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# Orders of magnitude (numbers)

Orders of magnitude

LengthMassTimeAreaVolumePowerTemperatureDensityNumbersDataU.S. money

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

(and Rowlett)
Power of ten Decimal value Name
Smaller than 10−36
10-36

10-33

10-30

10-27

10-24

10-21

10-18

10-15

10-12
10-9 0.000 000 001
• 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.
• 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
• 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
• 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
• 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
• Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10-3
10-3 0.001 one thousandth
• Poker: The odds of being dealt a flush in poker are 508 to 1 against, for a probability of 1.9 × 10-3
• Poker: The odds of being dealt a straight in poker are 254 to 1 against, for a probability of 4 × 10-3
• α = 0.007 297 352 533(27), the fine structure constant
10-2 0.01 one hundredth
• HIV: About 1.2% of all 15-49 year-old humans were infected with HIV at the end of 2001
• 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%)
• 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%)
• 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%)
• 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
• Poker: The odds of being dealt only one pair in poker are about 4 to 3 against (1.37 to 1), for a probability of 0.42 (42%).
• 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
• there are 10 fingers on a pair of human hands
• In Olympic basketball, the roster limit for a team is 12 (and they are limited to wearing numbers 4 through 15).
• there are 26 letters in the Latin alphabet
• 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.
102 100 hundred
• 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.
• there are 128 characters in the ASCII character set
• there were 191 member states of the United Nations as of 2003
103 1 000 thousand
• 2000-3000 letters on a typical typed page of text
• the DNA of the simplest viruses has some 5000 base pairs.
104 10 000 ten thousand
• Each neuron in the human brain is estimated to connect to 10,000 others
• There are 20,000 - 40,000 distinct Chinese characters, depending on how you count them
• Each human being is estimated to have 30,000 to 40,000 genes
• 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 (both short scale and long scale)
• 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.
• 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).
• Chess: There are 2 279 184 solutions to n-Queens Problem for n = 15
• Playing cards: There are 2 598 960 different 5-card poker hands that can be dealt from a standard 52-card deck.
• Web sites: as of July 2003, the Netcraft web survey estimates that there are 42 million distinct web sites
• 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
109 1 000 000 000 1 billion (short scale), 1 milliard (long scale)
• Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects
• 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.
• Base pairs in the genome: approximately 3×109 base pairs in the human genome
• Web pages: approximately 3 × 109 web pages indexed by Google as of 2003
• Living human beings: approximately 6.3×109 human beings living as of mid 2003
• Observable galaxies: between 1×1010 and 8×1010 galaxies in the observable (as of 2003) Universe
• Neurons in the brain: approximately 1011 neurons in the human brain
• Stars in our Galaxy: approximately 4 × 1011 stars in the Milky Way galaxy
1012 1 000 000 000 000 1 trillion (short scale), 1 billion (long scale)
• Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000
• Cells in the human body: the human body consists of roughly 1014 cells
1015 1 000 000 000 000 000 1 quadrillion (short scale), 1 billiard (long scale)
• Bacteria in the human body: there are roughly 1015 bacteria in the human body
• Grains of sand: all the world's beaches put together hold roughly 2 × 1015 grains of sand
1018 1 000 000 000 000 000 000 1 quintillion (short scale), 1 trillion (long scale)
• Insects: It has been estimated that the insect population of the Earth comprises roughly 1018 insects.
• Rubik's Cube: There are 4.3 × 1019 different positions of a Rubik's Cube
1021 1 sextillion (short scale), 1 trilliard (long scale)
1024 1 septillion (short scale), 1 quadrillion (long scale)

1027 1 octillion (short scale), 1 quadrilliard (long scale)
• Atoms in the human body: the average human body contains roughly 7×1027 atoms, see [2]
1030 1 nonillion (short scale), 1 quintillion (long scale)
1033 1 decillion (short scale), 1 quintilliard (long scale)
1036

Larger
• The Eddington-Dirac number is roughly 1040.
• About 1047 molecules of water on Earth
• Earth consists of roughly 1050 atoms
• 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.
• 10100 , a googol
• 107,235,733, order of magnitude of largest known prime number, as of May 2004. The exact value of that record prime is 224036583 - 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.
• 1080,000,000,000,000,000, largest named number in Archimedes' Sand Reckoner
• 10googol ($10^{10^{100}}$), a googolplex
• $10^{10^{10^{34}}}$, order of magnitude of an upper bound that occurred in a proof of Skewes
• $10^{10^{10^{1000}}}$, order of magnitude of another upper bound in a proof of Skewes
• ...

Note: To correctly interpret the last few entries, keep in mind that (for example):

$10^{10^{100}} \mbox{ means } 10^{(10^{100})}$