Numbers


last update: 23 July 2020




https://en.wikipedia.org/wiki/English_numerals#Ordinal_numbers
https://en.wikipedia.org/wiki/Orders_of_magnitude_(length)

Quiz questions where the answer is a number are very popular, but questions about number themselves are quite rare. Here are a few examples:-

How many zeros are there is a Googol? Answer - 100 as in 10100
People tend to think that the word 'googol' relates to Google, but in fact the word already appeared in 1937 with Edward Kasner (American, 1878-1955). It is said that the word was invented by the 9-year-old nephew of Kasner. The idea was that a googol had 100 zeros, and Kasner also introduced a googolplex as a number with as many zeros as you could write before getting tired. In fact it is said that the name Google came from a misspelling of googol.




Big Numbers


Apparently there for very large and very small numbers there are two different scales, the long scale and the short scale (they are the same from 1 to 109). The difference is in the name, and we have listed the short name first.

1= 100 = one
10 = 101 = Ten = deca (da)
100 = 102 = Hundred = hecto (h)
1000 = 103 = Thousand = kilo (k) (=10001)
1000000 = 106 = Million = mega (M) (=10002)
109 = Billion = giga (G) = thousand million (=10003)
1012 = Trillion = tera (T) = billion (=10004)
1015 = Quadrillion = peta (P) = thousand billion (=10005)
1018 = Quintillion = exa (E) = trillion (=10006)
1021 = Sextillion = zetta (Z) = thousand trillion (=10007)
1024 = Septillion = yotta (Y) = quadrillion (=10008)
1027 = Octillion
1030 = Nonillion
1033 = Decillion
1036 = Undecillion
1039 = Duodecillion
1042 = Tredecillion
1045 = Quattuordecillion
1048 = Quindecillion
1051 = Sexdecillion
1054 = Septendecdecillion
1057 = Octodecillion
1060 = novemdecillion
1063 = Vigintillion


So there can be some confusion between the short scale (e.g. septillion) and the long scale (e.g. quadrillion), so it best to use the matrix prefix 1024.

And in English stick to using the short scale (e.g. septillion).

And we should not forget 0, zero, nought, nil, nothing, null, zilch, zip, duck, blank
Which of course brings us to other words used for 1, 2, …, such as:-
1, ace, solo, unity, …
2, couple, brace, pair, duce, duo, …
3, trey, trio, hat-trick, …
4, quartet, quad, …
5, quintet, quint, …
6, sextet, half-a-dozen, …
7, septet, …
8, octet, …
9, nonet, …
10, decet, decade, …
11, banker's dozen, …
12, dozen
13, bakers dozen, …
20, score, …
50, half-century, …
100, century, ton, …
144, gross, …
1000, grand, kilo-,
10,000, a hundred-hundred or myriad

There are also multiplicative number adverbs such as once, twice, and thrice, as well as numbers expressed solitary, double, triple, quadruple, quintuple, sextuple or hextuple, septuple or heptuple, …, as well as singular, twofold, threefold, …, hundredfold, …

Small Numbers


Apparently there for very large and very small numbers there are two different scales, the long scale and the short scale (they are the same from 1 down to 106). The difference is in the name, and we have listed the short name first.

1= 100 = one
0.1 = 10-1 = one tenth = deci- (d)
0.01 = 10-2 = one hundreth = centi- (c)
0.001 = 10-3 = one thousandth = milli- (m)
0.00001 = 10-4 = one ten-thousandth
0.000001 = 10-5 = one hundred-thousandth
0.0000001 = 10-6 = one millionth = micro- (µ)
10-9 = one billionth = nano- (n)
10-12 = one tillionth = pico- (p)
10-15 = one quadriillionth = femto- (f)
10-18 = one quintillionth = atto- (a)
10-21 = one sextillionth = zepto- (z)
10-24 = one septillionth = yocto- (y)
10-27 = one Octillionth

Context


Wikipedia has a webpage on the Orders of Magnitude which contextualise what small and big numbers can mean. I'm now using it to add the occasional tit-bit.

