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Encyclopedia > List of numbers

This is a list of articles about numbers (not about numerals). A number is an abstract entity that represents a count or measurement. ... A numeral is a symbol or group of symbols that represents a number. ...

In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ...

### 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 10k-100k 100k-1M 1M-10M 10M-100M 100M-1000M Larger #s

#### Powers of ten

See: Orders of magnitude (numbers)

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

### Integers

The integers are commonly denoted by the above symbol. ...

#### Notable integers

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

Minus forty is the unique temperature (in degrees) at which the Celsius and Fahrenheit scales read the same; it is often referred to as 40 below. ... In mathematics, &#8722;1 is the integer greater than negative two (&#8722;2) and less than 0. ... 211 is the natural number between 210 and 212. ... 221 (two hundred [and] twenty-one) is the natural number following 220 and preceding 222. ... 222 (two hundred [and] twenty-two) is the natural number following 221 and preceding 223. ... 223 is the natural number between 222 and 224. ... 227 is the natural number between 226 and 228. ... 228 is the natural number between 227 and 229. ... 229 is the natural number between 228 and 230. ... 233 is the natural number between 232 and 234. ... 235 is the integer after 234 and before 236. ... 239 (two hundred [and] thirty-nine) is the natural number following 238 and preceding 240. ... 241 is the natural number between 240 and 242. ... 242 is the natural number following 241 and preceding 243. ... 251 is the natural number between 250 and 252. ... 255 (two hundred [and] fifty-five, CCLV) is the natural number following 254 and preceding 256. ... 256 (two hundred [and] fifty-six, CCLVI) is the natural number following 255 and preceding 257. ... 257 is the natural number between 256 and 258. ... 263 is the natural number between 262 and 264. ... 269 is the natural number between 268 and 270. ... Two hundred seventy-three (273, CCLXXIII) is a natural number that comes after 272 and before 274. ... Two hundred eighty-four (284, CCLXXXIV) is the natural number following 283 and preceding 285. ... 360ï¼ˆThree hundred sixtyï¼‰ is the natural number following 359 and preceding 361. ... 420 is the natural number following 419 and preceding 421. ... 451 (Four hundred and fifty-one) is the natural number following 450 and preceding 452. ... Four hundred and ninety-six is the natural number following four hundred and ninety-five and preceding four hundred and ninety-seven. ... 555 is the natural number following 554 and preceding 556. ... 666 is the natural number following 665 and preceding 667. ... Seven hundred twenty is the natural number following 719 and preceding 721. ... 786 is the integer coming after 785 and before 787. ... 911 (nine hundred eleven) is the number following 910 and preceding 912. ... 1001 is the natural number preceding 1002 and following 1000. ... 1089 is the number after 1088 and before 1090. ... This article does not adequately cite its references or sources. ... 1729 Cardinal One thousand seven hundred [and] twenty-nine Ordinal 1729th Factorization Divisors 7, 13, 19, 91, 133, 247 Roman numeral MDCCXXIX Binary 11011000001 Octal 3301 Duodecimal 1001 Hexadecimal 6C1 1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G. H. Hardy regarding... 3600 is a number that is equal to 3000 + 600. ... 6174 is known as Kaprekars constant or Kaprekars Operation[1][2][3] after the Indian mathematician D. R. Kaprekar. ... Cardinal seven thousand seven hundred [and] forty-four Ordinal 7744th (seven thousand seven hundred [and] forty-fourth) Factorization Divisors 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 242, 352, 484, 704, 968, 1,936, 3,872 Roman numeral Binary 1111001000000 Octal 17100 Duodecimal 4594 Hexadecimal 1E40 7... Cardinal eight thousand one hundred [and] twenty-eight Ordinal 8128th (eight thousand one hundred [and] twenty-eighth) Factorization Divisors 2, 4, 8, 11, 16, 22, 32, 44, 64, 127, 254, 508, 1,016, 2,032, 4,064 Roman numeral Binary 1111111000000 Octal 17700 Duodecimal 4854 Hexadecimal 1FC0 8,128 is... The number 69,105 was used as an in-joke at the United States computer game manufacturer Infocom. ... 142,857 is the best-known cyclic number. ... 6000000 is the number after 5999999 and before 6000001. ...

