Appendix:English numerals
This appendix discusses numbers or numerals in English generally. "Numerals" is also a grammatical part of speech, but only applies to certain types of numbers. (See #Parts of speech.)
Naming rules (short scale)
editEnglish generally uses a decimal counting system for natural numbers. The names of the cardinal and ordinal numbers can be constructed from the below tables and a set of combining rules.
Each of the numbers specifically listed has a literal name that can be used on its own.
 To name numbers 21 through 99 that are not multiples of 10, a multiple of ten is followed by a single digit number 19, and the value is the sum. For example, "42" is "fortytwo", which places a numeral "4" before a numeral "2" to indicate that the 4 represents "forty", or 4 times 10. "Zero" never combines with other numbers in the naming system; it is only pronounced in the name for 0.
 To name numbers 101 through 999 that are not multiples of 100, the name of a digit 19 is followed by "hundred" (the individual values are multiplied together) to express the first digit, and the rules for smaller numbers are used for the remainder (the values of the hundreds part and the remainder are summed). For example, "642" is "six hundred and forty two" and "919" is "nine hundred and nineteen".
 For larger numbers, each additional numeral at the beginning of the string generally represents another power of ten. Every additional (up to) three digits are grouped using the rules for numbers 1999, then paired with a multiplier.
 So with the multiplier "thousand" for example: 2,001 is "two thousand one" and 1,234 is "one thousand two hundred and thirty four".
 One informal variant omits the use of the word thousand for example "fifteen hundred" instead of "one thousand five hundred". This variant tends to be used only in cases where it results in shorter pronunciation.
 When writing in numerals, to aid comprehension these groups of three digits are typically separated—for example, with a comma in countries where the decimal mark is the period. (To be manipulated by machine, these separators are usually omitted. Lists/columns and tables of numbers may use spatial alignment in addition to or instead of commas.)
 Similarly, when writing numbers with words, these groups are written using the rules for 1999 followed by the multiplier. (Any group that is "000" is neither written in words nor pronounced.) Due to the impractical length, it is uncommon to find numbers with more than a few nonzero digits in words; more often they are simply written using Arabic numerals. Examples:
 375,000 has each numeral at the place in the string of numerals that represents its power of ten. Written fully in words ("threehundred and seventyfive thousand"), the group "threehundred and seventyfive" modifies the word "thousand".
 Compare 3,750, for which each word representing a numeral is immediately modified by a word representing its power of ten: "threethousand", "sevenhundred", "and" "fifty".
 954,020,672: "nine hundred and fifty four million twenty thousand six hundred and seventy two" (uncommonly seen due to length)
 20,000,000: "twenty million" (commonly seen due to brevity)
Ordinal numbers
editWhen constructing names for ordinal numbers, the ordinal variant given in the charts below is only used for the final word. For example:
 first
 second
 third
 fourth
 twentieth
 twentyfirst (not twentieth first)
Ordinal numbers can also be written with Arabic numerals, in which case the last two letters of what would be the final word in the writtenout form are appended to the numerals. For example:
 1st
 2nd
 3rd
 4th
 20th
 21st
Systematic variations
editThe words for numbers less than one hundred are varied as follows: Those not expressible by a single word can when written be joined by a hyphen, as in "six hundred fortytwo". In British English, the word "and" is typically inserted before them. (Some speakers of North American English also insert "and", especially when the number is below 20.) Examples:
 six hundred and two (instead of "six hundred two")
 six hundred and fortytwo
 two thousand and one
 one thousand two hundred and thirtyfour
 one million and one
 six hundred and twentytwo million one thousand and five
As shown on the charts below, there are two systems for the names of multipliers, known as the "long system" and "short system", though the short system is generally now preferred in English, to avoid confusion.
In countries where the comma or middle dot is used as the decimal mark, spaces or periods are used for thousands separators. Some style guides prefer no digits separator for fourdigit numbers (10009999).
In less formal speech, the names for the numbers 1199 (except powers of ten) can be combined with "hundred" as an alternative to a longer systematic name using both "thousand" and "hundred". For example "eleven hundred" can replace "one thousand one hundred" but "twenty hundred and two" never replaces "two thousand and two" except poetically.
For large round numbers, familiar multipliers are sometimes repeated instead of using less familiar multipliers. For example, "one billion billion" instead of "one quintillion".
In British English, the phrases "thousand million", "thousand billion", and "thousand trillion" are sometimes used in place of "billion", "trillion", and "quadrillion", respectively.
The determiners a or the can grammatically substitute for "one", as in "a hundred" or "the first thousand"; and "a couple" can be used to mean two (though to some speakers "a couple" means "a few" which could perhaps range from two to five or higher).
