Appendix:English numerals

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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)

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English 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 1-9, and the value is the sum. For example, "42" is "forty-two", 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 1-9 is followed by "hundred" (the individual values are multiplied together) to express the first digit, then the word "and", and the rules for smaller numbers are used for the remainder (the values of the hundreds part and the remainder are summed). For example, "101" is "one hundred and one", "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 1-999, 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 1-999 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 non-zero 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 ("three-hundred and seventy-five thousand"), the group "three-hundred and seventy-five" 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: "three-thousand", "seven-hundred", "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

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When 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
  • twenty-first (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 written-out form are appended to the numerals. For example:

  • 1st
  • 2nd
  • 3rd
  • 4th
  • 20th
  • 21st

Systematic variations

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The 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 forty-two". 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 forty-two
  • two thousand and one
  • one thousand two hundred and thirty-four
  • one million and one
  • six hundred and twenty-two 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 four-digit numbers (1000-9999).

In less formal speech, the names for the numbers 11-99 (except multiples 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 non-counting 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 old-fashioned. 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 non-counting 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

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Single digits

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Cardinal 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: 10-19

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Cardinal number Ordinal number Abbreviation of ordinal number
10 ten tenth 10th
11 eleven eleventh 11th
12 twelve twelfth 12th
13 thirteen thirteenth 13th
14 fourteen fourteenth 14th
15 fifteen fifteenth 15th
16 sixteen sixteenth 16th
17 seventeen seventeenth 17th
18 eighteen eighteenth 18th
19 nineteen nineteenth 19th

Multiples of ten

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Cardinal number Ordinal number Abbreviation of ordinal number
20 twenty twentieth 20th
30 thirty thirtieth 30th
40 forty fortieth 40th
50 fifty fiftieth 50th
60 sixty sixtieth 60th
70 seventy seventieth 70th
80 eighty eightieth 80th
90 ninety ninetieth 90th

Fractions

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English Wikipedia has an article on:
Wikipedia

Common fractions

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Common 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) one-half
1/3 one-third
2/3 two-thirds
1/4 one-fourth one-quarter
2/4 two-fourths (but typically normalized to one half) two-quarters
1/5 one-fifth
1/6 one-sixth
1/7 one-seventh
1/8 one-eighth
1/9 one-ninth
1/10 one-tenth
1/11 one-eleventh
1/12 one-twelfth
3/4 three-fourths three-quarters
3/5 three-fifths
3/8 three-eighths
4/5 four-fifths
7/8 seven-eighths

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.

one-thousandth
two-thirds
two one-thousandths
twenty-three thirtieths
twenty-one thirty-seconds
three-fourths of an inch"[1]

Decimal fractions

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Decimal fractions are typically written as Hindu-Arabic 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

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Short and long scale

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Cardinal number Ordinal number Abbreviation of ordinal number
100 hundred hundredth 100th
1,000 thousand thousandth 1,000th
10,000 ten thousand ten-thousandth 10,000th
100,000 hundred thousand hundred-thousandth 100,000th
1,000,000 million millionth 1,000,000th

For 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 106 106 ✓ ✓ ✓ ✓ ✓ ✓ *
milliard   109 ✓ ✓ ✓ ✓
billion 109 1012 ✓ ✓ ✓ ✓ ✓ ✓ ✓ *
billiard   1015         *   * ✓
trillion 1012 1018 ✓ ✓ ✓ ✓ ✓ ✓ ✓ *
trilliard   1021 *       *   * ✓
quadrillion 1015 1024 ✓ ✓ ✓ ✓ ✓ ✓ *
quintillion 1018 1030 ✓ ✓ ✓ ✓ ✓ ✓ *
sextillion 1021 1036 ✓ ✓ ✓ ✓ ✓ ✓ *
septillion 1024 1042 ✓ ✓ ✓ ✓ ✓ ✓ *
octillion 1027 1048 ✓ ✓ ✓ ✓ ✓ ✓ *
nonillion 1030 1054 ✓ ✓ ✓ ✓ ✓ ✓ *
decillion 1033 1060 ✓ ✓ ✓ ✓ ✓ ✓ *
undecillion 1036 1066 ✓ ✓ ✓ *
duodecillion 1039 1072 ✓ ✓ ✓ *
tredecillion 1042 1078 ✓ ✓ ✓ *
quattuordecillion 1045 1084 ✓ ✓ ✓ *
quindecillion 1048 1090 ✓ ✓ ✓ *
sexdecillion 1051 1096 ✓ ✓ ✓ *
septendecillion 1054 10102 ✓ ✓ ✓ *
octodecillion 1057 10108 ✓ ✓ ✓ *
novemdecillion 1060 10114 ✓ ✓ ✓ *
vigintillion 1063 10120 ✓ ✓ ✓ ✓ ✓ ✓ *
googol 10100 10100 ✓ ✓ ✓ ✓ ✓ ✓ *
centillion 10303 10600 ✓ ✓ ✓ *
googolplex 1010100 1010100 ✓ ✓ ✓ ✓ ✓ ✓

