Chess: Shannon number, 10120, an estimation of the game-tree complexity of chess.
  • Physics: 8, 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, approximate number of Planck volumes in the observable universe.
  • Computing: 1.7976931348623157 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.
  • Mathematics: 26384405 + 44052638 is a 15071-digit Leyland prime; the largest which has been proven as of 2007.
  • 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: 10150006 + 7426247×1075000 + 1 is a 150007-digit happy prime. It is also a palindromic prime.
  • Mathematics: 392113# + 1 is a 169966-digit primorial prime; the largest known as of 2007.
  • Mathematics: approximately 7.76 · 10206544 cattle in the smallest herd which satisfies the conditions of the Archimedes' cattle problem.
  • Mathematics: 232,582,657 − 1 is a 9,808,358-digit Mersenne prime; the largest known prime as of September 2006.
  • Mathematics: 232,582,656 × (232,582,657 − 1) is a 19,616,714-digit perfect number, the largest known as of 2007.
  • Mathematics: (232,582,657 − 1)2 is a 19,616,715-digit semiprime, the largest known as of 2007.
  • Mathematics - History: 1080,000,000,000,000,000, largest named number in Archimedes' Sand Reckoner.
  • Mathematics: 10googol (10^{10^{100}}), a googolplex.
  • Mathematics: 10^{,!10^{10^{34}}}, order of magnitude of an upper bound that occurred in a proof of Skewes.
  • Mathematics: 10^{,!10^{10^{1000}}}, 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; 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,

10^{,!10^{100}} mbox{ means } 10^{,!(10^{100})}

See also

External links



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