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| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic Eastern Arabic Khmer |
Indian family Brahmi Thai |
| East Asian numerals | |
| Chinese Suzhou Counting rods |
Japanese Korean |
| Alphabetic numerals | |
| Abjad Armenian Cyrillic Ge'ez |
Hebrew Greek (Ionian) Āryabhaṭa |
| Other systems | |
| Attic Babylonian Egyptian English |
Etruscan Mayan Roman Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 1, 3, 9, 12, 20, 24, 30, 36, 60, more… | |
English numerals is a system of saying numbers that is used in English-speaking cultures.
Contents |
Cardinal numbers refer to the size of a group.
| 0 | zero (nought) | ||||
| 1 | one | 11 | eleven | 10 | ten |
| 2 | two | 12 | twelve | 20 | twenty |
| 3 | three | 13 | thirteen | 30 | thirty |
| 4 | four | 14 | fourteen | 40 | forty (no "u") |
| 5 | five | 15 | fifteen (note "f", not "v") | 50 | fifty (note "f", not "v") |
| 6 | six | 16 | sixteen | 60 | sixty |
| 7 | seven | 17 | seventeen | 70 | seventy |
| 8 | eight | 18 | eighteen (only one "t") | 80 | eighty (only one "t") |
| 9 | nine | 19 | nineteen | 90 | ninety (note the "e") |
If a number is in the range 21 to 99, and the second digit is not zero, one should write the number as two words separated by a hyphen.
| 21 | twenty-one |
| 25 | twenty-five |
| 32 | thirty-two |
| 58 | fifty-eight |
| 64 | sixty-four |
| 79 | seventy-nine |
| 83 | eighty-three |
| 99 | ninety-nine |
In English, the hundreds are perfectly regular, except that the word hundred remains in its singular form regardless of the number preceding it (nevertheless, one may on the other hand say "hundreds of people flew in", or the like)
| 100 | one hundred |
| 200 | two hundred |
| … | … |
| 900 | nine hundred |
So too are the thousands, with the number of thousands followed by the word "thousand"
| 1,000 | one thousand |
| 2,000 | two thousand |
| … | … |
| 10,000 | ten thousand |
| 11,000 | eleven thousand |
| … | … |
| 20,000 | twenty thousand |
| 21,000 | twenty-one thousand |
| 30,000 | thirty thousand |
| 85,000 | eighty-five thousand |
| 100,000 | one hundred thousand |
| 999,000 | nine hundred and ninety-nine thousand (British English) nine hundred ninety-nine thousand (American English) |
| 1,000,000 | one million |
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'. 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, the British dialect can seemingly adopt the American way of counting, but it is specific to the situation (in this example, bus numbers).
| Common British vernacular | Common American vernacular | Common British vernacular | |
| "How many marbles do you have?" | "What is your house number?" | "Which bus goes to the high street?" | |
| 101 | "A hundred and one." | "One-oh-one." Here, "oh" is used for the digit zero. |
"One-oh-one." |
| 109 | "A hundred and nine." | "One-oh-nine." | "One-oh-nine." |
| 110 | "A hundred and ten." | "One-ten." | "One-one-oh." |
| 117 | "A hundred and seventeen." | "One-seventeen." | "One-one-seven." |
| 120 | "A hundred and twenty." | "One-twenty." | "One-two-oh", "One-two-zero." |
| 152 | "A hundred and fifty-two." | "One-fifty-two." | "One-five-two." |
| 208 | "Two hundred and eight." | "Two-oh-eight." | "Two-oh-eight." |
| 334 | "Three hundred and thirty-four." | "Three-thirty-four." | "Three-three-four." |
Note: When writing a cheque (or check), the number 100 is always written "one hundred". It is never "a hundred".
Note that 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". For details, see American and British English differences.
For numbers above a million, there are two different systems for naming numbers in English:
| Number notation | Power notation |
Short scale | Long scale |
|---|---|---|---|
| 1,000,000 | 106 | one million | one million |
| 1,000,000,000 | 109 | one billion a thousand million |
one milliard a thousand million |
| 1,000,000,000,000 | 1012 | one trillion a thousand billion |
one billion a million million |
| 1,000,000,000,000,000 | 1015 | one quadrillion a thousand trillion |
one billiard a thousand billion |
| 1,000,000,000,000,000,000 | 1018 | one quintillion a thousand quadrillion |
one trillion a million billion |
Although British English has traditionally followed the long-scale numbering system, the short-scale usage has become increasingly common in recent years. For example, the UK Government and BBC websites use the newer short-scale values exclusively.