#### Named integers

Grahams number, named after Ronald Graham, is often described as the largest number that has ever been seriously used in a mathematical proof. ... This article is about the number 1729. ... In number theory, Skewes number is by definition the smallest natural number x for which Ï€(x) âˆ’ Li(x) â‰¥ 0 where Ï€(x) is the prime counting function and Li(x) is the offset logarithmic integral. ... In mathematics, Mosers polygon notation is a means of expressing certain extremely large numbers. ... The Number of the Beast is a concept from the Book of Revelation of the New Testament of the Christian Bible. ... 6174 is known as Kaprekars constant or Kaprekars Operation[1][2][3] after the Indian mathematician D. R. Kaprekar. ...

### Prime numbers

A prime number is a positive integer which has exactly two divisors: one and itself. In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ...

The first 100 prime numbers: There are infinitely many prime numbers. ...

 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541

â€œIIâ€ redirects here. ... This article discusses the number three. ... Look up five in Wiktionary, the free dictionary. ... Seven Days of Creation - 1765 book, title page Seven (7) is the sixth successor of one (1). ... 11 (eleven) is the natural number following 10 and preceding 12. ... 13 (thirteen) is the natural number following 12 and preceding 14. ... 17 (seventeen) is the natural number following 16 and preceding 18. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... This article is about the number 23. ... 29 (twenty-nine) is the natural number following 28 and preceding 30. ... 31 (thirty-one) is the natural number following 30 and preceding 32. ... 37 (thirty-seven) is the natural number following 36 and preceding 38. ... 41 (forty-one) is the natural number following 40 and preceding 42. ... 43 (forty-three) is the natural number following 42 and preceding 44. ... 47 (forty-seven) is the natural number following 46 and followed by 48. ... 53 (fifty-three) is the natural number following 52 and preceding 54. ... 59 (fifty-nine) is the natural number following 58 and preceding 60. ... 61 (sixty-one) is the natural number following 60 and preceding 62. ... 67 is the natural number following 66 and preceding 68. ... 71 is the natural number following 70 and preceding 72. ... 73 (seventy-three) is the natural number following 72 and preceding 74. ... 79 (seventy-nine) is the natural number following 78 and preceding 80. ... 83 (eighty-three) is the natural number following 82 and preceding 84. ... 89 (eighty-nine) is the natural number following 88 and preceding 90. ... 97 is the natural number following 96 and preceding 98. ... 101 (one hundred [and] one) is the natural number following 100 and preceding 102. ... 103 is the natural number following 102 and preceding 104. ... 107 is the natural number following 106 and preceding 108. ... 109 is the natural number following 108 and preceding 110. ... 113 is the natural number following 112 and preceding 114. ... 127 is the natural number following 126 and preceding 128. ... 131 is the natural number following 130 and preceding 132. ... 137 is the natural number following 136 and preceding 138. ... 139 (One hundred thirty-nine) is the natural number following 138 and preceding 140. ... 149 is the natural number between 148 and 150. ... 151 is a natural number. ... 157 is the number equal to 100 + 50 + 7, following 156 and preceding 158. ... 163 is the natural number following one hundred sixty-two and preceding one hundred sixty-four. ... 167 is the natural number following 166 and preceding 168. ... 173 is the natural number between 172 and 174. ... 179 is the natural number between 178 and 180. ... 181 is the natural number between 180 and 182. ... 191 is the natural number between 190 and 192. ... 193 is the natural number between 192 and 194. ... 197 is the natural number between 196 and 198. ... 199 is the natural number between 198 and 200. ... 211 is the natural number between 210 and 212. ... 223 is the natural number between 222 and 224. ... 227 is the natural number between 226 and 228. ... 229 is the natural number between 228 and 230. ... 233 is the natural number between 232 and 234. ... 239 (two hundred [and] thirty-nine) is the natural number following 238 and preceding 240. ... 241 is the natural number between 240 and 242. ... 251 is the natural number between 250 and 252. ... 257 is the natural number between 256 and 258. ... 263 is the natural number between 262 and 264. ... 269 is the natural number between 268 and 270. ...

### Perfect numbers

A perfect number is an integer which is the sum of its positive proper divisors (all divisors except itself). In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number. ...

The first ten perfect numbers:

1 6 28 496 8 128 33 550 336 8 589 869 056 137 438 691 328 2 305 843 008 139 952 128 2 658 455 991 569 831 744 654 692 615 953 842 176 191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216

### 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). Aleph-0, the smallest infinite cardinal In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. ... A dialect (from the Greek word Î´Î¹Î¬Î»ÎµÎºÏ„Î¿Ï‚, dialektos) is a variety of a language characteristic of a particular group of the languages speakers. ... British English (BrE) is a broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere. ... For other uses, see American English (disambiguation). ...

