English numerals

Cardinal numbers

Cardinal numbers refer to the size of a group. In English, these words are numerals.

If a number is in the range 21 to 99, and the second digit is not zero, one typically writes the number as two words separated by a hyphen.

In English, the hundreds are perfectly regular, except that the word hundred remains in its singular form regardless of the number preceding it.

So too are the thousands, with the number of thousands followed by the word "thousand".

In American usage, four-digit numbers with non-zero hundreds are often named using multiples of "hundred" and combined with tens and ones: "One thousand one", "Eleven hundred three", "Twelve hundred twenty-five", "Four thousand forty-two", or "Ninety-nine hundred ninety-nine." In British usage, this style is common for multiples of 100 between 1,000 and 2,000 (e.g. 1,500 as "fifteen hundred") but not for higher numbers.

Americans may pronounce four-digit numbers with non-zero tens and ones as pairs of two-digit numbers without saying "hundred" and inserting "oh" for zero tens: "twenty-six fifty-nine" or "forty-one oh five". This usage probably evolved from the distinctive usage for years; "nineteen-eighty-one", or from four-digit numbers used in the American telephone numbering system which were originally two letters followed by a number followed by a four-digit number, later by a three-digit number followed by the four-digit number. It is avoided for numbers less than 2500 if the context may mean confusion with time of day: "ten ten" or "twelve oh four".

Intermediate numbers are read differently depending on their use. Their typical naming occurs when the numbers are used for counting. Another way is for when they are used as labels. The second column method is used much more often in American English than British English. The third column is used in British English but rarely in American English (although the use of the second and third columns is not necessarily directly interchangeable between the two regional variants). In other words, British English and American English can seemingly agree, but it depends on a specific situation (in this example, bus numbers).

Note: When writing a cheque (or check), the number 100 is always written "one hundred". It is never "a hundred".

In American English, many students are taught not to use the word and anywhere in the whole part of a number, so it is not used before the tens and ones. It is instead used as a verbal delimiter when dealing with compound numbers. Thus, instead of "three hundred and seventy-three", one would say "three hundred seventy-three". Despite this rule, the and is used by some Americans in reading numbers containing tens and ones as an alternative variant. For details, see American and British English differences.

Very large numbers

For numbers above a million, there are three main systems for naming numbers in English (for the use of prefixes such as kilo- for a thousand, mega- for a million, milli- for a thousandth, etc. see SI units):

the long scale (formerly used in British English but now obsolete) designates a system of numeric names in which a thousand million is called a milliard, and billion is used for a million million. This system is still used in several other European languages.

the short scale (always used in American English and almost invariably in British English) designates a system of numeric names in which a thousand million is called a billion, and the word milliard is not used.

the Indian numbering system, used widely in South Asia.

The numbers past a trillion in the short scale system, in ascending powers of 1000, are as follows: quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion, undecillion, duodecillion, tredecillion, quattuordecillion, and quindecillion (which is 10 to the 48th power, or a one followed by 48 zeros). The highest number listed in Robert Munafo's table is a milli-millillion. That's 10 to the 3,000,003rd power.

The googolplex has often been nominated as the largest named number in the world. If a googol is ten to the one hundredth, then a googolplex is one followed by a googol of zeros (that is, ten to the power of a googol). There is the coinage, of very little use, of ten to the googolplex power, of the word googolplexplex.

The terms arab, kharab, padm and shankh are more commonly found in old books on Indian mathematics.

Here are some approximate composite large numbers in American English:

Often, large numbers are written with (preferably non-breaking) half-spaces or thin spaces separating the thousands (and, sometimes, with normal spaces or apostrophes) instead of commas—to ensure that confusion is not caused in countries where a decimal comma is used. Thus, a million is often written 1 000 000.

In some areas, a point (. or ·) may also be used as a thousands' separator, but then, the decimal separator must be a comma.

