Orders of magnitude (numbers)

This list compares various sizes of finite numbers, including counts of things, dimensionless numbers and probabilities. See also the order of magnitude lists on length, area, volume, mass and time and the overview article orders of magnitude, which has pointers to other similar lists.

10^-24
10^-21
10^-18
10^-15
10^-12
10^-9
- Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball Multistate Lottery, with a single ticket, under the current rules, 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 current rules, are 13,983,816 to 1 against, for a probability of 7 × 10^-8.
10^-6
- 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
- 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
- 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 current rules, are 54 to 1 against, for a probability of about 1.8%
- Poker: The odds of being dealt a three of a kind in poker are 46 to 1 against, for a probability of 2.1%
- Lottery: The odds of winning any prize in the US Powerball Multistate Lottery, with a single ticket, under the current rules, are 36.06 to 1 against, for a probability of 2.8%
- Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 4.8%.
10^-1
- 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 1, for a probability of about 0.5 (50%).
one
- φ ≈ 1.618, the golden mean
- e ≈ 2.718281828, the base of the natural logarithm
- &pi ≈ 3.141592, the ratio of a circle's diameter to its circumference
- 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously thought of by the human mind
- nine planets in the solar system
10
- there are 10 fingers on a pair of human hands
- there are 26 letters in the Latin alphabet
10²
- there are 128 characters is the ASCII character set
- there were 191 member states of the United Nations as of 2003
10³
- 2000-3000 letters on a typical typed page of text
- the DNA of the simplest viruses has some 5000 base pairs.
10⁴
- 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
10⁵
- Hairs on a head: The average human head has about 100,000-150,000 hairs
- English words: The New Oxford Dictionary of English claims to contain 350,000 definitions for English words
- 564,000 words in War and Peace
- The freedb database holds information for around 700,000 different compact discs
10⁶ -- 1 million
- 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).
- 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
- Compact Disc: Depending on type and other factors, a compact disk contains about 600-750 million bytes of information. A modern computer CD drive can read or write this information in a few minutes.
10⁹ -- 1 billion
- Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects
- Base pairs in the genome: approximately 3×10⁹ base pairs in the human genome
- Web pages: approximately 3 × 10⁹ web pages indexed by Google in 2003
- Living human beings: approximately 6.3×10⁹ human beingss 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 trillion
- Bits on a disk: As of 2003, an inexpensive (200 Gbyte) hard disk drive stored 1.6 × 10¹² bits
- Known digits of pi: As of 2003, the number of known digits of pi was 1,241,100,000,000
- Cells in the human body: the human body consists of roughly 10¹³ cellss
- Bacteria in the human body: there are roughly 10¹⁴ bacteria in the human body
10¹⁵ -- 1 quadrillion
- Grains of sand: it has been estimated that all the world's beaches put together hold roughly 2 × 10¹⁵ grains of sand
10¹⁸
- 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
- 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: [1]
- there are roughly 6.022 × 10²³ molecules in one mole of any substance (Avogadro's number)
10²⁴
10²⁷
- Atoms in the human body: the average human body contains roughly 7×10²⁷ atoms, see [1]
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
- 10^4,053,946, order of magnitude of largest known prime number, as of Q3 2003. 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.
- 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner
- 10^googol (), a googolplex
- , order of magnitude of an upper bound that occurred in a proof of Skewes
- , order of magnitude of another upper bound in a proof of Skewes
- ...

External links

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