numbers and fractions

numbers and fractions
This entry deals with:
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numbers, such as 4, 108, and 1,001
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Roman numerals, such as IV, XII, and XXXII
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ordinal numbers, such as `seventh', `twenty-first', and `63rd'
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fractions, decimals, and percentages, such as *41/2, 3.142, and 21%
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• ways of indicating approximate numbers
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The following table shows the names of numbers. These numbers are sometimes called cardinal numbers. You can see from the numbers in this table how to form all the other numbers.
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In the past, British speakers used `billion' to mean a million million. However, nowadays they usually use it to mean a thousand million, like American speakers.
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When you use `hundred', `thousand', `million', or `billion', they remain singular even when the number in front of them is greater than one.

...six hundred miles.

...a thousand billion pounds.

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You do not use `of' after these words when referring to an exact number. For example, you do not say `five hundred of people'; you say `five hundred people'.
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For information on using these words to refer to less exact numbers, see the section on approximate numbers later in this entry.
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`Dozen' is used in a similar way to these words. It is used to refer to twelve things. See entry at ↑ dozen.
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expressing numbers
Numbers over 100 are generally written in figures. However, if you want to say them aloud, or want to write them in words rather than figures, you put `and' in front of the number expressed by the last two figures. For example, 203 is said or written as `two hundred and three' and 2840 is said or written as `two thousand, eight hundred and forty'.

Four hundred and eighteen men were killed and a hundred and seventeen wounded.

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`And' is usually omitted in American English.

...one hundred fifty dollars.

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If you want to say or write in words a number between 1000 and 1,000,000, there are various ways of doing it. For example, the number 1872 is usually said or written in words as `one thousand, eight hundred and seventy-two' when it is being used to refer to a quantity of things. Four-figure numbers ending in 00 can also be said or written as a number of hundreds. For example, 1800 can be said or written as `eighteen hundred'.
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If the number 1872 is being used to identify something, it is said as `one eight seven two'. You always say each figure separately like this with telephone numbers. If a telephone number contains a double number, you use the word `double'. For example, 1882 is said as `one double eight two'.
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If you are mentioning the year 1872, you usually say `eighteen seventy-two'. See entry at ↑ Days and dates.
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When numbers over 9999 are written in figures, a comma is usually put after the fourth figure from the end, the seventh figure from the end, and so on, dividing the figures into groups of three, for example 15,000 or 1,982,000. With numbers between 1000 and 9999, a comma is sometimes put after the first figure, for example 1,526.
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When you use a determiner and a number in front of a noun, you put the determiner in front of the number.

...the three young men.

...my two daughters.

All three candidates are coming to Blackpool later this week.

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When you put a number and an adjective in front of a noun, you usually put the number in front of the adjective.

...two small children.

...fifteen hundred local residents.

...three beautiful young girls.

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However, you can put a few adjectives such as `following' and `only' after numbers. See the section on specifying adjectives in the entry at ↑ Adjectives.
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When you use any number except `one' in front of a noun, you use a plural noun and a plural verb.

...a hundred years.

Seven guerrillas were wounded.

There were ten people there, all men.

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However, when you are talking about an amount of money, a period of time, or a distance, speed, or weight, you usually use a singular verb.

Three hundred pounds is a lot of money.

Ten years is a long time.

90 miles an hour is much too fast.

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numbers as pronouns
When it is clear what sort of thing you are referring to, you can use a number without a noun following it. Numbers can be used on their own or with a determiner.

They bought eight companies and sold off five.

These two are quite different.

The best thirty have the potential to be successful journalists.

The two in front stared glumly ahead.

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You use `of' to indicate the group that a number of people or things belong to.

I saw four of these programmes.

All four of us wanted to get away from the Earl's Court area.

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numbers in compound adjectives
Numbers can be used as part of compound adjectives. These adjectives are usually hyphenated.

He took out a five-dollar bill.

I wrote a five-page summary.

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Note that the noun remains singular even when the number is two or more and that compound adjectives formed like this cannot be used as complements. For example, you cannot say `My essay is five-hundred-word'. Instead you would probably say `My essay is five hundred words long'.
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'one'
`One' is used as a number in front of a noun to emphasize that there is only one thing or to show that you are being precise. It is also used when you are talking about a particular member of a group. `One' is followed by a singular noun and is used with a singular verb.

There was only one gate into the palace.

This treaty was signed one year after the Suez Crisis.

One member declared that he would never vote for such a proposal.

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When no emphasis or precision is wanted, you use `a' instead.

A car came slowly up the road.

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'zero'
The number 0 is not used in ordinary English to indicate that the number of things you are talking about is zero. Instead the determiner `no' or the pronoun `none' is used, or `any' is used with a negative.

She had no children.

Sixteen people were injured but luckily none were killed.

There weren't any seats.

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See entries at ↑ no and ↑ none.
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There are several ways of expressing the number 0:
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• as `zero', when expressing some numerical values, for example temperatures, taxes, and interest rates

It was fourteen below zero when they woke up.

