List of numbers

This is a list of articles about numbers.

Contents

1 Rational numbers 1.1 Notable rational numbers 1.1.1 Natural numbers 1.1.2 Powers of ten 1.2 Integers 1.2.1 Notable integers 1.2.2 Named integers 1.3 Cardinal numbers 1.3.1 Small numbers 1.3.2 English names for powers of 10 1.3.3 Proposed systematic names for powers of 10 1.3.3.1 Gillion system 1.3.3.2 Myriad system 1.3.3.3 Googol and others 1.4 Fractional numbers 2 Irrational numbers 2.1 Algebraic numbers 2.2 Transcendental numbers 3 Hypercomplex numbers 3.1 Algebraic complex numbers 3.2 Other hypercomplex numbers 4 Transfinite numbers 5 Numbers representing measured quantities 6 Numbers without specific values 7 Bases 8 See also 9 Further reading 10 External links

Rational numbers

Notable rational numbers

Natural numbers

0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
40	41	42	43	44	45	46	47	48	49
50	51	52	53	54	55	56	57	58	59
60	61	62	63	64	65	66	67	68	69
70	71	72	73	74	75	76	77	78	79
80	81	82	83	84	85	86	87	88	89
90	91	92	93	94	95	96	97	98	99
100	101	102	103	104	105	106	107	108	109
110	111	112	113	114	115	116	117	118	119
120	121	122	123	124	125	126	127	128	129
130	131	132	133	134	135	136	137	138	139
140	141	142	143	144	145	146	147	148	149
150	151	152	153	154	155	156	157	158	159
160	161	162	163	164	165	166	167	168	169
170	171	172	173	174	175	176	177	178	179
180	181	182	183	184	185	186	187	188	189
190	191	192	193	194	195	196	197	198	199
200	210	220	230	240	250	260	270	280	290
			300	400	500	600	700	800	900
	1000	2000	3000	4000	5000	6000	7000	8000	9000

Powers of ten

See: Orders of magnitude (numbers)

Integers

Notable integers

Other numbers that are notable for their mathematical properties or cultural meanings include:

• -40
• -1
• 222
• 239
• 255
• 256
• 273
• 284
• 360
• 420
• 496
• 666
• 720
• 911
• 1,001
• 1,729
• 3,600
• 7,744
• 8,128
• 69,105
• 142,857
• 6,000,000

Named integers

• Graham's number
• Hardy-Ramanujan number
• Skewes' number
• Steinhaus' Mega and Megiston, Moser's number

Cardinal numbers

In the following tables, [and] indicates that the word and is used in some dialects (such as British English), and omitted in other dialects (such as American English).

Small numbers

This table demonstrates the standard English construction of small cardinal numbers up to ten million -- names for which all variants of English agree.

Value	Name	Alternate names
0	Zero	aught, cipher, cypher, nil, none, nought, nowt, null, ought, oh, zilch, squat
1	One	ace, single, singleton, unary, unit, unity
2	Two	binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duet, duo, dyad, pair, span, twain, twosome, yoke
3	Three	deuce-ace, leash, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika
4	Four	foursome, quadruplet, quatern, quaternary, quaternion, quaternity, quartet, tetrad
5	Five	cinque, fin, fivesome, pentad, quint, quintet, quintuplet
6	Six	half dozen, hexad, sestet, sextet, sextuplet, sise
7	Seven	heptad, septet, septuplet
8	Eight	octad, octet, octonary, octuplet, ogdoad
9	Nine	ennead
10	Ten	decade
11	Eleven
12	Twelve	dozen
13	Thirteen	baker's dozen, long dozen
14	Fourteen
15	Fifteen
16	Sixteen
17	Seventeen
18	Eighteen
19	Nineteen
20	Twenty	score
21	Twenty-one
22	Twenty-two
23	Twenty-three
24	Twenty-four	two dozen
25	Twenty-five
26	Twenty-six
27	Twenty-seven
28	Twenty-eight
29	Twenty-nine
30	Thirty
31	Thirty-one
40	Forty
50	Fifty
60	Sixty
70	Seventy
80	Eighty
90	Ninety
100	One hundred	centred, century
101	One hundred [and] one
110	One hundred [and] ten
111	One hundred [and] eleven
120	One hundred [and] twenty
121	One hundred [and] twenty-one
144	One hundred [and] forty-four	gross, dozen dozen, small gross
200	Two hundred
300	Three hundred
1,000	One thousand	chiliad, grand, thou, yard, kilo (often shortened to K)
1,001	One thousand [and] one
1,010	One thousand [and] ten
1,011	One thousand [and] eleven
1,100	One thousand one hundred
1,101	One thousand one hundred [and] one
1,728	One thousand seven hundred [and] twenty-eight	great gross, long gross, dozen gross
2,000	Two thousand
10,000	Ten thousand	myriad
100,000	One hundred thousand	lakh
1,000,000	One million	meg, mil
10,000,000	Ten million	crore