#### 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, goose egg, nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip
1 One ace, single, singleton, unary, unit, unity
2 Two binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twosome, yoke
3 Three deuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika
5 Five cinque, fin, fivesome, pentad, quint, quintet, quintuplet
6 Six half dozen, hexad, sestet, sextet, sextuplet, sise
8 Eight octad, octave, octet, octonary, octuplet, ogdoad, byte (in computing terms)
10 Ten deca
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 Half - century
60 Sixty shock
70 Seventy three-score and ten
80 Eighty four-score
87 Eighty-seven four-score and seven
90 Ninety
100 One hundred centred, century, ton, short hundred
101 One hundred [and] one
110 One hundred [and] ten
111 One hundred [and] eleven
120 One hundred [and] twenty long hundred, great hundred, (obsolete) hundred
121 One hundred [and] twenty-one
144 One hundred [and] forty-four gross, dozen dozen, small gross
200 Two hundred
300 Three hundred
666 Six Hundred [and] sixty-six Number of the Beast
1 000 One thousand chiliad, grand (or G), 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
1 024 One thousand [and] twenty-four kilo (in computing, see binary prefix) (often shortened to K)
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
100 000 One hundred thousand lakh
1 000 000 One million meg, mil, (often shortened to M)
1 048 576 One million forty-eight thousand five hundred [and] seventy-six meg (in computing, see binary prefix) (often shortened to M)
10 000 000 Ten million crore

A brace of something is a way of defining the quantity of them as there being two of the items. ... Thirteen items in a rectangular space, 3+2+3+2+3 arrangement with aspect ratio near 3:2 Thirteen items in a rectangular space, 4+5+4 arrangement with aspect ratio near 11:6 A bakers dozen, also known as long dozen, is 13, one more than a proper... The Gettysburg Address is the most famous speech of U.S. President Abraham Lincoln and one of the most quoted speeches in United States history. ... Categories: | | ... The Number of the Beast is a concept from the Book of Revelation of the New Testament of the Christian Bible. ... Memory (Random Access Memory) Look up computing in Wiktionary, the free dictionary. ... In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten. ... Myriad is a classical Greek name for the number 104 = 10 000, or a group of 10 000 people, etc. ... A lakh (Hindi: à¤²à¤¾à¤–, Urdu: Ù„Ú©Ú¾, Bengali: , Tamil : à®‡à®²à®Ÿà¯à®šà®®à¯) is a unit in the Indian numbering system, widely used both in official and other contexts in Bangladesh, India, Sri Lanka, and Pakistan. ... Memory (Random Access Memory) Look up computing in Wiktionary, the free dictionary. ... In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten. ... A crore is a unit in the Indian numbering system, still widely used in Bangladesh, India, Myanmar, Sri Lanka, and Pakistan. ...

#### 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 names of numbers in English or English-language numerals for more information on naming numbers. Here are examples of how to name numbers in English. ... See also List of numbers (to be merged) There are two main English-language systems of number names: the short scale system (used in the United States, Canada and much of the English-speaking world) and the long scale system (used in most Germanic and Romance languages). ...