...zero tax liability.

...lending capital to their customers at low or zero rates of interest.

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• as `nought', when expressing some numerical values. For example, 0.89 is said as `nought point eight nine'.

x equals nought.

...linguistic development between the ages of nought and one, one and two etc.

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• as `nothing', when talking informally about calculations

Subtract nothing from that and you get a line on the graph like that.

`What's the difference between this voltage and that voltage?' —-`Nothing.'

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• like `oh' or the letter O, when reading out numbers figure by figure. For example, the telephone number 021 4620 is said as `oh two one, four six two oh'; and the decimal number .089 is said as `point oh eight nine'.
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• as `nil', in sports scores and informal speech and writing

The England Women's XI beat them by one goal to nil.

It used to be a community of 700 souls. Now the population is precisely nil.

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In a few situations, numbers are expressed in Roman numerals. Roman numerals are in fact letters:
I = 1, V = 5, X = 10, L = 50, C = 100, M = 1000
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These letters are used in combination to express all numbers. A smaller Roman numeral is subtracted from a larger one if put in front of it. It is added to a larger numeral if put after it. For example, IV is 4 and VI is 6.
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Roman numerals are used after the name of a king or queen when other kings or queens have had the same name.

...Queen Elizabeth II.

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This would be said as `Queen Elizabeth the Second'.
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Roman numerals are often used to number chapters and sections of books, plays, or other pieces of writing.

Chapter IV: Summary and Conclusion.

...stalking upstage as the curtain fell on Act I.

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Roman numerals are also sometimes used to express dates formally, for example at the end of films and television programmes. For example, `1992' can be written as `MCMXCII'.
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ordinal numbers
If you want to identify or describe something by indicating where it comes in a series or sequence, you use an ordinal number.

Quietly they took their seats in the first three rows.

Flora's flat is on the fourth floor of this five-storey block.

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The following table shows the ordinal numbers.
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written forms
As shown in the table, ordinals can be written in abbreviated form, especially in dates.

He lost his job on January 7th.

...the 1st Division of the Sovereign's Escort.

Our address is: 5th Floor Waterloo House, Waterloo Street, Leeds.

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ordinals as modifiers
Ordinals are used in front of nouns, preceded by a determiner. They are not usually used as complements after link verbs like `be'.

He took the lift to the sixteenth floor.

...on her twenty-first birthday.

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They are used after `come' or `finish' when giving the results of a race or competition.

An Italian came second.

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Ordinals are included in the small group of adjectives that are put in front of cardinal numbers, not after them.

The first two years have been very successful.

Your second three minutes are up, caller.

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ordinals as pronouns
When it is clear what sort of thing you are referring to, you can use an ordinal number without a noun following it. Note that you must use a determiner.

A second pheasant flew up. Then a third and a fourth.

There are two questions to be answered. The first is `Who should do what?' The second is `To whom should he be accountable?'

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You use `of' to indicate the group that the person or thing belongs to.

This is the third of a series of programmes from the University of Sussex.

Tony was the second of four sons.

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When you want to indicate how large a part of something is compared to the whole of it, you use a fraction, such as `a third' or `two fifths', followed by `of' and a noun group referring to the whole thing. Most fractions are based on ordinal numbers. The exceptions are the words `half' (one of two equal parts) and `quarter' (one of four equal parts).
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You can write a fraction in figures. For example, `a half' can be written as *41/2, `a quarter' as *41/4, `three-quarters' as *43/4, and `two thirds' as *42/3.
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When referring to one part of something, you usually use `a'. You only use `one' in formal speech and writing or when you want to emphasize the amount.

This state produces a third of the nation's oil.

You can take out a fifth of your money on demand.

...one quarter of the total population.

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You do not usually use `a' with `half', except when using it in combination with a whole number. Also, `half' can be used in front of a noun group without `of' after it. See entry at ↑ half - half of.
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Plural fractions are often written with a hyphen.

More than two-thirds of the globe's surface is water.

He was not due at the office for another three-quarters of an hour.

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You can put an adjective in front of a fraction, after `the'.

...the southern half of England.

...in the last quarter of 1980.

...the first two-thirds of this century.

...the remaining three-quarters of the population.

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When you use `a half' and `a quarter' in combination with whole numbers, they come in front of the plural noun you are using.

...one and a half acres of land.

...four and a half centuries.

...five and a quarter days.

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However, if you are using `a' instead of the number `one', the noun is singular and comes in front of the fraction.

...a mile and a half below the surface.

...a mile and a quarter of motorway.

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When you talk about part of a single thing, you use a singular form of a verb.

Half of our work is to design programmes.

Two fifths of the forest was removed.

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However, when you talk about part of a group of things, you use a plural form of the verb.

Two fifths of the dwellings have more than six people per room.

A quarter of the students were seen individually.

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fractions as pronouns
When it is clear who or what you are referring to, you can use fractions without `of' and a noun group.