Specialized numbers

A few numbers have special names (in addition to their regular names):

0: has several other names, depending on context:

zero: formal scientific usage

naught / nought: mostly British usage

aught: Mostly archaic but still occasionally used when a digit in mid-number is 0 (as in "thirty-aught-six", the .30-06 Springfield rifle cartridge and by association guns that fire it)

oh: used when spelling numbers (like telephone, bank account, bus line [British: bus route])

nil: in general sport scores, British usage ("The score is two–nil.")

nothing: in general sport scores, American usage ("The score is two–nothing.")

null: used technically to refer to an object or idea related to nothingness. The 0th aleph number ( ℵ 0 ) is pronounced "aleph-null".

love: in tennis, badminton, squash and similar sports (origin disputed, often said to come from French l'œuf, "egg"; but the Oxford English Dictionary mentions the phrase for love, meaning nothing is at risk)

zilch, nada (from Spanish), zip: used informally when stressing nothingness; this is true especially in combination with one another ("You know nothing—zero, zip, nada, zilch!"); American usage

nix: also used as a verb; mostly American usage

cypher / cipher: archaic, from French chiffre, in turn from Arabic sifr, meaning zero

goose egg (informal)

duck (used in cricket when a batsman is dismissed without scoring)

blank the half of a domino tile with no pips

1:

ace in certain sports and games, as in tennis or golf, indicating success with one stroke, and the face of a die, playing card or domino half with one pip

birdie in golf denotes one stroke less than par, and bogey, one stroke more than par

solo

unit

linear the degree of a polynomial is 1; also for explicitly denoting the first power of a unit: linear meter

unity in mathematics

protagonist first actor in theater of Ancient Greece

2:

couple

brace, from Old French "arms" (the plural of arm), as in "what can be held in two arms".

pair

deuce the face of a die, playing card or domino half with two pips

eagle in golf denotes two strokes less than par

duo

quadratic the degree of a polynomial is 2

also square or squared for denoting the second power of a unit: square meter or meter squared

penultimate, second from the end

deuteragonist second actor in theater of Ancient Greece

3:

trey the face of a die or playing card with three pips, a three-point field goal in basketball, nickname for the third carrier of the same personal name in a family

trio

trips: three-of-a-kind in a poker hand. a player has three cards with the same numerical value

cubic the degree of a polynomial is 3

also cube or cubed for denoting the third power of a unit: cubic meter or meter cubed

albatross in golf denotes three strokes less than par. Sometimes called double eagle

hat-trick or hat trick: achievement of three feats in sport or other contexts

antepenultimate third from the end

tritagonist third actor in theater of Ancient Greece

turkey in bowling, three consecutive strikes

4:

cater: (rare) the face of a die or playing card with four pips

quartet

quartic or biquadratic the degree of a polynomial is 4

quad (short for quadruple or the like) several specialized sets of four, such as four of a kind in poker, a carburetor with four inputs, etc.,

condor in golf denotes four strokes less than par

preantepenultimate fourth from the end

5:

cinque or cinq (rare) the face of a die or playing card with five pips

quintet

nickel (informal American, from the value of the five-cent US nickel, but applied in non-monetary references)

quintic the degree of a polynomial is 5

quint (short for quintuplet or the like) several specialized sets of five, such as quintuplets, etc.

6:

half a dozen

sice (rare) the face of a die or playing card with six pips

sextet

sextic or hectic the degree of a polynomial is 6

7:

septet

septic or heptic the degree of a polynomial is 7

8:

octet

9:

nonet

10:

a metric dozen

dime (informal American, from the value of the ten-cent US dime, but applied in non-monetary references)

decet

decade, used for years but also other groups of 10 as in rosary prayers or Braille symbols

11: a banker's dozen

12: a dozen (first power of the duodecimal base), used mostly in commerce

13: a baker's dozen

20: a score (first power of the vigesimal base), nowadays archaic; famously used in the opening of the Gettysburg Address: "Four score and seven years ago..." The Number of the Beast in the King James Bible is rendered "Six hundred threescore and six". Also in The Book of Common Prayer, Psalm 90 as used in the Burial Service - "The days of our age are threescore years and ten; ...."

50: half-century, literally half of a hundred, usually used in cricket scores.

60: a shock: historical commercial count, described as "three scores".

100:

A century, also used in cricket scores and in cycling for 100 miles.

A ton, in Commonwealth English, the speed of 100 mph or 100 km/h.

A small hundred or short hundred (archaic, see 120 below)

120:

A great hundred or long hundred (twelve tens; as opposed to the small hundred, i.e. 100 or ten tens), also called small gross (ten dozens), both archaic

Also sometimes referred to as duodecimal hundred, although that could literally also mean 144, which is twelve squared

144: a gross (a dozen dozens, second power of the duodecimal base), used mostly in commerce

1000:

a grand, colloquially used especially when referring to money, also in fractions and multiples, e.g. half a grand, two grand, etc. Grand can also be shortened to "G" in many cases.