Short scale Long scale Power
Value American & Modern British Traditional British
(Nicolas Chuquet)
Continental European
(Jacques Peletier du Mans)
of a thousand of a million
100 One 1000-1+1 10000000
101 Ten
102 Hundred
103 Thousand 10000+1 10000000.5
106 Million 10001+1 10000001
109 Billion Thousand million Milliard 10002+1 10000001.5
1012 Trillion Billion 10003+1 10000002
1015 Quadrillion Thousand billion Billiard 10004+1 10000002.5
1018 Quintillion Trillion 10005+1 10000003
1021 Sextillion Thousand trillion Trilliard 10006+1 10000003.5
1030 Nonillion Quintillion 10009+1 10000005
1033 Decillion Thousand quintillion Quintilliard 100010+1 10000005.5
1036 Undecillion Sextillion 100011+1 10000006
1039 Duodecillion Thousand sextillion Sextilliard 100012+1 10000006.5
1042 Tredecillion Septillion 100013+1 10000007
1045 Quattuordecillion Thousand septillion Septilliard 100014+1 10000007.5
1048 Quindecillion Octillion 100015+1 10000008
1051 Sexdecillion Thousand octillion Octilliard 100016+1 10000008.5
1054 Septendecillion Nonillion 100017+1 10000009
1057 Octodecillion Thousand nonillion Nonilliard 100018+1 10000009.5
1060 Novemdecillion Decillion 100019+1 100000010
1063 Vigintillion Thousand decillion Decilliard 100020+1 100000010.5
1066 Unvigintillion Undecillion 100021+1 100000011
1069 Duovigintillion Thousand undecillion Undecilliard 100022+1 100000011.5
1072 Trevigintillion Duodecillion 100023+1 100000012
1075 Quattuorvigintillion ... ... 100024+1 100000011.5
... ... ... ... ...
1093 Trigintillion Thousand quindecillion Quindecilliard 100030+1 100000015.5
... ... ... ... ...
10120 Novemtrigintillion Vigintillion 100039+1 100000020
10123 Quadragintillion Thousand vigintillion Vigintilliard 100040+1 100000020.5
... ... ... ... ...
10153 Quinquagintillion Thousand duovigintillion Duovigintilliard 100050+1 100000025.5
... ... ... ... ...
10180 Novemquinquagintillion Trigintillion 100059+1 100000030
10183 Sexagintillion Thousand trigintillion Trigintilliard 100060+1 100000030.5
... ... ... ... ...
10213 Septuagintillion Thousand quintrigintillion Quintrigintilliard 100070+1 100000035.5
... ... ... ... ...
... ... ... ... ...
... ... ... ... ...
10300 Novemnonagintillion Quinquagintillion 100099+1 100000050
10303 Centillion Thousand quinquagintillion Quinquagintilliard 1000100+1 100000050.5
... ... ... ...
10360 Sexagintillion 1000119+1 100000060
10420 Septuagintillion 1000139+1 100000070
10480 Octogintillion 1000159+1 100000080
10540 Nonagintillion 1000179+1 100000090
10600 Centillion 1000199+1 1000000100
10603 ducentillion Thousand Centillion Centilliard 1000200+1 1000000100.5

The long and short scales are two different numerical systems used throughout the world. ... The long and short scales are two different numerical systems used throughout the world. ... Nicolas Chuquet (born 1445 (some sources say c. ... Jacques Peletier du Mans (1517 Le Mans â€“ 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... The number centillion refers to different quantities based on locality of usage. ... The number centillion refers to different quantities based on locality of usage. ... The standard dictionary numbers Throughout this article, exponential or scientific notation is used. ... The number centillion refers to different quantities based on locality of usage. ... The standard dictionary numbers Throughout this article, exponential or scientific notation is used. ...

#### Proposed systematic names for powers of 10

##### Gillion system

As proposed by Russ Rowlett, based on Greek-derived numerical prefixes: A numerical prefix is a prefix that denotes a number, which is usually a multiplier for the thing being prefixed. ...

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
1060 Icosillion
Value Name
1063 Icosihenillion
1066 Icosidillion
1069 Icositrillion
1072 Icositetrillion
1075 Icosipentillion
1078 Icosihexillion
1081 Icosiheptillion
1084 Icosioktillion
1087 Icosiennillion
1090 Triacontillion

Proposed by Donald E. Knuth: Donald Knuth adapted the familiar naming schemes to handle much larger numbers, dodging ambiguity by changing the -illion to -yllion. ...

Value Name Notation
100 One 1
101 Ten 10
102 Hundred 100
103 Ten hundred 1000
108 Myllion 1,0000,0000
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
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
${10}^{,! 4 * 2^{40}}$ Ragintyllion
${10}^{,! 4 * 2^{50}}$ 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 10N N-plex

A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). ... Googolplex is the number . ... // Throughout this article, exponential or scientific notation is used. ...

##### SI-derived
Value SI prefix Name Binary prefix Value
1 000 K Kilo (K) Ki 1024
1 000 000 M Meg (M) Mi 1 048 576
1 000 000 000 G Gig Gi 1 073 741 824

An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten. ...

### Fractional numbers

This is a table of English names for positive rational numbers less than or equal to 1. It also lists alternative names, but there is no widespread convention for the names of extremely small positive numbers. A cake divided into four equal quarters. ... In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ...

