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First of all, I would like to express my sincere and special gratitude to Mrs

Nguyen Thi Hoa, the supervisor, who have generously given us invaluable

assistance and guidance during the preparing for this research paper.

I also offer my sincere thanks to Ms. Tran Thi Ngoc Lien, the Dean of Foreign

Language Faculty at Haiphong Private University for her previous supportive

lectures that helped me in preparing my graduation paper

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ACKNOWLEDGEMENT

First of all, I would like to express my sincere and special gratitude to Mrs

Nguyen Thi Hoa, the supervisor, who have generously given us invaluable

assistance and guidance during the preparing for this research paper.

I also offer my sincere thanks to Ms. Tran Thi Ngoc Lien, the Dean of Foreign

Language Faculty at Haiphong Private University for her previous supportive

lectures that helped me in preparing my graduation paper.

Last but no least , my wholehearted thanks are presented to my family members

and all my friends for their constant support and encouragement in the process

of doing this research paper .My success in studying is contributed much by all

you .

Haiphong –June, 2009

Nguyen Thi Thu Trang

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TABLE OF CONTENT

I. PART A: INTRODUCTION

1. Rationale ……………………………………………………………………………….. 4

2. Aims of the study …………………………………………………………………… 4

3. Scope of the study ………………………………………………………………….. 4

4. Methods of study ……………………………………………………………………. 5

5. Design of study………………………………………………………………………. 5

II. PART B: DEVELOPMENT

Chapter 1: DEFINITION OF NUMERAL ………………………………………… 6

1.1. History of numeral ………………………………………………………………. 6

Definition ……………………………………………………………………………… 10

Chapter 2: CLASSIFICATION OF NUMERAL

2.1. Classification of numeral ……………………………………………………… 14

2.1.1. Cardinal numbers ………………………………………….. 14

2.1.2. Ordinal numbers ……………………………………………. 22

2.1.3. Dates ……………………………………………………………. 25

2.1.4. Fractions and decimals …………………………………… 30

2.1.5. Roman number ……………………………………………… 33

2.1.6. Specialised numbers ………………………………………. 35

2.1.7. Empty numbers …………………………………………….. 38

2.2. The major differences between numeral in English and Vietnamese .. 40

2.2.1. Dates ……………………………………………………………. 40

2.2.2. Phone numer ………………………………………………… 41

2.2.3. Zero number …………………………………………………. 42

2.2.4.Fraction ………………………………………………………… 43

Chapter 3: EXERCISE IN APPLICATION ……………………………………… 44

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III. PART C: CONCLUSION

1. Summary of study …………………………………………………………… 48

2. Suggestion for further study …………………………………………….. 49

REFERENCES ……………………………………………………………………… 50

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I. PART A: INTRODUCTION

1. Rationale:

English is one of the most widely used languages worldwide when being

used by over 60% the world population. It‘s used internationally in business,

political, cultural relation and education as well. Thanks to the widespread use

of English, different countries come close to each other to work out the

problems and strive for prosperous community.

Realizing the significance of English, almost all Vietnamese learners have

been trying to be good at English, Mastering English is the aim of every

learners.

However, there still remain difficulties faced by Vietnamese learner of

English due to both objective and subjective factors, especially in writing and

reading numeral because learners sometimes skip when they think that it is an

unimportant part.

Therefore, it is necessary to collect ground rule of reading and writing

English numeral. This will help learner avoid confusedness of English numeral.

2. Aims of the study:

As we know, English numbers often appear in document, even daily

communication. The leaner of English sometimes don‘t know how to read or

write them exactly. Therefore, this research is aimed at:

Collecting type of popular numeral in English document and daily

communication.

Instructing writing and reading numeral exactly.

3. Scope of the study

Numeral in English is a wide category including: mathematic, technology,

business.therefore I only collect numbers used in daily speaking cultures in

this research paper.

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4. Methods of the study

Being a student of Foreign Language Faculty with four years study at the

university , I have a chance to equip myself with the knowledge of many fields

in society such as :sociology , economy , finance, culture ,etcWith the

knowledge gained from professional teachers, specialized books, references and

with the help of my friends the experience gained at the training time , I have

put my mind on theme : ―writing and reading numeral in English‖ for my

graduation paper .

