List of numbers

From Academic Kids

This is a list of articles about numbers.

Contents

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

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-Lvy 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:

Hypercomplex numbers

Algebraic complex numbers

Other hypercomplex numbers

Transfinite numbers

Numbers representing measured quantities

Numbers without specific values

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

Bases

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

See also

Further reading

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

External links

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