English names for powers of 10

This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. See How to name numbers in English or English language numerals for more information on naming numbers.

	Short scale	Long scale
Value	American & Modern British	Traditional British (Nicolas Chuquet)	Continental European (Jacques Pelletier du Mans)	Power
100	One			1000-1+1
101	Ten
102	Hundred
103	Thousand			10000+1
106	Million			10001+1
109	Billion	Thousand million	Milliard	10002+1
1012	Trillion	Billion		10003+1
1015	Quadrillion	Thousand billion	Billiard	10004+1
1018	Quintillion	Trillion		10005+1
1021	Sextillion	Thousand trillion	Trilliard	10006+1
1024	Septillion	Quadrillion		10007+1
1027	Octillion	Thousand quadrillion	Quadrilliard	10008+1
1030	Nonillion	Quintillion		10009+1
1033	Decillion	Thousand quintillion	Quintilliard	100010+1
1036	Undecillion	Sextillion		100011+1
1039	Duodecillion	Thousand sextillion	Sextilliard	100012+1
1042	Tredecillion	Septillion		100013+1
1045	Quattuordecillion	Thousand septillion	Septilliard	100014+1
1048	Quindecillion	Octillion		100015+1
1051	Sexdecillion	Thousand octillion	Octilliard	100016+1
1054	Septendecillion	Nonillion		100017+1
1057	Octodecillion	Thousand nonillion	Nonilliard	100018+1
1060	Novemdecillion	Decillion		100019+1
1063	Vigintillion	Thousand decillion	Decilliard	100020+1
1066	Unvigintillion	Undecillion		100021+1
1069	Duovigintillion	Thousand undecillion	Undecilliard	100022+1
1072	Trevigintillion	Duodecillion		100023+1
...	...	...		...
1093	Trigintillion	Thousand quindecillion	Quindecilliard	100030+1
...	...	...		...
10120	Novemtrigintillion	Vigintillion		100039+1
10123	Quadragintillion	Thousand vigintillion	Vigintilliard	100040+1
...	...	...		...
10153	Quinquagintillion	Thousand duovigintillion	Duovigintilliard	100050+1
...	...	...		...
10180	Novemquinquagintillion	Trigintillion		100059+1
10183	Sexagintillion	Thousand trigintillion	Trigintilliard	100060+1
...	...	...		...
10213	Septuagintillion	Thousand quintrigintillion	Quintrigintilliard	100070+1
...	...	...		...
10240	Novemseptuagintillion	Quadragintillion		100079+1
10243	Octogintillion	Thousand quadragintillion	Quadragintilliard	100080+1
...	...	...		...
10273	Nonagintillion	Thousand quinquadragintillion	Quinquadragintilliard	100090+1
...	...	...		...
10300	Novemnonagintillion	Quinquagintillion		100099+1
10303	Centillion	Thousand quinquagintillion	Quinquagintilliard	1000100+1
...		...		...
10360		Sexagintillion		1000119+1
10420		Septuagintillion		1000139+1
10480		Octogintillion		1000159+1
10540		Nonagintillion		1000179+1
10600		Centillion		1000199+1
10603		Thousand Centillion	Centilliard	1000200+1

Template:Ssup There is no consistent and widely accepted way to extend cardinals beyond centillion (centilliard).