Most were women and about half were young with small children.

One fifth are appointed by the Regional Health Authority.

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Decimals are a way of expressing fractions. For example, 0.5 is the same as *41/2 and 1.4 is the same as 1*42/5.

...an increase of 16.4 per cent.

The library contains over 1.3 million books.

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You say the dot as `point'. For example, 1.4 is said as `one point four'.
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You do not use a comma in decimal numbers in English.
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Numbers which look like decimal numbers are used when referring to one of a number of sections, tables, or illustrations that are closely connected.

Domestic refuse, for example, can be dried and burnt to provide heat (see section 3.3).

The normal engineering drawing is quite unsuitable (figure 3.4).

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percentages
Fractions are often given a special form as a number of hundredths. This type of fraction is called a percentage. For example, `three hundredths', expressed as a percentage, is `three per cent'. This is often written as 3%.

About 20 per cent of student accountants are women.

...interest at 10% per annum.

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approximate numbers
You can refer to a large number imprecisely by using `several', `a few', or `a couple of' in front of `dozen', `hundred', `thousand', `million', or `billion'.

...several hundred people.

A few thousand cars have gone.

...life a couple of hundred years ago.

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You can be even more imprecise, and emphasize how large the number is, by using `dozens', `hundreds', `thousands', `millions', or `billions', followed by `of'.

That's going to take hundreds of years.

We travelled thousands of miles across Europe.

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People often use plural forms when they are exaggerating.

I was meeting thousands of people.

Do you have to fill in hundreds of forms before you go?

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The following expressions are used to indicate that a number is approximate and that the actual figure could be larger or smaller:
about, approximately, around, odd, or so, or thereabouts, roughly, some, something like
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You put `about', `approximately', `around', `roughly', `some', and `something like' in front of a number.

About 85 students were there.

It costs roughly £55 a year to keep a cat in food.

Harrington has cheated us out of something like thirty thousand quid over the past two years.

I found out where this man lived, and drove some four miles inland to see him.

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Note that this use of `some' is quite formal.
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You put `odd', `or so', and `or thereabouts' after a number or the noun that follows a number.

...a hundred odd acres.

The car should be here in ten minutes or so.

Get the temperature to 30°C or thereabouts.

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minimum numbers
The following expressions indicate that a number is a minimum figure and that the actual figure may be larger:
a minimum of, at least, from, minimum, more than, or more, over, plus
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You put `a minimum of', `from', `more than', and `over' in front of a number.

He needed a minimum of 26 Democratic votes.

...3 course dinner from £15.

...a school with more than 1300 pupils.

The British have been on the island for over a thousand years.

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You put `or more', `plus', and `minimum' after a number or after the noun that follows a number.

...a choice of three or more possibilities.

This is the worst disaster I can remember in my 25 years plus as a police officer.

They should be getting £38 a week minimum.

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`Plus' is sometimes written as the symbol `+', for example in job advertisements.

2+ years' experience of market research required.

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You usually put `at least' in front of a number.

She had at least a dozen brandies.

It was a drop of at least two hundred feet.

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However, this expression is sometimes put after a number or noun. This position is more emphatic.

I must have slept twelve hours at least.

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maximum numbers
The following expressions indicate that a number is a maximum figure and that the actual figure is or may be smaller:
almost, a maximum of, at most, at the maximum, at the most, fewer than, less than, maximum, nearly, no more than, or less, or under, under, up to
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You put `almost', `a maximum of', `fewer than', `less than', `nearly', `no more than', `under', and `up to' in front of a number.

The company now supplies almost 100 of Paris's restaurants.

...a puppy less than seven weeks old.

We managed to finish the entire job in under three months.

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You put `at the maximum', `at most', `at the most', `maximum', `or less', and `or under' after a number or the noun that follows a number.

They might have IQs of 10, or 50 at the maximum.

The area would yield only 200 pounds of rice or less.

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indicating a range of numbers
You can indicate a range of numbers using `between' and `and', or `from' and `to', or just `to'.

Most of the farms are between four and five hundred years old.

My hospital groups contain from ten to twenty patients.

...peasants owning two to five acres of land.

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`Anything' is used in front of `between' and `from' to emphasize how great a range is.

An average rate of anything between 25 and 60 per cent is usual.

It is a job that takes anything from two to five weeks.

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A hyphen is used between two figures to indicate a range. It is said as `to'.

Allow to cool for 10-15 minutes.

In 1965-9, people drank a little more, namely 6.0 litres of alcohol.

...the Tate Gallery (open 10 a.m.-6 p.m., Sundays, 2-6).

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When mentioning two numbers that follow each other in a range or sequence, you can use the symbol ` / ' (said aloud as `stroke', `slash', or `to').

The top ten per cent of income earners gained 25.8 per cent of all earned income in 1975/6.

Write for details to 41/42 Berners Street, London.

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Useful english dictionary. 2012.

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