Usage notes

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  1. 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.
  2. 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, Merriam-Webster.
  • 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 109, which is what Americans call a billion.
    billiard unit of quantity equal to 1015, 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 1021, 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

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In 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 1 100 1 one
ten 10 101 10 ten
one hundred 100 102 100 one hundred
one thousand 1,000 103 1,000 one thousand
ten thousand 10,000 104 10,000 ten thousand
one lakh (also lac) 1,00,000 105 100,000 one hundred thousand
ten lakh 10,00,000 106 1,000,000 one million
one crore 1,00,00,000 107 10,000,000 ten million
ten crore 10,00,00,000 108 100,000,000 one hundred million
one arab / one hundred crore 1,00,00,00,000 109 1,000,000,000 one billion
one thousand crore / ten arab 10,00,00,00,000 1010 10,000,000,000 ten billion
ten thousand crore / one kharab / one hundred arab 1,00,00,00,00,000 1011 100,000,000,000 one hundred billion
one lakh crore / ten kharab / one thousand arab 10,00,00,00,00,000 1012 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 1013 10,000,000,000,000 ten trillion
one crore crore / ten neel 10,00,00,00,00,00,000 1014 100,000,000,000,000 one hundred trillion
one padm / one hundred neel / ten crore crore 1,00,00,00,00,00,00,000 1015 1,000,000,000,000,000 one quadrillion
ten padm / one hundred crore crore 10,00,00,00,00,00,00,000 1016 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 1017 100,000,000,000,000,000 one hundred quadrillion

General rules for very large numbers (short and long scale)

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See also: Appendix:Very large numbers

Depending 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 ducenti-quinquaginta-quattor-illion 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

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Number 1 2 3 4 5
Modifier single double / twofold triple / threefold quadruple / fourfold quintuple / pentuple / fivefold
Whole loner / singleton / monad pair / couple / twosome / dyad trio / threesome / triad / troika foursome / tetrad fivesome
Part only one / singlet twin / one of two / doublet triplet / one of three quadruplet / one of four quintuplet / pentuplet / one of five
Number 6 7 8 9 10
Modifier sextuple / hextuple / sixfold septuple / heptuple / sevenfold octuple / eightfold ninefold / nonuple tenfold / decuple
Whole sixsome sevensome eightsome ninesome tensome / decad
Part sextuplet / hextuplet / one of six one of seven / septuplet / heptuplet octuplet / one of eight one of nine / nonuplet one of ten / decuplet
Number 11 12 13 100 many
Modifier elevenfold / undecuple / hendecuple twelvefold / duodecuple thirteenfold / tredecuple a hundredfold / centuple multiple
Whole elevensome twelvesome thirteensome hundredsome
Part one of eleven / undecuplet / hendecuplet one of twelve / duodecuplet one of thirteen / tredecuplet one of a hundred / centuplet one of many / multiplet

Greek-based prefixes

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English Wikipedia has an article on:
Wikipedia

Greek-based prefixes:

Historical numerals

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Numbers from a base-12 number system, base-20 numbers, and other historical numbers.

Duodecimal (base 12)

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Number 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)

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Number 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

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  • 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 ("thirty-one 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

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Footnotes

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Notes

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  1. ^ Especially for the 103-illion and the 300-illion, this method gives the same name of Trecentillion to them and causes the confusion.

References

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  1. ^ 6. Compounding Rules in U.S. Government Printing Office Style Manual, govinfo.gov
  2. ^ http://home.earthlink.net/~mrob/pub/math/largenum.html

Further reading

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