Proposed systematic names for powers of 10

Gillion system

As proposed by Russ Rowlett, based on Greek-derived numerical prefixes:

Value Name 103 Thousand 106 Million 109 Gillion 1012 Tetrillion 1015 Pentillion 1018 Hexillion 1021 Heptillion 1024 Oktillion 1027 Ennillion 1030 Dekillion

Value Name 1033 Hendekillion 1036 Dodekillion 1039 Trisdekillion 1042 Tetradekillion 1045 Pentadekillion 1048 Hexadekillion 1051 Heptadekillion 1054 Oktadekillion 1057 Enneadekillion 1060 Icosillion

Value Name 1063 Icosihenillion 1066 Icosidillion 1069 Icositrillion 1072 Icositetrillion 1075 Icosipentillion 1078 Icosihexillion 1081 Icosiheptillion 1084 Icosioktillion 1087 Icosiennillion 1090 Triacontillion

Myriad system

Proposed by Donald E. Knuth:

Value	Name	Notation
100	One	1
101	Ten	10
102	Hundred	100
103	Thousand	1000
104	Myriad	1,0000
105	Ten myriad	10,0000
106	Hundred myriad	100,0000
107	Thousand myriad	1000,0000
108	Myllion	1;0000,0000
1012	Myriad myllion	1,0000;0000,0000
1016	Byllion	1:0000,0000;0000,0000
1024	Myllion byllion	1;0000,0000:0000,0000;0000,0000
1032	Tryllion	1 0000,0000;0000,0000:0000,0000;0000,0000
1064	Quadryllion	1'0000,0000;0000,0000:0000,0000;0000,0000 0000,0000;0000,0000:0000,0000;0000,0000
10128	Quintyllion
10256	Sextyllion
10512	Septyllion
101024	Octyllion
102048	Nonyllion
104096	Decyllion
108192	Undecyllion
1016,384	Duodecyllion
1032,768	Tredecyllion
1065,536	Quattuordecyllion
10131,072	Quindecyllion
10262,144	Sexdecyllion
10524,288	Septendecyllion
101,048,576	Octodecyllion
102,097,152	Novemdecyllion
104,194,304	Vigintyllion
104,294,967,296	Trigintyllion
<math>{10}^{\,\! 4 * 2^{40}}<math>	Quadragintyllion
<math>{10}^{\,\! 4 * 2^{50}}<math>	Quinquagintyllion
<math>{10}^{\,\! 4 * 2^{60}}<math>	Sexagintyllion
<math>{10}^{\,\! 4 * 2^{70}}<math>	Septuagintyllion
<math>{10}^{\,\! 4 * 2^{80}}<math>	Octogintyllion
<math>{10}^{\,\! 4 * 2^{90}}<math>	Nonagintyllion
<math>{10}^{\,\! 4 * 2^{100}}<math>	Centyllion
<math>{10}^{\,\! 4 * 2^{1000}}<math>	Millyllion
<math>{10}^{\,\! 4 * 2^{10000}}<math>	Myryllion

Googol and others

10100	Googol
<math>{10}^{\,\!10^{100}}<math>	Googolplex
10-N	N-minex
10N	N-plex

Fractional numbers

This is a table of English names for positive rational numbers less than 1. It also lists alternative names, but there is no widespread convention for the names of extremely small positive numbers.

Keep in mind that rational numbers like 0.12 can be represented in infinite ways, e.g. twenty-four two-hundredths <math>\left({24 \over 200}\right)<math>, twelve hundredths <math>\left({12 \over 100}\right)<math>, six fiftieths <math>\left({6 \over 50}\right)<math>, three twenty-fifths <math>\left({3 \over 25}\right)<math>, zero-point-one-two (0.12), and twelve percent (12%).