Documents for research are selected from reliable sources, for example

―books published by oxford, website Furthermore, I illustrate with examples

quoted from books, internet, etc

5. Design of the study

The study is divided into three main parts of which the second one is the

most important part.

Part one is introduction that gives out the rationale for choosing the topic

of this study , pointing out the aim ,scope as well as methods of the study

Part two is development that consists of.chapter

Part three is the conclusion of the study, in which all the issues mentioned

in previous part of the study are summarized.

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PART B: DEVELOPMENT

Chapter 1: DEFINITION OF NUMERAL

1.1. History of counting systems and numeral

Nature’s abacus

Soon after language develops, it is safe to assume that humans begin

counting – and that fingers and thumbs provide nature’s abacus. The decimal

system is no accident. Ten has been the basis of most counting systems in history.

When any sort of record is needed, notches in a stick or a stone are the

natural solution. In the earliest surviving traces of a counting system, numbers are

built up with a repeated sign for each group of 10 followed by another repeated

sign for 1.

Egyptian numbers: 3000-1600 BC

In Egypt, from about 3000 BC, records survive in which 1 is represented

by a vertical line and 10 is shown as ^. The Egyptians write from right to left, so

the number 23 becomes lll^^

If that looks hard to read as 23, glance for comparison at the name of a

famous figure of our own century – Pope John XXIII. This is essentially the

Egyptian system, adapted by Rome and still in occasional use more than 5000

years after its first appearance in human records. The scribes of the Egyptian

pharaohs (whose possessions are not easily counted) use the system for some

very large numbers – unwieldy though they undoubtedly are.

From about 1600 BC Egyptian priests find a useful method of shortening the

written version of numbers. It involves giving a name and a symbol to every

multiple of 10, 100, 1000 and so on.

So 80, instead of being to be drawn, becomes; and 8000 is not but . The

saving in space and time in writing the number is self-evident. The disadvantage

is the range of symbols required to record a very large number – a range

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impractical to memorize, even perhaps with the customary leisure of temple

priests. But for everyday use this system offers a real advance, and it is later

adopted in several other writing systems – including Greek, Hebrew and early

Arabic

Babylonian numbers: 1750 BC

The Babylonians use a numerical system with 60 as its base. This is

extremely unwieldy, since it should logically require a different sign for every

number up to 59 (just as the decimal system does for every number up to 9).

Instead, numbers below 60 are expressed in clusters of ten – making the written

figures awkward for any arithmetical computation.

Through the Babylonian pre-eminence in astronomy, their base of 60 survives

even today in the 60 seconds and minutes of angular measurement, in the 180

degrees of a triangle in the 360 degrees of a circle. Much later, when time can be

accurately measured, the same system is adopted for the subdivisions of an hour

The Babylonians take one crucial step towards a more effective numerical

system. They introduce the place-value concept, by which the same digit has a

different value according to its place in the sequence. We now take for granted

the strange fact that in the number 222 the digit ‘2’ means three quite different

things – 200, 20 and 2 – but this idea is new and bold in Babylon.

For the Babylonians, with their base of 60, the system is harder to use. For a

number as simple as 222 is the equivalent of 7322 in our system (2 x 60 squared

+ 2 x 60 + 2).

The place-value system necessarily involves a sign meaning ’empty’, for

those occasions where the total in a column amounts to an exact multiple of 60.

If this gap is not kept, all the digits before it will appear to be in the wrong

column and will be reduced in value by a factor of 60.

Another civilization, that of the Maya, independently arrives at a place-value

system – in their case with a base of 20 – so they too have a symbol for zero.

Like the Babylonians, they do not have separate digits up to their base figure.

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They merely use a dot for 1 and a line for 5 (writing 14, for example, as 4 dots

with two lines below them).

Zero, decimal system, Arabic numerals: from 300 BC

In the Babylonian and Mayan systems the written number is still too

unwieldy for efficient arithmetical calculation, and the zero symbol is only

partly effective.

For zero to fulfil its potential in mathematics, it is necessary for each

number up to the base figure to have its own symbol. This seems to have been

achieved first in India. The digits now used internationally make their

appearance gradually from about the 3rd century BC, when some of them

feature in the inscriptions of Asoka.