The names of noncounting numbers — like in a code or a sequence or a naming scheme as for years or addresses — typically use a form of the "hundreds replace thousands" variation that also drops the "hundreds". Years and addresses are never written with commas as digit separators. For example, the year 1,984 is pronounced "nineteen eighty four"; referring to that year with the systematic reading "nineteen hundred and eighty four" sounds oldfashioned. Sequence numbers with zero digits have additional variations. More commonly than not, a zero in only the tens place is read as "oh" (as in the letter o), like "nineteen oh four". A zero in the hundreds place triggers use of the systematic name or the "hundreds replacement" variant. Examples:
 2,001: "two thousand and one" or rarely "twenty oh one"
 2,015: "two thousand and fifteen" or very commonly "twenty fifteen"
One complete variation for such noncounting numbers is to read individual digits. Informally, "oh" can once again substitute for zero in this scheme. For example, "1024" could be read "one zero two four" or "one oh two four".
Small whole numbers
editSingle digits
editCardinal number  Ordinal number  Abbreviation of ordinal number  

0  zero  zeroth  0th 
1  one  first  1st 
2  two  second  2nd 
3  three  third  3rd 
4  four  fourth  4th 
5  five  fifth  5th 
6  six  sixth  6th 
7  seven  seventh  7th 
8  eight  eighth  8th 
9  nine  ninth  9th 
Irregular numbers: 1019
editMultiples of ten
editFractions
editCommon fractions
editCommon fractions are indicated by using the cardinal form for the numerator and the ordinal form for the denominator, with a few exceptions for small numbers. Fractions are typically but not always normalized to proper fractions or integers with proper fraction components.
Number  Regular form  Irregular form 

1/1  (none; one first is incorrect and would be interpreted as an ordinal)  one whole 
1/2  (none; one second is incorrect and would be interpreted as a measure of time, 1/60th of a minute)  onehalf 
1/3  onethird  
2/3  twothirds  
1/4  onefourth  onequarter 
2/4  twofourths (but typically normalized to one half)  twoquarters 
1/5  onefifth  
1/6  onesixth  
1/7  oneseventh  
1/8  oneeighth  
1/9  oneninth  
1/10  onetenth  
1/11  oneeleventh  
1/12  onetwelfth  
3/4  threefourths  threequarters 
3/5  threefifths  
3/8  threeeighths  
4/5  fourfifths  
7/8  seveneighths 
GPO manual states: "Print a hyphen between the elements of a fraction, but omit it between the numerator and the denominator when the hyphen appears in either or in both.
 onethousandth
 twothirds
 two onethousandths
 twentythree thirtieths
 twentyone thirtyseconds
 threefourths of an inch"^{[1]}
Decimal fractions
editDecimal fractions are typically written as HinduArabic numerals (like 0.125). When written as words, the symbols are generally translated one at a time, for example "zero point one two five". Zero or nought can also be written as oh, but this may be considered casual and is more common when being spoken.
Multiplying numbers
editShort and long scale
editFor higher multiplying terms, the ordinal suffix is always "th".
Name  Short scale (modern) 
Long scale (dated) 
Authorities  

AHD4  COD  OED2  OEDnew  RHD2  SOED3  W3  UM  
million  10^{6}  10^{6}  ✓  ✓  ✓  ✓  ✓  ✓  *  
milliard  10^{9}  ✓  ✓  ✓  ✓  
billion  10^{9}  10^{12}  ✓  ✓  ✓  ✓  ✓  ✓  ✓  * 
billiard  10^{15}  *  *  ✓  
trillion  10^{12}  10^{18}  ✓  ✓  ✓  ✓  ✓  ✓  ✓  * 
trilliard  10^{21}  *  *  *  ✓  
quadrillion  10^{15}  10^{24}  ✓  ✓  ✓  ✓  ✓  ✓  *  
quintillion  10^{18}  10^{30}  ✓  ✓  ✓  ✓  ✓  ✓  *  
sextillion  10^{21}  10^{36}  ✓  ✓  ✓  ✓  ✓  ✓  *  
septillion  10^{24}  10^{42}  ✓  ✓  ✓  ✓  ✓  ✓  *  
octillion  10^{27}  10^{48}  ✓  ✓  ✓  ✓  ✓  ✓  *  
nonillion  10^{30}  10^{54}  ✓  ✓  ✓  ✓  ✓  ✓  *  
decillion  10^{33}  10^{60}  ✓  ✓  ✓  ✓  ✓  ✓  *  
undecillion  10^{36}  10^{66}  ✓  ✓  ✓  *  
duodecillion  10^{39}  10^{72}  ✓  ✓  ✓  *  
tredecillion  10^{42}  10^{78}  ✓  ✓  ✓  *  
quattuordecillion  10^{45}  10^{84}  ✓  ✓  ✓  *  
quindecillion  10^{48}  10^{90}  ✓  ✓  ✓  *  
sexdecillion  10^{51}  10^{96}  ✓  ✓  ✓  *  
septendecillion  10^{54}  10^{102}  ✓  ✓  ✓  *  
octodecillion  10^{57}  10^{108}  ✓  ✓  ✓  *  
novemdecillion  10^{60}  10^{114}  ✓  ✓  ✓  *  
vigintillion  10^{63}  10^{120}  ✓  ✓  ✓  ✓  ✓  ✓  *  
googol  10^{100}  10^{100}  ✓  ✓  ✓  ✓  ✓  ✓  *  
centillion  10^{303}  10^{600}  ✓  ✓  ✓  *  
googolplex  10^{10100}  10^{10100}  ✓  ✓  ✓  ✓  ✓  ✓ 

Usage notes
edit An asterisk (*) denotes that it has not been verified whether the term so marked is or is not mentioned in the specified work of reference.