Value	Fraction	Common names	Alternative names
1	<math>1 \over 1<math>	One
0.9	<math>9 \over 10<math>	Nine tenths, zero point nine
0.8	<math>4 \over 5<math>	Four fifths, eight tenths, zero point eight
0.7	<math>7 \over 10<math>	Seven tenths, zero point seven
0.6	<math>3 \over 5<math>	Three fifths, six tenths, zero point six
0.5	<math>1 \over 2<math>	One half, five tenths, zero point five
0.4	<math>2 \over 5<math>	Two fifths, four tenths, zero point four
0.3 (333 333)...	<math>1 \over 3<math>	One third
0.3	<math>3 \over 10<math>	Three tenths, zero point three
0.25	<math>1 \over 4<math>	One quarter, one fourth, twenty-five hundredths, zero point two five
0.2	<math>1 \over 5<math>	One fifth, two tenths, zero point two
0.16 (666 666)...	<math>1 \over 6<math>	One sixth
0.142 857 (142 857)...	<math>1 \over 7<math>	One seventh
0.141 592 920 353 982 300 884 955 752 212 389 380 530 973 451 327 433 628 318 584 070 796 460 176 991 150 442 477 876 106 194 690 265 486 725 663 716 8 (141 592)...	<math>16 \over 113<math>	Sixteen one-hundred-[and]-thirteenths
0.125	<math>1 \over 8<math>	One eighth, one-hundred-[and]-twenty-five thousandths, zero point one two five
0.1 (111 111)...	<math>1 \over 9<math>	One ninth
0.1	<math>1 \over 10<math>	One tenth, zero point one	One perdecime, one perdime
0.090 (909 090)...	<math>1 \over 11<math>	One eleventh
0.09	<math>9 \over 100<math>	Nine hundredths, zero point zero nine
0.083 (333 333)...	<math>1 \over 12<math>	One twelfth
0.08	<math>2 \over 25<math>	Two twenty-fifths, eight hundredths, zero point zero eight
0.0625	<math>1 \over 16<math>	One sixteenth, six-hundred-[and]-twenty-five ten-thousandths, zero point zero six two five
0.05	<math>1 \over 20<math>	One twentieth, zero point zero five
0.047 619 (047 619)...	<math>1 \over 21<math>	One twenty-first
0.045 (454 545)...	<math>1 \over 22<math>	One twenty-second
0.043 478 260 869 565 217 3913 (043 478)...	<math>1 \over 23<math>	One twenty-third
0.03 (333 333)...	<math>1 \over 30<math>	One thirtieth
0.016 (666 666)...	<math>1 \over 60<math>	One sixtieth	One minute
0.01	<math>1 \over 100<math>	One hundredth, zero point zero one	One percent
0.001	<math>1 \over 1000<math>	One thousandth, zero point zero zero one	One permille
0.000 27 (777 777)...	<math>1 \over 3600<math>	One thirty-six hundredth	One second
0.000 1	<math>1 \over 10000<math>	One ten-thousandth, zero point zero zero zero one	One myriadth, one permyria
0.000 01	<math>10^{-5}<math>	One hundred-thousandth	One lakhth, one perlakh
0.000 001	<math>10^{-6}<math>	One millionth	One perion
0.000 000 1	<math>10^{-7}<math>	One ten-millionth	One crorth, one percrore
0.000 000 01	<math>10^{-8}<math>	One hundred-millionth	One awkth, one perawk
0.000 000 001	<math>{10}^{-9}<math>	One billionth (in some dialects)
0	<math>0 \over 1<math>	Zero