Keep in mind that rational numbers like 0.12 can be represented in infinitely many ways, e.g. zero-point-one-two (0.12), twelve percent (12%), three twenty-fifths $left({3 over 25}right)$, nine seventy-fifths $left({9 over 75} right)$, six fiftieths $left({6 over 50}right)$, twelve hundredths $left({12 over 100}right)$, twenty-four two-hundredths $left({24 over 200}right)$, etc. Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ...

Value Fraction Common names Alternative names
1 $1 over 1$ One 0.999...
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
0.125 $1 over 8$ 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
0.012345679 (012345679) $1 over 81$ One eighty-first
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, one permyriad, one basis point
0.000 01 $1 over 10^5$ One hundred-thousandth One lakhth, one perlakh
0.000 001 $1 over 10^6$ One millionth One perion, one ppm
0.000 000 1 $1 over 10^7$ One ten-millionth One crorth, one percrore
0.000 000 01 $1 over 10^8$ One hundred-millionth One awkth, one perawk
0.000 000 001 $1 over 10^9$ One billionth (in some dialects) One ppb
0 $0 over 1$ Zero

In mathematics, the recurring decimal 0. ... One half is the irreducible fraction resulting from dividing one by two (Â½), or any number by its double; multiplication by one half is equivalent to division by two. ... Look up quarter in Wiktionary, the free dictionary. ... A minute is a unit of time equal to 1/60th of an hour and to 60 seconds. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ... A permille or per mille is a tenth of a percent or one part per thousand. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 â‰ˆ 7. ... unit that is equal to 1/100th of 1%, and is used to denote the change in a financial instrument. ... Parts per million (ppm) is a measure of concentration that is used where low levels of concentration are significant. ... Parts per billion (ppb) is a measure of concentration that is used where low levels of concentration are significant. ...

## Irrational numbers

In mathematics, an irrational number is any real number that is not a rational number, i. ...

### Algebraic numbers

Expression Value Notes
${sqrt{5} - 1} over 2$ 0.618 033 988 749 894 848 204 586 834 366... Golden ratio conjugate $left(hatphiright)$, reciprocal of and one less than the golden ratio.
$sqrt[12]{2}$ 1.059 463 094 359 295 264 561 825 294 946... Twelfth root of two.
Proportion between the frequencies of adjacent semitones in the equal temperament scale.
$sqrt[3]{2}$ 1.259 921 049 894 873 164 767 210 607 278... Cube root of two.
Length of the edge of a cube with volume two. See doubling the cube for the significance of this number.
$sqrt[3]{frac{1}{2}+frac{1}{6}sqrt{frac{23}{3}}}+$
$sqrt[3]{frac{1}{2}-frac{1}{6}sqrt{frac{23}{3}}}$
1.324 717 957 244 746 025 960 908 854 478... Plastic number.
$sqrt{2}$ 1.414 213 562 373 095 048 801 688 724 210... $sqrt{2} = 2 sin 45^circ = 2 cos 45^circ$
Square root of two a.k.a. Pythagoras' constant.
Ratio of diagonal to side length in a square.
Proportion between the sides of paper sizes in the ISO 216 series (originally DIN 476 series).
${sqrt{5} + 1} over 2$ 1.618 033 988 749 894 848 204 586 834 366... Golden ratio $left(phiright)$.
$sqrt{3}$ 1.732 050 807 568 877 193 176 604 123 437... $sqrt{3} = 2 sin 60^circ = 2 cos 30^circ$
Square root of three a.k.a. the measure of the fish.
Length of the diagonal of a cube with edge length 1.
Length of the diagonal of a $1 times sqrt{2}$ rectangle.
Altitude of an equilateral triangle with side length 2.
Twice the altitude of an equilateral triangle with side length 1.
Altitude of a regular hexagon with side length 1 and diagonal length 2.
$sqrt{5}$ 2.236 067 977 499 789 805 051 477 742 381... Square root of five.
Length of the diagonal of a $1 times 2$ rectangle.
Length of the diagonal of a $sqrt{2} times sqrt{3}$ rectangle.
Length of the diagonal of a $1 times sqrt{2} times sqrt{2}$ rectangular box.
$sqrt{2} + 1$ 2.414 213 562 373 095 048 801 688 724 210... Silver ratio $left(delta_Sright)$.
$sqrt{6}$ 2.449 489 742 783 177 881 335 632 264 381... $sqrt{2} cdot sqrt{3}$ = area of a $sqrt{2} times sqrt{3}$ rectangle.
Length of the diagonal of a $1 times 1 times 2$ rectangular box.
Length of the diagonal of a $1 times sqrt{5}$ rectangle.
Length of the diagonal of a $2 times sqrt{2}$ rectangle.
Length of the diagonal of a $sqrt{3} times sqrt{3}$ rectangle.
$sqrt{7}$ 2.645 751 311 064 590 716 171 096 573 817... Length of the diagonal of a $1 times 2 times sqrt{2}$ rectangular box.
Length of the diagonal of a $1 times sqrt{6}$ rectangle.
Length of the diagonal of a $2 times sqrt{3}$ rectangle.
Length of the diagonal of a $sqrt{2} times sqrt{5}$ rectangle.
$sqrt{8}$ 2.828 427 124 746 190 290 949 243 717 478... $2 sqrt{2}$
Volume of a cube with edge length $sqrt{2}$.
Length of the diagonal of a $2 times 2$ rectangle.
Length of the diagonal of a $1 times sqrt{7}$ rectangle.
Length of the diagonal of a $sqrt{2} times sqrt{6}$ rectangle.
Length of the diagonal of a $sqrt{3} times sqrt{5}$ rectangle.
$sqrt{10}$ 3.162 277 660 168 379 522 787 063 251 599... $sqrt{2} cdot sqrt{5}$ = area of a $sqrt{2} times sqrt{5}$ rectangle.
Length of the diagonal of a $1 times 3$ rectangle.
Length of the diagonal of a $2 times sqrt{6}$ rectangle.
Length of the diagonal of a $sqrt{3} times sqrt{7}$ rectangle.
Length of the diagonal of a $sqrt{5} times sqrt{5}$ rectangle.
$sqrt{11}$ 3.316 624 790 355 399 849 114 932 736 671 Length of the diagonal of a $1 times 1 times 3$ rectangular box.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
3.464 101 615 137 754 587 054 892 683 012...
Length of the diagonal of a cube with edge length 2.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.

