8. Decide whether the statements below are true or false:

1. The origins of the real number system can be traced to ancient Egyptian, Babylonian (Sumerian), and Chinese roots.

2. The natural numbers are also called the whole numbers, or positive irrational integers.

3. The natural number n is identified with the positive fraction n/1.

4. The totality of the rational and irrational numbers puts together the real number system.

5. Number is a letter or symbol used to designate quantities.

6. Similarly, the ratio of the circumference to the radius of a circle is not a rational number.

7. The positive and negative integers and fractions, and the number 0, form the rational number system.

1	2	3	4	5	6	7
T	T	T	T	T	T	T
F	F	F	F	F	F	F

LISTENING

9. Listen and practise.

Money

£ 400 50 p € 9.40 € 47.99 ¥ 5,000 $ 100

Fractions

1/4 3/4 2/3 7/8 12 ½

Decimal and percentage

6.2 17.25 50% 75.7% 100%

Dates

1995 2020 1789 15/7/94 30/10/02

Phone numbers

01865-556890 800 451-7545 919 677-1303

10. Listen to the conversations. Write the numbers.

Conversattion 1:

“When you are going away on holiday?”

“On the ________.”

“And when do you get back?”

“On the __________ I’ll give you a ring when we get home.”

Conversation 2:

And now the business news. The unemployment rate has risen slightly this month. The national unemployment rate is now __________ and in our area, an estimated __________ people are out of work.”

Conversation 3:

“Can I pay by visa?

“Yes, that’s fine. Erm – what’s your card number, please?”

“It’s __________”

“Let me read that back. _____ … _____ … _____ … _____.”

“That’s right.”

SPEAKING

11. Work in pairs. What numbers do people usually consider lucky and unlucky and why?

12. Find out the answers to these questions and discuss them with your partner:

-Who introduced Arabic numbers to European maths?

-Who developed the idea of ‘zero’?

WRITING

13. Think of a number you like (your fortunate number), or not like (your unfortunate number). Write a short paragraph (60 - 80 words) to explain your choice. You may use the following opening phrases to express your opinion:

- I think that …

- From my point of view …

- In my opinion …

- To my mind …

- It seems to me …

GRAMMAR IN USE

These tasks can help you to practise the Future Simple Passive (See Appendix 1 p. 228 – 230) and do the following exercises.

14. Complete the sentences with the future passive form of the verbs in brackets, as in the example.

e.g. 0. This model will be produced in the new factory in Poland.

1. German cars ….. (to sell) all over the world in future.

2. The orders ….. (to place) by fax or online.

3. The cars ….. (to assemble) by robots.

4. Spare parts ….. (to buy) from your local dealer.

5. The interiors ….. (to design) by computer.

6. Next year tyres ….. (to replace) before they wear down completely.

7. These machine tools ….. (to check) tomorrow.

15. Rewrite the sentences in the passive in two ways, as in the example.

e.g. 0. His father will give Billy a new bicycle.

Billy will be given a new bicycle by his father.

A new bicycle will be given to Billy by his father.

1. Fred has offered Mary a watch.

2. Lisa will send Tim an invitation.

3. She’ll bring me some devices.

4. Ted will buy her a present.

5. Sonia will lend me some money.

6. Jack will show me the new car.

7. They pay him a lot of money for the job.

16. Rewrite the sentences in the passive, where possible.

1. Her mother will drive her to school tomorrow.

2. Paul will drive to work tomorrow.

3. Sue asked the waiter to bring some water.

4. She will move to her new house next month.

5. He moved the boxes out of his way.

6. They will open the new sports centre soon.

7. The teacher will mark the essays.

17. Translate the following sentences into English.

1. Всі спостереження будуть проведені групою відомих вчених.

2. Магніт притягує залізо.

3. Усім відомо, що метали використовували багато років тому.

4. Вони побудують новий міст через 2 роки.

5. Текст перекладуть українською мовою.

6. Біля нашого університетету будують багатоповерховий будинок.

7. Наступного року в Японії зроблять нові транзистори.

UNIT 14

NUMERALS

LEAD-IN

1. Look at the picture and read the following Roman numerals.

2. Match the Arabic and Roman numbers. Why are Arabic numbers used in mathematics?

1	500	a	M
2	40	b	C
3	10	c	I
4	1000	d	D
5	50	e	LX
6	1	f	L
7	5	g	V
8	800	h	XL
9	100	i	X
10	60	j	DCCC

READING

3. Read the text and match the sentences (A-C) to the numbered spaces (1-3) in the text:

A. Positional notation is made possible by the use of a symbol for zero.

B. Such a system is inconvenient when dealing with large numbers, and as early as 3400 BC in Egypt and 3000 BC in Mesopotamia a special symbol was adopted for the number 10.

C. The symbols are usually added together.

Numerals

N

1

umerals are signs or symbols for graphic representation of numbers. The earliest forms of number notation were simply groups of straight lines, either vertical or horizontal, each line corresponding to the number 1.

The addition of this second number symbol made it possible to express the number 11 with 2 instead of 11 individual symbols and the number 99 with 18 instead of 99 individual symbols. Later numeral systems introduced extra symbols for a number between 1 and 10 and additional symbols for numbers greater than 10.

ROMAN NUMERALS. The system of number symbols created by the Romans had the merit of expressing all numbers from 1 to 1,000,000 with a total of seven symbols: I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 1000.

R

2

oman numerals are read from left to right. The symbols representing the largest quantities are placed at the left; immediately to the right of those are the symbols representing the next largest quantities, and so on.

For example, LX = 60, and MMCIII = 2103. When a numeral is smaller than the numeral to the right, however, the numeral on the left should be subtracted from the numeral on the right. For instance, XIV = 14 and IX = 9. A small bar (¯) placed over the numeral multiplies the numeral by 1000. Thus, theoretically, it is possible, by using an infinite number of bars, to express the numbers from 1 to infinity. The Roman system's one drawback, however, is that it is not suitable for rapid written calculations.

ARABIC NUMERALS. The common system of number notation in use in most parts of the world today is the Arabic system. This system was first developed by the Hindus and was in use in India in the 3rd century BC. The Hindu numeral system was probably introduced into the Arab world about the 7th or 8th century AD. The first recorded use of the system in Europe was in ad 976.

T

3

he important innovation in the Arabic system was the use of positional notation, in which individual number symbols assume different values according to their position in the written numeral.

The symbol 0 makes it possible to differentiate between 11, 101, and 1001, and all numbers can be expressed in terms of ten symbols, the numerals from 1 to 9 plus 0.

LANGUAGE DEVELOPMENT