Put the questions into the Passive Voice
1. When did Pasteur discover Penicillin?
2. Where do people speak Mandarin?
3. Did Spain win the last basketball Olympics?
4. Do people speak English in Hawaii?
5. How many paintings did the police find?
6. When did Cook discover Australia?
7. Did the government order them to build a new bridge?
Complete the following report of an accident which happened in a factory. Use the correct form of the verbs in brackets.
On Friday morning at 9.25 a worker in the chemical plant (a) ….. ( to find) by female colleague. He (b) ….. (to lie) on the floor. His colleague (c) ….. (to check) that he (d)….. still ….. (to breathe) and then (e) ….. (to call) the emergency services. The injured man (f) ….. (to take) to hospital where he later (g) ….. (to recover). An investigation at the factory (h) ….. (to find) that a bottle containing a dangerous chemical liquid (i) ….. (to leave) open. Vapour from the liquid (j) ….. (to escape) into the air. While he had been working in the room he (k) ….. (to become) unwell. He (l) ….. (to become) drowsy and then (m) ….. (to fall) unconscious. Investigating officers are interviewing everyone who (n) ….. (to work) in the factory that morning.
UNIT 13
NUMBERS
LEADIN
1. How are numbers classified? Give examples of rational and irrational numbers.
Work in pairs. Take turns to give examples of everyday use of numbers in our lives. Look at the pictures and say the time.
READING
3. Read the text and find the expressions which mean:
a. the totality of the rational and irrational numbers;
b. a positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a dot (decimal point);
c. the positive and negative integers and fractions, and the number 0.
Numbers
Number is a word or symbol used to designate quantities.
RATIONAL NUMBERS. The simplest numbers are the natural numbers, 1, 2, 3, .... The natural numbers are also called the whole numbers, or positive rational integers. The natural numbers are closed with respect to addition and multiplication—that is, the sum and product of two natural numbers are always natural numbers. Because the quotient (the result of dividing) of two natural numbers, however, is not always a natural number, it is convenient to introduce the positive fractions to represent the quotient of any two natural numbers. The natural number n is identified with the fraction n/1. Furthermore, because the difference of two positive fractions is not always a positive fraction, it is expeditious to introduce the negative fractions and the number zero (0). The positive and negative integers and fractions, and the number 0, comprise the rational number system.
IRRATIONAL NUMBERS. The development of geometry indicated the need for more numbers; the length of the diagonal of a square with sides one unit long cannot be expressed as a rational number. Similarly, the ratio of the circumference to the diameter of a circle is not a rational number. These and other needs led to the introduction of the irrational numbers. For example, Ã = 1.4142135623 ... and p = 3.1415926535 ... are irrational numbers. The totality of the rational and irrational numbers makes up the real number system.
NUMBER SYSTEM is any of various sets of symbols and the rules for using them to express quantities as the basis for counting, comparing amounts, performing calculations, determining order, making measurements, etc.
Our modern decimal, or base10, number system is a positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a dot (decimal point).
The origins of the decimal number system can be traced to ancient Egyptian, Babylonian (Sumerian), and Chinese roots. The bulk of the credit for the base10 system, however, complete with a symbol for zero, goes to the Hindu mathematicians of the fifth and sixth centuries. After their discovery of the system it was transmitted to mathematicians in the Islamic world who developed it to include decimal fractions during the period from the 9th to 11th centuries AD. The introduction of the system into the West took place with the translation of the treatise of Muḥammad ibn MūsāalKhwārizmī (780–850) in Spain in the twelfth century.