In mathematics, an algebraic number is any number that is a root of an algebraic equation, a non-zero polynomial with integer (or equivalently, rational) coefficients. ... The golden ratio is a number, approximately 1. ... Look up reciprocal in Wiktionary, the free dictionary. ... The golden section is a line segment sectioned into two according to the golden ratio. ... The Twelfth root of two is a quantity representing the frequency ratio between any two consecutive notes of a modern chromatic scale in equal temperament. ... A semitone (also known in the USA as a half step) is a musical interval. ... An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... Plot of y = In mathematics, the cube root of a number, denoted or x1/3, is the number a such that a3 = x. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... Doubling the cube is one of the three most famous geometric problems unsolvable by straightedge and compass alone. ... The plastic number (also known as the plastic constant or silver number) is the unique real solution of the equation and has the value which is approximately 1. ... The square root of two is the positive real number which, when multiplied by itself, gives a product of two. ... The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... For other uses, see Square. ... Comparison of the most common paper sizes. ... ISO 216 specifies international standard (ISO) paper sizes, used in most countries in the world today. ... Look up din in Wiktionary, the free dictionary. ... The golden section is a line segment sectioned into two according to the golden ratio. ... In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ... The Vesica Piscis The vesica piscis is a symbol made from two circles of the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A regular hexagon. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... In anatomy, the cuboid bone is a bone in the foot. ... The silver ratio is a mathematical constant. ... Area is a physical quantity expressing the size of a part of a surface. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In anatomy, the cuboid bone is a bone in the foot. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In anatomy, the cuboid bone is a bone in the foot. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... Area is a physical quantity expressing the size of a part of a surface. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In anatomy, the cuboid bone is a bone in the foot. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ...

### Transcendental numbers

• Khinchin-Lévy constant: 1.186 569 110 4...[1]
• 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: In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ... In mathematics LÃ©vys constant (sometimes known as the Khinchin-LÃ©vy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. ... The mathematical constant e (occasionally called Eulers number after the Swiss mathematician Leonhard Euler, or Napiers constant in honor of the Scottish mathematician John Napier who introduced logarithms) is the base of the natural logarithm function. ... When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ...