 The dictionary abbreviations are as follows:
 AHD4 — the American Heritage Dictionary, 4th edition, →ISBN. [1].
 COD — Cambridge Dictionaries Online, Cambridge, UK: Cambridge University Press.
 OED2 — Oxford English Dictionary, 2nd edition, Oxford, UK: Oxford University Press. →ISBN (and addenda since publication in 1989).
 OEDnew — Oxford English Dictionary, New Edition, Oxford, UK: Oxford University Press. [2] (subscription required), checked April 2007.
 RHD2 — The Random House Dictionary, 2nd Unabridged Edition, 1987, Random House.
 SOED3 — Shorter Oxford English Dictionary, 3rd edition, 1993, Oxford: Clarendon Press.
 W3 — Webster's Third New International Dictionary, Unabridged, 1993, MerriamWebster.
 UM — How Many? A Dictionary of Units of Measures, published by Russ Rowlett and the University of North Carolina at Chapel Hill, online, accessed 1 April 2007.
 milliard[1] a unit of quantity equal to 10^{9}, which is what Americans call a billion.
 billiard unit of quantity equal to 10^{15}, which is one quadrillion in American terminology or 1000 billion in traditional British terminology. The name is coined to parallel milliard, which has long been a name for 1000 million.
 trilliard a unit of quantity equal to 10^{21}, which is one sextillion in American terminology or 1000 trillion in traditional British terminology. The name is coined to parallel milliard, which has long been a name for 1000 million.
South Asian numbering system
editIn South Asian varieties of English, the traditional South Asian numbering system is commonly used instead of or alongside the short and long scale. This groups higher digits in pairs instead of triplets.
South Asian English  Indian figure  Power notation  Arabic figure  Short scale English 

one  1  10^{0}  1  one 
ten  10  10^{1}  10  ten 
one hundred  100  10^{2}  100  one hundred 
one thousand  1,000  10^{3}  1,000  one thousand 
ten thousand  10,000  10^{4}  10,000  ten thousand 
one lakh (also lac)  1,00,000  10^{5}  100,000  one hundred thousand 
ten lakh  10,00,000  10^{6}  1,000,000  one million 
one crore  1,00,00,000  10^{7}  10,000,000  ten million 
ten crore  10,00,00,000  10^{8}  100,000,000  one hundred million 
one arab / one hundred crore  1,00,00,00,000  10^{9}  1,000,000,000  one billion 
one thousand crore / ten arab  10,00,00,00,000  10^{10}  10,000,000,000  ten billion 
ten thousand crore / one kharab / one hundred arab  1,00,00,00,00,000  10^{11}  100,000,000,000  one hundred billion 
one lakh crore / ten kharab / one thousand arab  10,00,00,00,00,000  10^{12}  1,000,000,000,000  one trillion 
ten lakh crore / one neel / one hundred kharab / ten thousand arab  1,00,00,00,00,00,000  10^{13}  10,000,000,000,000  ten trillion 
one crore crore / ten neel  10,00,00,00,00,00,000  10^{14}  100,000,000,000,000  one hundred trillion 
one padm / one hundred neel / ten crore crore  1,00,00,00,00,00,00,000  10^{15}  1,000,000,000,000,000  one quadrillion 
ten padm / one hundred crore crore  10,00,00,00,00,00,00,000  10^{16}  10,000,000,000,000,000  ten quadrillion 
one shankh / one hundred padm / one thousand crore crore / one lakh lakh crore  1,00,00,00,00,00,00,00,000  10^{17}  100,000,000,000,000,000  one hundred quadrillion 
General rules for very large numbers (short and long scale)
editDepending on whether you are using the old European system of powers of a million, or the more current system of powers of a thousand, then the name of a number can be created by extracting the name of the power from this table and then adding illion to the end. This method should be treated with caution,^{[notes 1]} and it is common to find slight spelling variations, normally to aid with the pronunciation of the resulting word. In most situations it is preferable to write numbers such as these using standard form instead of words.^{[2]}
Units  Tens  Hundreds  

1  un  deci  centi 
2  duo  viginti  ducenti 
3  tre  triginta  trecenti 
4  quattor  quadraginta  quadringenti 
5  quinqua  quinquaginta  quingenti 
6  sex  sexaginta  sescenti 
7  septe  septuaginta  septigenti 
8  octo  octoginta  octingenti 
9  novem  nonaginta  nongenti 
For an example of how this might work consider . This can be written as using the modern system. This is then interpreted as ducentiquinquagintaquattorillion using the above table. The hyphens are normally removed leaving one ducentiquinquagintaquattorillion. In the older system it would be written as and interpreted as one centivigintiseptillion, noting that the ‘e’ from ‘septe’ has been elided.