Here are some approximate composite large numbers in American English:
| Quantity | Written | Pronounced |
|---|---|---|
| 1,200,000 | 1.2 million | one point two million |
| 3,000,000 | 3 million | three million |
| 250,000,000 | 250 million | two hundred fifty million |
| 6,400,000,000 | 6.4 billion | six point four billion |
| 23,380,000,000 | 23.38 billion | twenty three point three eight billion |
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.
A few numbers have special names (in addition to their regular names):
) is pronounced "aleph-null".
: googolplex (1 followed by a googol of zeros)
: googolplexplex (1 followed by a googolplex of zeros)Combinations of numbers in most sports scores are read as in the following examples:
Naming conventions of Tennis scores (and related sports) work a lot differently to most other sports.
A few numbers have specialised multiplicative numerals expresses how many fold or how many times: once, twice, thrice.[1]
Ordinal numbers refer to a position in a series. Common ordinals include:
| 0th | zeroth or noughth (see below) | 10th | tenth | ||
| 1st | first | 11th | eleventh | ||
| 2nd | second | 12th | twelfth (note "f", not "v") | 20th | twentieth |
| 3rd | third | 13th | thirteenth | 30th | thirtieth |
| 4th | fourth | 14th | fourteenth | 40th | fortieth |
| 5th | fifth | 15th | fifteenth | 50th | fiftieth |
| 6th | sixth | 16th | sixteenth | 60th | sixtieth |
| 7th | seventh | 17th | seventeenth | 70th | seventieth |
| 8th | eighth (only one "t") | 18th | eighteenth | 80th | eightieth |
| 9th | ninth (no "e") | 19th | nineteenth | 90th | ninetieth |
Zeroth only has a meaning when counts start 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.
| 21st | twenty-first |
| 25th | twenty-fifth |
| 32nd | thirty-second |
| 58th | fifty-eighth |
| 64th | sixty-fourth |
| 79th | seventy-ninth |
| 83rd | eighty-third |
| 99th | ninety-ninth |
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.
| If the units digit is: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| write this after the number | th | st | nd | rd | th | th | th | th | th | th |
These ordinal abbreviations are actually hybrid contractions of a numeral and a word. 1st is "1" + "st" from "first". Similarly, we use "nd" 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"
Any ordinal name that doesn't end in "first", "second", or "third", ends in "th".
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. The favorable pronunciation is determined by number of syllables.
| Year | Most common pronunciation method | Alternative methods |
|---|---|---|
| 1 BC | (The year) One BC | 1 Before Christ (BC) 1 before the Common/Christian era (BCE) |
| 1 | (The year) One | Anno Domini (AD) 1 1 of the Common/Christian era (CE) In the year of Our Lord 1 |
| 235 | Two thirty-five | Two-three-five Two hundred (and) thirty-five |
| 911 | Nine eleven | Nine-one-one Nine hundred (and) eleven |
| 999 | Nine ninety-nine | Nine-nine-nine Nine hundred (and) ninety-nine Triple nine |
| 1000 | One thousand | Ten hundred 1K Ten aught Ten oh |
| 1004 | Ten oh-four | One thousand (and) four |
| 1010 | Ten ten | One thousand (and) ten |
| 1050 | Ten fifty | One thousand (and) fifty |
| 1225 | Twelve twenty-five | One-two-two-five One thousand, two hundred (and) twenty-five Twelve-two-five |
| 1900 | Nineteen hundred | One thousand, nine hundred Nineteen aught Nineteen oh |
| 1901 | Nineteen oh-one | Nineteen hundred (and) one One thousand, nine hundred (and) one Nineteen aught one |
| 1919 | Nineteen nineteen | Nineteen hundred (and) nineteen One thousand, nine hundred (and) nineteen |
| 1999 | Nineteen ninety-nine | Nineteen hundred (and) ninety-nine One thousand, nine hundred (and) ninety-nine |
| 2000 | Two thousand | Twenty hundred Two triple-oh 2K Twenty aught Twenty oh |
| 2001 | Two thousand (and) one | Twenty oh-one Twenty hundred (and) one 2K1 |
| 2009 | Two thousand (and) nine | Twenty oh-nine Twenty hundred (and) nine 2K9 |
| 2010 | Twenty-ten | Two thousand (and) ten Twenty hundred (and) ten |
| 2013 | Twenty-thirteen | Two thousand (and) thirteen Twenty hundred (and) thirteen |
| 2020 | Twenty-twenty | Two thousand (and) twenty Twenty hundred (and) twenty |
| 2025 | Twenty twenty-five | Two thousand (and) twenty five Twenty hundred (and) twenty five |
| 2099 | Twenty ninety-nine | Two thousand (and) ninety-nine Twenty hundred (and) ninety-nine |
| 2100 | Twenty-one hundred | Two thousand, one hundred Twenty-one-oh Twenty-one-aught |
| 2101 | Twenty-one-oh-one | Two thousand, one hundred (and) one Twenty one hundred (and) one |
Years are rarely read explicitly as ordinal numbers, as "[...] in the one thousand one hundred and ninety-seventh year of our Lord" (that is, 1197), even though ordinal numbers are implicit in traditional western calendrical systems. Also, years are numbered with cardinal numbers in astronomical usage, and in the Hindu and Mayan calendrical systems (see Year zero). Some Quaker communities refer to days of the week in ordinal fashion; in this usage "First Day" is Sunday, "Second Day" is Monday, etc.