• Euler-Mascheroni constant: γ = 0.577 215 664 901 532 860 606 512 090 082 ...
• Gauss-Kuzmin-Wirsing constant: 0.303 663 002 9...[2]
• Laplace limit: ε=0.662 743 419 3...[3]
• Khinchin's constant: 2.685 452 001...[4]
• Feigenbaum constants: δ = 4.6692 ... and α = 2.5029 ...

The Euler-Mascheroni constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series and the natural logarithm: Its approximate value is Î³ â‰ˆ 0. ... In mathematics, the Gauss-Kuzmin-Wirsing operator occurs in the study of continued fractions; it is also related to the Riemann zeta function. ... In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, the infinitely many terms ai of the continued fraction expansion of x have an astonishing property: their geometric mean is a constant, known as Khinchins constant, which is independent of the value of x. ... There are two mathematical constants called Feigenbaum constants, named after mathematician Mitchell Feigenbaum. ...

## Hypercomplex numbers

The term hypercomplex number has been used in mathematics for the elements of algebras that extend or go beyond complex number arithmetic. ...

### Algebraic complex numbers

In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = âˆ’1. ... In mathematics, the imaginary unit (sometimes also represented by the Latin or the Greek iota) allows the real number system to be extended to the complex number system . ...

### Other hypercomplex numbers

In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In mathematics, the octonions are a nonassociative extension of the quaternions. ... The sedenions form a 16-dimensional algebra over the reals obtained by applying the Cayley-Dickson construction to the octonions. ... A variety of dualities in mathematics are listed at duality (mathematics). ... In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...

## Transfinite numbers

Transfinite numbers, also known as infinite numbers, are numbers that are not finite. ... This article or section is not written in the formal tone expected of an encyclopedia article. ... In the branch of mathematics known as set theory, aleph usually refers to a series of numbers used to represent the cardinality (or size) of infinite sets. ... In the branch of mathematics known as set theory, aleph usually refers to a series of numbers used to represent the cardinality (or size) of infinite sets. ... In mathematics, the Hebrew letter (aleph) with various subscripts represents various infinite cardinal numbers (see aleph number). ... In mathematics, the cardinality of a set is a measure of the number of elements of the set. There are two approaches to cardinality â€“ one which compares sets directly using bijections, injections, and surjections, and another which uses cardinal numbers. ... In mathematics, the word continuum sometimes denotes the real line. ...

## Numbers representing measured quantities

The word pair, derived via the French words pair/paire from the Latin par equal, can mean: the French equivalent of peer, holder of a French Pairie, French high title roughly equivalent to a member of the British peerage 2 (number), two of something Couple, various senses for two joined... Look up binary in Wiktionary, the free dictionary. ... A numeral is a symbol or group of symbols, or a word in a natural language that represents a number. ... Dozen is another word for the number twelve. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... Thirteen items in a rectangular space, 3+2+3+2+3 arrangement with aspect ratio near 3:2 Thirteen items in a rectangular space, 4+5+4 arrangement with aspect ratio near 11:6 A bakers dozen, also known as long dozen, is 13, one more than a proper... 20 (twenty) is the natural number following 19 and preceding 21. ... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... Look up gross, groÃŸ in Wiktionary, the free dictionary. ... A great gross is equal to a dozen gross, i. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ...

## Numbers without specific values

See placeholder names

Placeholder names are words that refer to objects or people whose names are either irrelevant or unknown in the context which it is being discussed. ...

## Bases

See also List of numbers (to be merged) There are two main English-language systems of number names: the short scale system (used in the United States, Canada and much of the English-speaking world) and the long scale system (used in most Germanic and Romance languages). ... The following is a table of the numbers 0 through 10 in a sample of the languages and writings of the world. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... A cake divided into four equal quarters. ... The interesting number paradox is a semi-humorous paradox that arises from attempting to classify numbers as interesting or dull. ... For information on how large numbers are named in English, see names of large numbers. ... There are infinitely many prime numbers. ... A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ... // Throughout this article, exponential or scientific notation is used. ... A negative number is a number that is less than zero, such as &#8722;3. ... Different cultures have different traditional numeral systems used for writing numbers and for naming large numbers. ... This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities. ... Commonly, ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... Within a set of positive numbers, a number is small if it is close to zero. ... In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similar to superreal numbers and hyperreal numbers. ... This table contains the integer factorization for the numbers from 1 to 1002. ...

• Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0-7167-4447-3

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 List of numbers - definition of List of numbers in Encyclopedia (625 words) Other numbers that are notable for their mathematical properties or cultural meanings include: 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.
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