10-100 Googolth
10-31 Electron mass (ca. 9.1x10-31 kg)
10-30
10-29
10-28
10-27 Proton mass (ca. 1.6x10-27 kg), Neutron mass (ca. 1.6x10-27 kg)
10-26
10-25
10-24
10-23
10-22 Radius of an electron (ca. 1x10-22 metres)
10-21
10-20
10-19 Electron charge (ca. -1.6x10-19 coulombs), Proton charge (ca. 1.6x10-19 coulombs)
10-18 Electron orbit radius upper limit (ca. 1x10-18 metres)
10-17 Range of the weak force (ca. 1x10-17 metres)
10-16 Radius of the proton (ca. 8.4x10-16 metres)
10-15 Diameter of an atomic nucleus (1.76-11.71x10-15 metres)
10-14
10-13
10-12 Gamma ray wavelength (ca. 10-12 metres), Length of a covalent bond (ca. 1.5x10-12 metres)
10-11 Diameter of a nucleus + electron cloud (5.3-15.6x10-11 metres), Hard X-ray wavelength (ca. 10-11 metres). Probability of a bridge player being dealt a complete suit (2.52x10-11), Bohr radius (distance between nucleus an electron in a hydrogen atom) is fixed at 5.29x10-11 metres (the diameter of a hydrogen atom would be twice the Bohr radius)
10-10 Length of one base pair on a human DNA molecule (ca. 3.4x10-10 metres),
10-9 Soft X-ray wavelength (ca. 10-9 to 10-10 metres), Size of a virus (ca. 5-500x10-9 metres), Thickness of a cell membrane (ca. 6-10x10-9 metres)
10-8
10-7 Visible Light wavelength (ca. 3.8-7.4x10-7 metres), length of a bacterium (ca. 5-50x10-7 metres)
10-6 Diameter of spider silk (ca. 4x10-6 metres), Size of red blood cell (ca. 7x10-6 metres)
10-5 Size of a fog water droplet (ca. 1.0-1.5x10-5 metres), Diameter of human hair (ca. 1.7-18.1x10-5 metres), Thickness of paper (ca. 7-18x10-5 metres)
10-4 Average size of grain of sand, salt, and sugar (ca. 5x10-4 metres)
10-3 Size of a mosquito (ca. 3-6x10-3 metres), Size of a flea (ca. 1-10x10-3 metres), Average size of grain of rice (ca. 5x10-3 metres)
10-2
10-1
100 Monotheistic Religions (one God), Binary System (0 and 1), UHF wavelength (1 metre), Height of Everest (8.8 km)
101 Decimal System, English Alphabet (26 letters), Chromosomes (46 in every human cell), Hours in a Day (24) Average human life span (75 years) Period of Mercury (87.97 days), Length of Panama Canal (82 km)
102 Chemical Elements (118), United Nations (193 members and 2 observers), Days in a Year (365), Neutron mean lifetime (8.8x102 second), Burj Khalifa (829.8 metres), Length of the Suez Canal (163 km)
103 Radius of Moon (1.74x103 km), Radius of Mercury (2.44x103 km), Radius of Venus w/o gas (6.05x103 kg), Radius of Earth (6.37x103 km), Radius of Mars (3.39x103 km), Radius of Pluto (1.19x103 km), Nile (6.65x103 km), Meghalayan age (4,200 years ago until present day), Length of Trans-Siberian Railway (9.29x103 km)
104 Radius of Jupiter (6.9x104 km), Radius of Saturn w/o rings (5.8x104 km), Radius of Uranus (2.5x104 km), Radius of Neptune (2.5x104 kg), Height of Olympus Mons on Mars (2.13x104 metres), Mauna Kea from seafloor (1.02x104 metres), Holocene epoch (11,650 years ago until present day)
105 Oxford English Dictionary (360,000 definitions), Orbit of Moon around Earth (3.6-4.1x105 km)
106 Named Species (1.4 million), Wikipedia (over 6 million articles in English), Orbit of Mercury (3.4-6.9x106 km), definitions of an epoch range over 3-10 million years
107
108 Items held in the worlds biggest libraries (ca. 150 million), Websites (>550 million), Speed of light in a vacuum (299,792,458 m/s), Orbit of Venus (1.07-1.08x108 km), Orbit of Earth (1.47-1.52x108 km), Orbit of Mars (2.07-2.49x108 km), Orbit of Jupiter (7.41-8.17x108 km), UHF frequency (3x108 Hz), definitions of an era range over several hundred million years
109 Population (in billions, World 7.75, China 1.44, India 1.38, Africa 1.0), Base Pairs (3x109 in human genome) Age of the universe (13.8x109 years), Orbit of Saturn (1.35-1.51x109 km), Orbit of Uranus (ca. 3x109 km), Orbit of Neptune (4.46-4.54x109 km), Orbit of Pluto (4.4-7.4x109 km), definitions of an eon start at over ½ billion years
1010 Bacteria in human mouth (1010), Webpages (5.6x1010)
1011 Neurons in human brain (ca. 1011), Number of humans that ever lived (ca. 1.2x1011), Milky Way galaxy (ca. 1011 stars), Synapses in human brain (ca. 1011)
1012 Andromeda Galaxy (ca. 1012 stars), Bacteria on human body (1012), Galaxies in observable universe (ca. 2x1012), Trees on Earth (ca. 3x1012), Fish in Oceans (ca. 3.5x1012), One light year (9.46x1012 km)
1013 Distance to nearest star Proxima Centauri (4.02x1013 km)
1014 Synapses in human brain (ca. 1014), Cells in the human body (ca. 1014 of which only ca. 1013 are human), Visible Light (ca. 4.05-7.9x1014 Hz). Total length of DNA molecules in human body (ca. 2x1014 metres)
1015 Number of ants (1015 to 1016)
1017 Soft X-ray frequency (ca. 3-30x1017 Hz)
1018
1019 Number of insects on Earth (ca. 1019), Hard X-ray frequency (ca. 3x1019 Hz), Distance to Andromeda Galaxy (ca. 2.37x1019 km)
1020 Gamma ray frequency (ca. 3x1020 Hz)
1021 Grains of sand (ca. 1021), Number of transistors produced worldwide annually (>3x1021)
1022 Mass of Moon (7.3x1022 kg), Mass of Pluto (1.3x1022 kg)
1023 Avogadro constant (ca. 6.02x1023), Number of stars in observable universe (1023 to 1024), Mass of Mercury (3.3x1023 kg), Mass of Mars (6.4x1023 kg)
1024 Mass of Venus (4.9x1024 kg), Mass of Earth (6.0x1024 kg)

1025 Mass of Uranus (8.7x1025 kg)
1026 'Diameter' of the observable universe 8.8x1026 metres), Mass of Saturn (5.7x1026 kg), Mass of Neptune (1.0x1026 kg)
1027 Atoms in the human body (ca. 7x1027), Mass of Jupiter (1.9x1027 kg)
1028 Electron mean lifetime (6.6x1028 years)
1029 Proton mean lifetime (>2.1x1029 years)
1030 Bacteria cells on Earth (ca. 5x1030)

1080 Atoms in the observable universe (ca. 1x1080)

10100 One Googol

10Googol One Googolplex