The Fractions and percentage

 

A unit or an aggregate of units is called a whole number or an integer; a part of a unit is called a fractional number.

Arithmetical numbers are represented by symbols called numerals, as the Arabic figures (1, 2, 3, etс.) and the Roman figures (I, V, X).

Every fraction must contain two numbers, a denominator and a numerator. The denominator tells into how many equal parts the unit is divided. The numerator shows how many of these parts are taken. The fraction 4½ is read four and one half.

A decimal fraction is a fraction having a denominator of 10, 100, 1000, or some similar multiple of 10. All figures to the left of the decimal point are whole numbers, everything that comes after the decimal point (to the right of it) is a fraction, or part of a unit.

0.2 is read two tenths; 52.23 is read fifty-two and (or: point) twenty three hundredths.

Percentage is a particular kind of a decimal fraction, of which the denominator is always 100. Instead of writing the denominator we use the term ― percent to indicate that the denominator is 100. When we speak of “6 per cent” we mean 6/100 or 0.06. These all mean the same thing; namely, 6 parts out of 100. Instead of writing out the words “per cent” we more often use the sign % after the number, as for instance 6%, which means “six per cent”.

Active Vocabulary

unit - единица; единица измерения; агрегат, секция, блок

aggregate - совокупность, агрегат; собирать в одно целое

integer - зд.целое число

number - число, количество; номер, цифра

figure - фигура, диаграмма, чертеж, цифра

denominator - знаменатель

numerator - числитель; счетчик

contain - содержать

equal - равный

fraction - дробь; частица

multiple - умножать; увеличивать

decimal - десятичный; десятичная дробь

indicate - показывать, указывать; означать

mean - значить, означать, иметь значение; иметь в виду

instead - вместо, взамен

sign - знак, символ; подписывать; отмечать

for instance - например

 

EXERCISES

I. Read the numbers: 1/2; 0.5; 0.25; 3 1/3; 4 1/5; 0.3; 1.235; 3%; 100%

II. Translate into English:

1. How do you translate the words number and numerical?

2. What do we mean by 6%?

3. This is a figure.

4. The needle has a sharp point.

5. The gram is a unit of weight.

6. " Fe" is the symbol for iron.

7. How much is ten per cent of fifty?

 

III. Complete the sentences: 1. Every fraction contains ….2. The fraction 5½ is read ….3. A fraction having a denominator of 10, 100, etc. is called ….4. Percentage is a ….5. We use the sign % ….6. An integer is a ….7

IV. Choose the terms from the text and give their definitions:

Например: The denominator. The denominator tells into how many equal parts the unit is divided.

 

V. Answer the questions:

1. What is called an integer?

2. How do we call a part of a unit?

3. What does a fraction contain?

4. What does the numerator (denominator) show?

5. What do the figures to the left of the decimal point show?

6. What does the term ― per cent‖ indicate?

7. How do we identify the figures 3, 5, 6 and the figures I, V, X?

 

VI. Translate into English: 1. В техникумах мы изучаем элементы высшей математики. 2. Вместо слова «процент» вы можете написать знак %. 3. Если числитель меньше знаменателя, то дробь называется правильной (proper). 4. Такая дробь всегда меньше единицы.

 

Text B: The Metric System

Read and translate the text. Pay attention to the use of abbreviations.

 

The Metric System

 

Physics measures such physical quantities as time, length, mass, density, velocity, area, volume, temperature and energy. Different units of length and mass exist. Nearly all of them are interrelated. Nowadays, three main systems of measurement are widely used: the British system of unity, the metric system of units and the International system of units (SI).