K, originally from the abbreviation of kilo-, e.g. "He only makes $20K a year."

1728: a great gross (a dozen gross, third power of the duodecimal base), used historically in commerce

10,000: a myriad (a hundred hundred), commonly used in the sense of an indefinite very high number

100,000: a lakh (a hundred thousand), in Indian English

10,000,000: a crore (a hundred lakh), in Indian English and written as 100,00,000.

10¹⁰⁰: googol (1 followed by 100 zeros), used in mathematics; not to be confused with the name of the company Google (which was originally a misspelling of googol)

10^googol: googolplex (1 followed by a googol of zeros)

10^googolplex: googolplexplex (1 followed by a googolplex of zeros)

Combinations of numbers in most sports scores are read as in the following examples:

1–0    British English: one-nil; American English: one-nothing, one-zip, or one-zero

0–0    British English: nil-nil, or more rarely nil all; American English: zero-zero or nothing-nothing, (occasionally scoreless or no score)

2–2    two-two or two all; American English also twos, two to two, even at two, or two up.

Naming conventions of Tennis scores (and related sports) are different from other sports.

The centuries of Italian culture have names in English borrowed from Italian:

duecento "(one thousand and) two hundred" for the years 1200 to 1299, or approximately 13th century

trecento 14th century

quattrocento 15th century

cinquecento 16th century

seicento 17th century

settecento 18th century

ottocento 19th century

novecento 20th century

Multiplicative adverbs

A few numbers have specialised multiplicative numbers (adverbs) which express how many times some event happens:

Compare these specialist multiplicative numbers to express how many times some thing exists (adjectives):

English also has some multipliers and distributive numbers, such as singly.

Other examples are given in the Specialist Numbers.

Negative numbers

The name of a negative number is the name of the corresponding positive number preceded by "minus" or (American English) "negative". Thus −5.2 is "minus five point two" or "negative five point two". For temperatures, North Americans colloquially say "below"—short for "below zero"—so a temperature of −5° is "five below" (in contrast, for example, to "two above" for 2°). This is occasionally used for emphasis when referring to several temperatures or ranges both positive and negative. This is particularly common in Canada where the use of Celsius in weather forecasting means that temperatures can regularly drift above and below zero at certain times of year.

Ordinal numbers

Ordinal numbers refer to a position in a series. Common ordinals include:

Zeroth only has a meaning when counting starts with zero, which happens in a mathematical or computer science context.

Ordinal numbers such as 21st, 33rd, etc., are formed by combining a cardinal ten with an ordinal unit.

Higher ordinals are not often written in words, unless they are round numbers (thousandth, millionth, billionth). They are written using digits and letters as described below. Here are some rules that should be borne in mind.

The suffixes -th, -st, -nd and -rd are occasionally written superscript above the number itself.

If the tens digit of a number is 1, then write "th" after the number. For example: 13th, 19th, 112th, 9,311th.

If the tens digit is not equal to 1, then use the following table:

For example: 2nd, 7th, 20th, 23rd, 52nd, 135th, 301st.

These ordinal abbreviations are actually hybrid contractions of a numeral and a word. 1st is "1" + "st" from "first". Similarly, "nd" is used for "second" and "rd" for "third". In the legal field and in some older publications, the ordinal abbreviation for "second" and "third" is simply "d".

For example: 42d, 33d, 23d.

NB: The practice of using "d" to denote "second" and "third" is still often followed in the numeric designations of units in the US armed forces, for example, 533d Squadron, and in legal citations for the second and third series of case reporters.

Any ordinal name that doesn't end in "first", "second", or "third", ends in "th".

Dates

There are a number of ways to read years. The following table offers a list of valid pronunciations and alternate pronunciations for any given year of the Gregorian calendar.

Fractions and decimals

In spoken English, ordinal numbers are also used to quantify the denominator of a fraction. Thus "fifth" can mean the element between fourth and sixth, or the fraction created by dividing the unit into five pieces. In this usage, the ordinal numbers can be pluralized: one seventh, two sevenths. The sole exception to this rule is division by two. The ordinal term "second" can only refer to location in a series; for fractions English speakers use the term 'half' (plural "halves").

