physics - List of numbers

This is a list of articles about numbers.

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:

Named integers

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

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
10^16,384	Duodecyllion
10^32,768	Tredecyllion
10^65,536	Quattuordecyllion
10^131,072	Quindecyllion
10^262,144	Sexdecyllion
10^524,288	Septendecyllion
10^1,048,576	Octodecyllion
10^2,097,152	Novemdecyllion
10^4,194,304	Vigintyllion
10^{4,294,967,296}	Trigintyllion
${10}^{\,\! 4 * 2^{40}}$	Quadragintyllion
${10}^{\,\! 4 * 2^{50}}$	Quinquagintyllion
${10}^{\,\! 4 * 2^{60}}$	Sexagintyllion
${10}^{\,\! 4 * 2^{70}}$	Septuagintyllion
${10}^{\,\! 4 * 2^{80}}$	Octogintyllion
${10}^{\,\! 4 * 2^{90}}$	Nonagintyllion
${10}^{\,\! 4 * 2^{100}}$	Centyllion
${10}^{\,\! 4 * 2^{1000}}$	Millyllion
${10}^{\,\! 4 * 2^{10000}}$	Myryllion

Googol and others

10¹⁰⁰	Googol
${10}^{\,\!10^{100}}$	Googolplex
10^-N	N-minex
10^N	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 $\left({24 \over 200}\right)$ , twelve hundredths $\left({12 \over 100}\right)$ , six fiftieths $\left({6 \over 50}\right)$ , three twenty-fifths $\left({3 \over 25}\right)$ , zero-point-one-two (0.12), and twelve percent (12%).

Value	Fraction	Common names	Alternative names
1	$1 \over 1$	One
0.9	$9 \over 10$	Nine tenths, zero point nine
0.8	$4 \over 5$	Four fifths, eight tenths, zero point eight
0.7	$7 \over 10$	Seven tenths, zero point seven
0.6	$3 \over 5$	Three fifths, six tenths, zero point six
0.5	$1 \over 2$	One half, five tenths, zero point five
0.4	$2 \over 5$	Two fifths, four tenths, zero point four
0.3 (333 333)...	$1 \over 3$	One third
0.3	$3 \over 10$	Three tenths, zero point three
0.25	$1 \over 4$	One quarter, one fourth, twenty-five hundredths, zero point two five
0.2	$1 \over 5$	One fifth, two tenths, zero point two
0.16 (666 666)...	$1 \over 6$	One sixth
0.142 857 (142 857)...	$1 \over 7$	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)...	$16 \over 113$	Sixteen one-hundred-[and]-thirteenths
0.125	$1 \over 8$	One eighth, one-hundred-[and]-twenty-five thousandths, zero point one two five
0.1 (111 111)...	$1 \over 9$	One ninth
0.1	$1 \over 10$	One tenth, zero point one	One perdecime, one perdime
0.090 (909 090)...	$1 \over 11$	One eleventh
0.09	$9 \over 100$	Nine hundredths, zero point zero nine
0.083 (333 333)...	$1 \over 12$	One twelfth
0.08	$2 \over 25$	Two twenty-fifths, eight hundredths, zero point zero eight
0.0625	$1 \over 16$	One sixteenth, six-hundred-[and]-twenty-five ten-thousandths, zero point zero six two five
0.05	$1 \over 20$	One twentieth, zero point zero five
0.047 619 (047 619)...	$1 \over 21$	One twenty-first
0.045 (454 545)...	$1 \over 22$	One twenty-second
0.043 478 260 869 565 217 3913 (043 478)...	$1 \over 23$	One twenty-third
0.03 (333 333)...	$1 \over 30$	One thirtieth
0.016 (666 666)...	$1 \over 60$	One sixtieth	One minute
0.01	$1 \over 100$	One hundredth, zero point zero one	One percent
0.001	$1 \over 1000$	One thousandth, zero point zero zero one	One permille
0.000 27 (777 777)...	$1 \over 3600$	One thirty-six hundredth	One second
0.000 1	$1 \over 10000$	One ten-thousandth, zero point zero zero zero one	One myriadth, one permyria
0.000 01	$10 - 5$	One hundred-thousandth	One lakhth, one perlakh
0.000 001	$10 - 6$	One millionth	One perion
0.000 000 1	$10 - 7$	One ten-millionth	One crorth, one percrore
0.000 000 01	$10 - 8$	One hundred-millionth	One awkth, one perawk
0.000 000 001	$10 - 9$	One billionth (in some dialects)
0	$0 \over 1$	Zero

Irrational numbers

Algebraic numbers

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