Irrational numbers

Algebraic numbers

Expression	Value	Notes
<math>{\sqrt{5} - 1} \over 2<math>	0.618 033 988 749 894 848 204 586 834 366...	golden ratio conjugate <math>\left(\hat\phi\right)<math> reciprocal of and one less than the golden ratio
<math>\sqrt{2}<math>	1.414 213 562 373 095 048 801 688 724 210...	length of the diagonal of a square with side length 1; "Pythagoras' constant"[1] (http://mathworld.wolfram.com/PythagorassConstant.html)
<math>{\sqrt{5} + 1} \over 2<math>	1.618 033 988 749 894 848 204 586 834 366...	golden ratio <math>\left(\phi\right)<math>
<math>\sqrt{3}<math>	1.732 050 807 568 877 193 176 604 123 437...	altitude of an equilateral triangle with side length 2
<math>\sqrt{5}<math>	2.236 067 977 499 789 805 051 477 742 381...
<math>\sqrt{2} + 1<math>	2.414 213 562 373 095 048 801 688 724 210...	silver ratio <math>\left(\delta_S\right)<math>
<math>\sqrt{6}<math>	2.449 489 742 783 177 881 335 632 264 381...
<math>\sqrt{7}<math>	2.645 751 311 064 590 716 171 096 573 817...
<math>\sqrt{8}<math>	2.828 427 124 746 190 290 949 243 717 478...
<math>\sqrt{10}<math>	3.162 277 660 168 379 522 787 063 251 599...

Transcendental numbers

• Khinchin-Lévy constant: 1.186 569 110 4...[2] (http://mathworld.wolfram.com/Khinchin-LevyConstant.html)
• Napier's constant: e = 2.718 281 828 459 045 235 360 287 471 353 ...
• pi: π = 3.141 592 653 589 793 238 462 643 383 279 ...

Suspected transcendentals:

• Euler-Mascheroni constant: γ = 0.577 215 664 901 532 860 606 512 090 082 ...
• Gauss-Kuzmin-Wirsing constant: 0.303 663 002 9...[3] (http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html)
• Laplace limit: ε=0.662 743 419 3...[4] (http://mathworld.wolfram.com/LaplaceLimit.html)
• Khinchin's constant: 2.685 452 001...[5] (http://mathworld.wolfram.com/KhinchinsConstant.html)
• Feigenbaum constants: δ = 4.6692 ... and α = 2.5029 ...

Hypercomplex numbers

Algebraic complex numbers

• Imaginary unit: <math>i = \sqrt{(-1)}<math>

Other hypercomplex numbers

• The quaternions
• The octonions
• The sedenions
• The dual numbers (with an infinitesimal)

Transfinite numbers

• Infinity in general: <math>\infty<math>
• Aleph-null: <math>\aleph_0<math>
• Aleph-one: <math>\aleph_1<math>
• Beth-one: (<math>\beth_1<math>) is the cardinality of the continuum: <math>2^{\aleph_0}<math>

Numbers representing measured quantities

• pair : 2
• dozen : 12
• score : 20
• gross : 144
• Avogadro's number: N_A = <math>6.022... \times 10^{23}<math>

Numbers without specific values

• Zillion (and variations)
  • bajillion
  • buhmillion
  • gazillion
  • jillion
  • kajillion
• lots
• many
• oodles
• umpteen

Bases

• base φ
• base 2
• base 3
• base 4
• base 5
• base 6
• base 8
• base 9
• base 10
• base 12
• base 13
• base 16
• base 20
• base 60
• base 64

Also see Positional Systems of numeral system for bases which might not be listed here.

See also

• English language numerals
• Numbers in various languages
• floating point
• fraction (mathematics)
• large number
• list of prime numbers
• mathematical constant
• names of large numbers
• negative number
• number names
• orders of magnitude (numbers)
• ordinal number
• small number
• surreal number
• table of prime factors

Further reading

• Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0716744473

External links

• A list of unusual properties for many of the first 1000 natural numbers (http://www.stetson.edu/~efriedma/numbers.html)
• See how to write big numbers (http://www.mathcats.com/explore/reallybignumbers.html)
• The MegaPenny Project - Visualizing big numbers (http://www.kokogiak.com/megapenny/)
• About big numbers (http://pages.prodigy.net/jhonig/bignum/indx.html)
• Robert P. Munafo's amazing Large Numbers page (http://home.earthlink.net/~mrob/pub/math/largenum.html)
• Different notations for big numbers - by Susan Stepney (http://www-users.cs.york.ac.uk/~susan/cyc/b/big.htm)
• Names for Large Numbers (http://www.unc.edu/~rowlett/units/large.html), in How Many? A Dictionary of Units of Measurement by Russ Rowlett

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