Compare:
The comma before the year is optional. It is usually used in American English (September 4, 2004) but now seldom used in British and International English (4 September 2004). In abbreviations of month names, such as "Aug" for August, the period or full stop is often left out.
For an explanation of British, American and International usage for dates written in numbers, such as 14/03/2004 or 3/14/2004 or 2004-03-14, see calendar date.
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 fractions (partitive numerals[2]):
| 1/16 | one-sixteenth |
| 1/10 or 0.1 | one-tenth |
| 1/8 | one-eighth |
| 2/10 or 0.2 | two-tenths |
| 1/4 | one-quarter or one-fourth |
| 3/10 or 0.3 | three-tenths |
| 1/3 | one-third |
| 3/8 | three-eighths |
| 4/10 or 0.4 | four-tenths |
| 1/2 | one half |
| 6/10 or 0.6 | six-tenths |
| 5/8 | five-eighths |
| 2/3 | two-thirds |
| 7/10 or 0.7 | seven-tenths |
| 3/4 | three-quarters or three-fourths |
| 8/10 or 0.8 | eight-tenths |
| 7/8 | seven-eighths |
| 9/10 or 0.9 | nine-tenths |
| 15/16 | fifteen-sixteenths |
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. (This form is not common in British English.)
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 (not common in British English); 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.
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.
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.
According to most copy editors and English teachers, the numbers zero through nine inclusive should be "written out" – meaning instead of "1" and "2", one would write "one" and "two".
After "nine", one can head straight back into the 10, 11, 12, etc., although some write out the numbers until "twelve".
Another common usage is to write out any number that can be expressed as one or two words, and use figures otherwise.
Numbers at the beginning of a sentence should also be written out.
The above rules are not always used. 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."
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:
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:
See also Placeholder name.
While there are a number of "rules" about ways of expressing numbers, the essential requirement must always be to avoid ambiguity. Different authorities do not always agree; for example the following sentence was found in a perfectly respectable document. "It has sold 10,000,000 copies. It was number 21 on a recent list of the 100 most important non-fiction books of the 20th century." This sentence is perfectly clear, and it is unlikely that any reader would change his attitude toward the author because of these "errors".
The usage of either a comma or a point in a number provides a degree of ambiguity too. The number 1,000 would be read as being one thousand in the US and the UK, and as Exactly One in most of Europe and elsewhere. Modern usage in ISO 31-0 shows either the point or the dot to be used for the "Exactly One" form, and for spaces to be used in very large or very small numbers, like in 1 000 000 or in 0.000 000 005 and so on.
With the rise of computers, use of the name of the letter "O" to signify both the letter "O" and numeric zero has become ambiguous. If numbers are typed into the computer as spoken, problems may arise if the numbers are used for anything other than simple display. If a house number is shown on screen as "12O" instead of "120", no harm is done. But if this error is made in a telephone number to be dialed, or in calculations, problems will arise. The simplest solution is always to say "zero" or "nought".
Numeric dates, as normally abbreviated, are ambiguous: the forms "mm/dd/yy", "dd/mm/yy" (where "yy" may be a 2-digit or 4-digit year), are used in different places; in the US, the former is used, and is reflected in the spoken convention for dates there, for example 10/04/05 would be read "October Fourth, Two Thousand Five", whereas in Britain, the latter naming convention is used, and would be spoken as "(The) Tenth of April, Two Thousand and Five". The international standard, with the form YYYY-MM-DD avoids ambiguity and 2005-07-09 always means 2005 July the 9th. This date is sometimes written without spaces or hyphens, 20050709.
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