Here are some common English fractions (known linguistically as "partitive numerals"):

Alternatively, and for greater numbers, one may say for 1/2 "one over two", for 5/8 "five over eight", and so on. This "over" form is also widely used in mathematics.

Numbers with a decimal point may be read as a cardinal number, then "and", then another cardinal number followed by an indication of the significance of the second cardinal number (mainly U.S.); or as a cardinal number, followed by "point", and then by the digits of the fractional part. The indication of significance takes the form of the denominator of the fraction indicating division by the smallest power of ten larger than the second cardinal. This is modified when the first cardinal is zero, in which case neither the zero nor the "and" is pronounced, but the zero is optional in the "point" form of the fraction.

For example:

0.002 is "two thousandths" (mainly U.S.); or "point zero zero two", "point oh oh two", "nought point zero zero two", etc.

3.1416 is "three point one four one six"

99.3 is "ninety-nine and three tenths" (mainly U.S.); or "ninety-nine point three".

In English the decimal point was originally printed in the center of the line (0·002), but with the advent of the typewriter it was placed at the bottom of the line, so that a single key could be used as a full stop/period and as a decimal point. In many non-English languages a full-stop/period at the bottom of the line is used as a thousands separator with a comma being used as the decimal point.

Fractions together with an integer are read as follows:

1 1/2 is "one and a half"

6 1/4 is "six and a quarter"

7 5/8 is "seven and five eighths"

A space is required between the whole number and the fraction; however, if a special fraction character is used like "½", then the space can be done without, e.g.

9 1/2

9½

Whether to use digits or words

With few exceptions, most grammatical texts rule that the numbers zero to nine inclusive should be "written out" – instead of "1" and "2", one would write "one" and "two".

Example: "I have two apples." (Preferred) Example: "I have 2 apples."

After "nine", one can head straight back into the 10, 11, 12, etc., although some write out the numbers until "twelve".

Example: "I have 28 grapes." (Preferred) Example: "I have twenty-eight grapes."

Another common usage is to write out any number that can be expressed as one or two words, and use figures otherwise.

Examples:

Numbers at the beginning of a sentence should also be written out, or the sentence rephrased.

The above rules are not always followed. In literature, larger numbers might be spelled out. On the other hand, digits might be more commonly used in technical or financial articles, where many figures are discussed. In particular, the two different forms should not be used for figures that serve the same purpose; for example, it is inelegant to write, "Between day twelve and day 15 of the study, the population doubled."

Empty numbers

Colloquial English has a small vocabulary of empty numbers that can be employed when there is uncertainty as to the precise number to use, but it is desirable to define a general range: specifically, the terms "umpteen", "umpty", and "zillion". These are derived etymologically from the range affixes:

"-teen" (designating the range as being between 10 and 20)

"-ty" (designating the range as being in one of the decades between 20 and 100)

"-illion" (designating the range as being above 1,000,000; or, more generally, as being extremely large).

The prefix "ump-" is added to the first two suffixes to produce the empty numbers "umpteen" and "umpty": it is of uncertain origin. There is a noticeable absence of an empty number in the hundreds range.

Usage of empty numbers:

The word "umpteen" may be used as an adjective, as in "I had to go to umpteen stores to find shoes that fit." It can also be used to modify a larger number, usually "million", as in "Umpteen million people watched the show; but they still cancelled it."

"Umpty" is not in common usage. It can appear in the form "umpty-one" (parallelling the usage in such numbers as "twenty-one"), as in "There are umpty-one ways to do it wrong." "Umpty-ump" is also heard, though "ump" is never used by itself.

The word "zillion" may be used as an adjective, modifying a noun. The noun phrase normally contains the indefinite article "a", as in "There must be a zillion pages on the World Wide Web."

The plural "zillions" designates a number indefinitely larger than "millions" or "billions". In this case, the construction is parallel to the one for "millions" or "billions", with the number used as a plural count noun, followed by a prepositional phrase with "of", as in "There are zillions of grains of sand on the beaches of the world."

Empty numbers are sometimes made up, with obvious meaning: "squillions" is obviously an empty, but very large, number; a "squintillionth" would be a very small number.

Some empty numbers may be modified by actual numbers, such as "four zillion", and are used for jest, exaggeration, or to relate abstractly to actual numbers.

Empty numbers are colloquial, and primarily used in oral speech or informal contexts. They are inappropriate in formal or scholarly usage.

See also Placeholder name.