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Vocabulary

notation n. – система представления чисел;

to relate (to) v. – 1) устанавливать связь; (to, with – между чем-л.);

2) быть связанным;

3) относиться, иметь отношение;

solid a. – 1) твердый, плотный; сплошной; n твердое тело;

– solution твердый раствор;

measurement n. – измерение;

vary a. – 1) менять; 2) меняться; 3) изменяться;

tremendously adv. – 1) очень сильно; 2) чрезвычайно;

to denote v. – обозначать;

cumbersome a. – громоздкий; трудоемкий;

scale n. – масштаб;

insulating layer – изолирующий слой затвора;

integrated circuits – интегральная схема;

power n. – мощность; производительность; степень;

lose track – потерять счет;

to deal with v. – иметь дело (чем-л.; с кем-л.);

decimal – десятичный;

significant digit /figure – значащая цифра;

multiplied by – умножать на;

value n. – ценность; важность; полезность; значение; смысл;

to convert v. – преобразовать;

in essence – в сущности, по существу;

to add v. – добавить; прибавить; суммировать;

I. Practice pronunciation of the following words:

physics ['fɪzɪks] decimal ['desɪməl ]

mathematics [ 'mæθə'mætɪks] equal ['i: kwəl ]

efficiently [ɪ'fɪʃntlɪ] convert [ kən'vɜ:t ]

accurately ['ækjʊrɪtlɪ] assume [ ə'sju: m ]

measurement ['meʒəmənt] digit ['dɪdʒɪt ]

cumbersome ['kʌmbəsəm] radius ['reɪdiəs ]

circuit ['sɜ:kɪt] significant [ sɪɡ'nɪfɪkənt ]

II. Read and translate the words having the same root

Physics – physicists – physical, science – scientist – scientific, relate – relation – related, multiply – multiplied, move – movement, add – addition – added, thick – thickness, integrate – integrative – integrated, assume – assumption – assumed, equal – equality.

III. Match the words in the left column with its antonym in the right column

IV. Find in the text the equivalents of the following word combinations and write them out.

1) тесно связаны

2) обозначения больших и маленьких чисел

3) значащие цифры

4) правильное значение

5) вернуться к исходному значению

6) записать это в научной системе представления чисел

7) умножить число на некоторую степень

8) использовать отрицательные степени

9) получить конечное значение

10) переместить десятичный знак

V. Give the degrees of comparison of the following words

Vary, difficult, high, large, long, useful, small, much, many, easy, little, significant, original, final.

VI. Read and translate the text

Scientific Notation

Although physics and mathematics aren't the same thing, they are in many ways closely related. Just like English is the language of this content, mathematics is the language of physics. A solid understanding of a few simple math concepts will allow us to communicate and describe the physical world both efficiently and accurately.

Because measurements of the physical world vary so tremendously in size (imagine trying to describe the distance across the United States in units of hair thicknesses), physicists often times use what is known as scientific notation to denote very large and very small numbers. These very large and very small numbers would become quite cumbersome to write out repeatedly. Imagine writing 4,000,000,000,000 over and over again. Your hand would get tired and your pen would rapidly run out of ink! Instead, it's much easier to write this number as 4×10¹². See how much easier that is? Or on the smaller scale, the thickness of the insulating layer (known as a gate dielectric) in the integrated circuits that power our computers and other electronics can be less than 0.000000001 m. It's easy to lose track of how many zeros you have to deal with, so scientists instead would write this number as 1×10^-9 m. See how much simpler life can be with scientific notation?

Scientific notation follows these simple rules. Start by showing all the significant figures in the number you're describing, with the decimal point after the first significant digit. Then, show your number being multiplied by 10 to the appropriate power in order to give you the correct value.

It sounds more complicated than it is. Let's say, for instance, you want to show the number 300,000,000 in scientific notation (a very useful number in physics), and let's assume we know this value to three significant digits. We would start by writing our three significant digits, with the decimal point after the first digit, as «3.00». Now, we need to multiply this number by 10 to some power in order to get back to our original value. In this case, we multiply 3.00 by 10⁸, for an answer of 3.00×10⁸. Interestingly, the power you raise the 10 to is exactly equal to the number of digits you moved the decimal to the left as you converted from standard to scientific notation. Similarly, if you start in scientific notation, to convert to standard notation, all you have to do is remove the 10⁸ power by moving the decimal point eight digits to the right. Now you are an expert in scientific notation!

But, what do you do if the number is much smaller than one? The same basic idea… let's assume we're dealing with the approximate radius of an electron, which is 0.00000000000000282 m. It's easy to see how unwieldy this could become. We can write this in scientific notation by writing our three significant digits, with the decimal point after the first digit, as «2.82». Again, we multiply this number by some power to 10 in order to get back to our original value. Because our value is less than 1, we need to use negative powers of 10. If we raise 10 to the power -15, specifically, we get a final value of 2.82×10^-15 m. In essence, for every digit we moved the decimal place, we add another power of 10. And if we start with scientific notation, all we do is move the decimal place left one digit for every negative power of (to) 10.

VII. Answer the questions on the text

1. In what way are physics and mathematics related?

2. What is meant by scientific notation?

3. What rules does it follow?

4. How many positions do you need to show the numbers in scientific notation?

5. Express the number 0.000470 in scientific notation.

Express the number 2,870,000 in scientific notation.