The Indians use a dot or small circle when the place in a number has no

value, and they give this dot a Sanskrit name – sunya, meaning ’empty’. The

system has fully evolved by about AD 800, when it is adopted also in Baghdad.

The Arabs use the same ’empty’ symbol of dot or circle, and they give it the

equivalent Arabic name, sifr.

About two centuries later the Indian digits reach Europe in Arabic

manuscripts, becoming known as Arabic numerals. And the Arabic sifr is

transformed into the ‘zero’ of modern European languages. But several more

centuries must pass before the ten Arabic numerals gradually replace the system

inherited in Europe from the Roman Empire.

The abacus: 1st millennium BC

In practical arithmetic the merchants have been far ahead of the scribes,

for the idea of zero is in use in the market place long before its adoption in

written systems. It is an essential element in humanity’s most basic counting

machine, the abacus. This method of calculation – originally simple furrows

drawn on the ground, in which pebbles can be placed – is believed to have been

used by Babylonians and Phoenicians from perhaps as early as 1000 BC.

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In a later and more convenient form, still seen in many parts of the world

today, the abacus consists of a frame in which the pebbles are kept in clear rows

by being threaded on rods. Zero is represented by any row with no pebble at the

active end of the rod.

Roman numerals: from the 3rd century BC

The completed decimal system is so effective that it becomes, eventually,

the first example of a fully international method of communication.

But its progress towards this dominance is slow. For more than a

millennium the numerals most commonly used in Europe are those evolved in

Rome from about the 3rd century BC. They remain the standard system

throughout the Middle Ages, reinforced by Rome’s continuing position at the

centre of western civilization and by the use of Latin as the scholarly and legal

language.

Binary numbers: 20th century AD

Our own century has introduced another international language, which

most of us use but few are aware of. This is the binary language of computers.

When interpreting coded material by means of electricity, speed in tackling a

simple task is easy to achieve and complexity merely complicates. So the

simplest possible counting system is best, and this means one with the lowest

possible base – 2 rather than 10.

Instead of zero and 9 digits in the decimal system, the binary system only

has zero and 1. So the binary equivalent of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 1, 10, 11,

100, 101, 111, 1000, 1001, 1010, 1011 and so ad infinitum

(Resource: “History of COUNTING SYSTEMS AND NUMERALS”)

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1.2. What is definition of number?

The question is a challenging one because defining the abstract idea of

number is extremely difficult. More than 2,500 years ago, the great number

enthusiast Pythagoras described number as “the first principle, a thing which is

undefined, incomprehensible, and having in itself all numbers.” Even today, we

still struggle with the notion of what numbers mean.

Numbers neither came to us fully formed in nature nor did they spring fully

formed from the human mind. Like other ideas, they have evolved slowly

throughout human history. Both practical and abstract, they are important in our

everyday world but remain mysterious in our imaginations.

Numbers in Life, Life in Numbers.

The Numbers within Our Lives: Early conceptual underpinnings of

numbers were used to express different ideas throughout different

cultures, all of which led to our current common notion of number.

The Lives within Our Numbers: Born from our imagination, numbers

eventually took on a life of their own within the larger structure of

mathematics. This area of study is known as number theory, and the more

it is explored, the more insight we gain into the nature of numbers.

Transcendental Meditation—The pi and e Stories: Perhaps the two most

important numbers in our universe, pi and e help us better understand

nature and our universe. They are also the gateway into an exploration of

transcendental numbers.

Algebraic and Analytic Evolutions of Number: Two mathematical

perspectives on how to create numbers, the algebraic view leads us to

imaginary numbers, while the analytical view challenges our intuitive

sense of what number should mean.

Infinity—”Numbers” Beyond Numbers: The idea of infinity, just like the

idea of numbers, can be understood and holds many fascinating features.

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Some of these features, paradoxically, require us to return to the earliest

notions of number.

There are many different types of numbers, each of which plays an

important role within both mathematics and the larger world.

real numbers: numbers that can be given by an infinite decimal

representation (e.g., 34.5837 … )

natural numbers: also known as counting numbers, these are numbers

used primarily for counting and ordering (e.g., 3)

prime numbers: natural numbers greater than 1 that can be divided by

only 1 and itself (e.g., 43)

rational numbers: numbers that can be expressed as the ratio of two

integers (e.g., ½)

irrational numbers: numbers that cannot be expressed as simple fractions

(e.g., v2)

transcendental numbers: irrational numbers that are not algebraic (e.g., pi)

(Taught by Edward B. Burger Williams College Ph.D., The University of

Texas at Austin)

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The following is some other definitions of numeral:

That which admits of being counted or reckoned; a unit, or an aggregate of

units; a numerable aggregate or collection of individuals; an assemblage made

up of distinct things expressible by figures.