Groups and multiplying words
editGreekbased prefixes
editGreekbased prefixes:
 1: mono
 2: di
 3: tri
 4: tetra
 5: penta
 6: hexa
 7: hepta
 8: octa
 9: ennea
 10: deca
 11: hendeca
 12: dodeca
 15: pentadeca
 20: icosa
 30: triaconta
 40: tetraconta
 50: pentaconta
 60: hexaconta
 70: heptaconta
 80: octaconta
 90: enneaconta
 100: hecta
 1,000: chilia
 10,000: myria
 1,000,000: mega
 1,000,000,000: giga
 1,000,000,000,000: tera
 1,000,000,000,000,000: peta
 1,000,000,000,000,000,000: exa
 1,000,000,000,000,000,000,000: zetta
 1,000,000,000,000,000,000,000,000: yotta
 1,000,000,000,000,000,000,000,000,000: ronna
 1,000,000,000,000,000,000,000,000,000,000: quetta
Historical numerals
editNumbers from a base12 number system, base20 numbers, and other historical numbers.
Duodecimal (base 12)
editNumber  Word  Mathematical formula 
6  half dozen  ½ × 12 
12  dozen  12 
13  baker's dozen  12 + 1 
13  long dozen  12 + 1 
72  half gross  ½ × (12 × 12) 
120  short gross  10 × 12 
120  small gross  10 × 12 
120  great hundred  12 × 10 
120  long hundred  12 × 10 
144  gross  12 × 12 
156  long gross  (12 + 1) × 12 
1200  long thousand  12 × 100 
1728  great gross  12 × 12 × 12 
Vigesimal (base 20)
editNumber  Word  Mathematical formula 
20  score  20 
40  twoscore  2 × 20 
60  threescore  3 × 20 
80  fourscore  4 × 20 
100  fivescore  5 × 20 
120  sixscore  6 × 20 
140  sevenscore  7 × 20 
160  eightscore  8 × 20 
180  ninescore  9 × 20 
200  tenscore  10 × 20 
Parts of speech
edit Cardinal numbers act as the part of speech known as "numerals". For example, in "two apples", "two" is a quantitative determiner (says how many there are) for the plural noun "apples".
 Ordinal numbers act as adjectives. For example, "the second apple" specifies a property of a specific apple, which identifies its position or rank.
 Fractional units act as nouns. For example, in "seven eighths", "seven" is a numeral that quantifies "eighths", a plural noun. Overall, this is a noun phrase. It can occur in predeterminer position ("she used only seven eighths the amount of flour called for by the recipe"), or with of in a partitive construction like "seven eighths of the apple".
 Unlike true numerals, terms like hundred, million, and dozen cannot function alone as determiners (*"hundred apples"). However, they can form a determiner when they follow a numeral ("thirtyone million", "two dozen"), or certain other determinatives ("the dozen apples", "several hundred apples"). These terms are most commonly classified as nouns, though some traditional grammars place them among adjectives.
Semantically, all these different parts of speech denote quantity or portion (albeit in different ways) and can be described as "numbers" (or numerals, as a synonym for numbers rather than as a grammatical part of speech).
See also
editFootnotes
editNotes
edit ^ Especially for the 103illion and the 300illion, this method gives the same name of Trecentillion to them and causes the confusion.
References
edit ^ 6. Compounding Rules in U.S. Government Printing Office Style Manual, govinfo.gov
 ^ http://home.earthlink.net/~mrob/pub/math/largenum.html
Further reading
edit English numerals on Wikipedia.Wikipedia
 Fraction (mathematics) on Wikipedia.Wikipedia
 Number  Grammar, dictionary.cambridge.org
 Choosing numerals or words  Style Manual, stylemanual.gov.au
 U.S. Government Printing Office Style Manual, govinfo.gov, chapter 12. Numerals
 S:U.S. Government Printing Office Style Manual/Numerals
 Expressing Numbers in English, thoughtco.com
 How to Say Big Numbers, eslblogs.waketech.edu
 Names for large numbers, home.hetnet.nl
 Integer Powers of One Thousand, home.comcast.net
 The Googolplex Page, fpx.de