With a few exceptions, all the nations of the world use the metric system. It is so easy that anyone who knows arithmetic can learn it quickly. Before the introduction of the metric system (metre-kilogram-second), the British foot-pound-second system was widely used. But the latter system (which is still in use in Great Britain and the USA) was very complicated and caused serious difficulties in the international trade. Fox example, in the British system 1 mile is equal to 1760 yards, 1 yard – to feet and 1 foot – to 12 inches. This means that it's very difficult to convert units. But in the metric system each unit is a multiple of the following lower unit by ten. Therefore, the conversion to a higher quantity is done by moving the decimal point to the right to the required number of places, and vice versa.

The idea of decimal system was realized only at the end of the 18^th century. In 1791, the French Academy of Science decided that the standard of length should be one ten-millionth part of the distance from the Equator to the North Pole. The two French scientists charged with the task took this distance on a line running through Paris and divided it in-to 10000000 equal parts. They called one of the parts a metre (“measure”), which became the main unit. Metre was also used to measure area and volume. Thus a square metre and a cubic metre appeared.

The main advantage of the system is that for shorter measurements the metre is divided by ten, so a decimal system was used. Shorter units had Latin prefixes and longer ones – Greek prefixes. So, “millimeter” is Latin for ― a thousandth part of a “metre” and “kilometer” is Greek for “a thousand metres”

As for the unit of mass, it was defined as the mass of a cubic centimeter of water at the temperature of 4°C (the temperature of its maximum density). As we know, the name of this unit is gramme.

The SI units is derived from the metric system and was internationally accepted in 1960. Besides metre (m), kilogram (kg) and seconds (s), its basic units are Kelwin (K), ampere (a), mole (mol), and candle (cd). This system was introduced in our country in the 1960s and every day we measure things by the units from this system.

 

Active Vocabulary

advantage –преимущество

area –площадь

basic –базовый

candle – 1.свеча2.кандела(единица измерения света)

cause –служить причиной

charge –поручать

complicated –сложный

conversion –пересчет, перевод

convent –переводить(единицы)

cubic –кубический

decimal –десятичный

define –определять

density –плотность

derive –выходить, происходить

distance –расстояние

equal –равный

exception –исключение

Greek –греческий, греческий язык

inch –дюйм

interrelated –взаимосвязанный

introduce –зд.вводить

kilogram(me) –килограмм

kilometre –километр

Latin –латинский; латинский язык

length –длина

line –линия

mass –масса

measure –мера

measurement –измерение

metric –метрический

millimetre –миллиметр

mole –моль(единица измерения)

multiply –умножать

North Pole –Северный полюс

pound –фунт

prefix – (линг.)приставка, префикс

quantity –количество

realize –зд.Реализовать

require –требовать

scientist –ученый

second –секунда

trade –торговля

square –квадрат, квадратный

standard –стандарт, стандартный

system –система

ten-millionth –десятимиллионный

thousand –тысяча

through –сквозь

thus –таким образом

unit –единица

unity –единство

USA (=the United States of America)–США

vice versa –лат.наоборот

volume –объем

 

EXERCISES

I. Translate the phrases: a science based, commonly used measuring device, units used to measure, the decimal system based on the metre and kilogram, using metric units, exact measurements.

 

II. Translate the words without a dictionary: physics, system, international, metre, kilogram, kilometre, gram, foot, yard, mile, minute, metric, universally, engineer, commerce, standard, symbol, code.

 

 

III. Check the translation of the following words in the dictionary. How are these words called? familiar, concept, fundamental, combination, distance, manipulate, list, capital.

 

IV. Answer the following questions:

1. What quantities does physics measure? Are most of them interrelated?

2. How many systems of measurement are widely used nowadays?

3. All the nations of the world use the metric system, don‘t they?

4. What was used before the metric system? Did the earlier system have any drawbacks?

5. When was the idea of decimal system realized?

6. What is the main unit of the metric system? How was it measured?

7. Were the units of area and volume defined as well?

8. Do shorter units have Greek or Latin prefixes?

9. What is a unit of mass?

10. Is there a difference between the metric system and the SI system?

11. When was the SI system introduced in the USSR?

12. What synonyms to the phrase “metric system” can you find in the text?

 

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