A collection of many individuals; a numerous assemblage; a multitude; many.

A numeral; a word or character denoting a number; as, to put a number on a

door.

Numerousness; multitude.

The state or quality of being numerable or countable.

Quantity, regarded as made up of an aggregate of separate things.

That which is regulated by count; poetic measure, as divisions of time or number

of syllables; hence, poetry, verse; — chiefly used in the plural.

The distinction of objects, as one, or more than one (in some languages, as one,

or two, or more than two), expressed (usually) by a difference in the form of a

word; thus, the singular number and the plural number are the names of the

forms of a word indicating the objects denoted or referred to by the word as one,

or as more than one.

The measure of the relation between quantities or things of the same kind; that

abstract species of quantity which is capable of being expressed by figures;

numerical value.

To count; to reckon; to ascertain the units of; to enumerate.

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To reckon as one of a collection or multitude.

To give or apply a number or numbers to; to assign the place of in a series by

order of number; to designate the place of by a number or numeral; as, to

number the houses in a street, or the apartments in a building.

To amount; to equal in number; to contain; to consist of; as, the army numbers

fifty thousand.

( Webster’s Revised Unabridged Dictionary (1913))

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Chapter 2: CLASSIFICATION OF NUMERAL

2.1. Classification of numeral

2.1.1. Cardinal numbers

0 zero (nought)

/’ziərou/

1 one /wʌ n/ 11

eleven /i’levn/

10 ten /ten/

2 two /tu:/ 12

twelve /twelv/

20

twenty /’twenti/

3

three /θri:/

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thirteen /θə:’ti:n/

30

thirty /θə:ti/

4

four /fɔ :/

14

fourteen /fɔ :’ti:n/

40

forty /’fɔ :ti/

(no “u”)

5

five /faiv/

15

fifteen /fif’ti:n/

(note “f”, not”v”) 50

fifty /’fifti/

(note “f”, not “v”)

6

six /siks/

16

sixteen/’siks’ti:n/

60

sixty/’siksti/

7

seven /’sevn/

17

seventeen//sevn’ti:n/

70

seventy /’sevnti/

8

eight/ eit/

18

eighteen /ei’ti:n/

(only one “t”) 80

eighty /’eiti/

(only one “t”)

9

nine /nain/

19

nineteen /nain’ti:n/

90

ninety /’nainti/

(note the “e”)

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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 /’twenti’wʌ n/

25

twenty-five /’twenti’faiv/

32

thirty-two /’θə:ti’tu/

58

fifty-eight /’fifti’eit/

64

sixty-four /’siksti fɔ :/

79

seventy-nine /’sevnti ‘nain/

83

eighty-three /’eiti’θri:/

99

ninety-nine /’nainti’nain/

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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 /’wʌ n’hʌ ndrəd/

200 two hundred /’tu’hʌ ndrəd/

900 nine hundred /’nain’hʌ ndrəd/

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

“thousand”

1,000 one thousand /’wʌ n’θauz(ə)nd/

2,000 two thousand /’tu’θauz(ə)nd/

10,000 ten thousand /’ten’θauz(ə)nd/

11,000

eleven thousand / i’levn’θauz(ə)nd/

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20,000 twenty thousand /’twenti’θauz(ə)nd/

21,000 twenty-one thousand /’twenti’wʌ n’θauz(ə)nd/

30,000 thirty thousand /’θə:ti ‘θauz(ə)nd/

85,000

eighty-five thousand /’eiti faiv’θauz(ə)nd/

100,000 one hundred thousand /’wʌ n’hʌ ndrəd’θauz(ə)nd/

999,000

nine hundred and ninety-nine thousand (British English)

/’nain’hʌ ndrəd ænd nainti-nain ‘θauz(ə)nd/

nine hundred ninety-nine thousand (American English)

/’nai

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Từ khóa: Acknowledgement