45.6723
+156.78
we discard the digits 2 and 3. But we do not simply ignore these discarded digits. They may cause a change in one of the digits we intend to use. If we have 45.6723
+ 156.7
then according to the following rule we must rewrite it as:
45.7
+ 156.7
If the first digit at left of the portion that is to be discarded is either 0,1,2,3, or 4, then the last digit on the right that is to be retained should be left unchanged. If the first digit at the left of the portion that is to be discarded is either 5,6,7,8, or 9, then the last digit on the right that is to be retained should be increased by 1. Such discarding of the unnecessary decimal places is known as the rounding of numbers.
When 45.6723 was rounded to one decimal place, that is to tenths, we obtained 45.7 because the first digit of the discarded portion was 7, and therefore, the last digit on the right (the 6) was increased by 1, and we thus obtained 7. The actual addition and subtraction of decimal fractions are performed in the same manner as in the case of the whole numbers so that decimal points are all in a vertical column as is shown below: 56.883 or 875.728
+123.784 - 648.917
25.075 226.811
205.742
Multiplication of Decimal Fractions
The only difference between multiplication of whole numbers and decimal fractions is that we must take into consideration that some portion of one or both factors is fractional, as indicated by the decimal points. Now, instead of multiplying decimal fractions let us multiply whole numbers 3,672 and 275. To obtain 3,672 from 3.672 we move the decimal point 3 places to the right, that is we multiply the number by 1,000 and to obtain 275 from 2.75 we move the decimal point two places to the right. That is we multiply it by 100. Thus, the product 3,672 x 275 is 1000 x 100 = 100,000 times the product 3.672 x 2.75. When the product of the whole numbers 3,672 x 275 is obtained, we must divide it by 100,000. That is, we move the decimal point 5 places to the left. The multiplication of the whole number looks as follows:
3.672
x 275
18360
+ 25704
7344
1009800
The decimal point (not written) is at present on the extreme right of the product, that is, we have 1,009,800 and after moving it 5 places to the left we have 10,098.
Notice that one factor has 3 decimal places, and the second factor has 2 decimal places. The product has 5 decimal places. That is the number of the decimal places in the product is equal to total number of decimal places in the factors.
Division of Decimal Fractions
The only difference between the division of whole numbers and that of numbers containing decimal fractions is that we must take into consideration the fact that some portion of either the dividend or the divisor or of both is fractional, as is indicated by the decimal point.
Furthermore, when we perform division with whole numbers, we often cannot complete this operation as we obtain a remainder. Thus, we have before us two questions:
1. Where shall we locate the decimal point in the quotient?
2. What shall we do in the case of a remainder?
We have examined the effect of moving of the decimal point. Let’s first examine the division of a decimal fraction by a whole number. For example 111.78 : 9. We shall proceed as in the division of whole numbers:
111.78 I 9
- 9 12
21
- 18
3
Note that the division of the whole part leaves a remainder 3, and that we have a fractional part 0.78. That is we are left with 3.78. From this point on we can't expect anything else but some fraction in the quotient if we continue the division. If now we bring down the next digit, that is 7, we shall have 3,7 or 370 tenths. If we divide 37 tenths by 9, we shall have a certain number of tenths in the quotient. We shall, therefore, place a decimal point after the 2 in the obtained
quotient and continue the division as usual. Then we shall have:
111.78 I 9 Check: I2.42
-9 12.42 x 9
21 111.78
-18
37
-36
18
-18
Thus we observe that division of a decimal fraction by a whole number is performed in the same manner as division of a whole number by a whole number.
The whole part of the decimal fraction will give the whole part of the quotient. As soon as we bring down the first digit from the decimal part of the dividend, we shall begin to obtain the decimal part (the fractional part) of the quotient. This procedure always serves for the division of decimal numbers by whole numbers.
Now we shall apply the results just obtained to the division of decimal fractions by decimal fractions. Let’s perform the division 176.28 : 2.6. We know that the multiplication of the dividend and of the divisor by the same number does not produce any change in the quotient. When we multiply the dividend by some number, the quotient is multiplied by the same number, but when we multiply the divisor by some number, the quotient is divided by the same number. This fact enables us to change the dividend 2.6 into a whole number. This change is accomplished by moving both decimal points one place to the right; thus, both the divisor and the dividend 176.28 and 2.6 are multiplied by 10. The divisor 2.6 becomes 26, and the dividend 176.28 becomes 1,762.8.
Quotients with Repeated Decimals
Very often the division of numbers, whole numbers or numbers with decimal fractions cannot be completed to give an exact result. At some stage of division we reach a situation where the quotient or a part of the quotient repeats itself, and thus the division may be carried on indefinitely. In all such cases, however, the exact quotient cannot be obtained. In such situations the process of division must be stopped at some place. Often the point where the division stops is determined in the statement of the problem. The following example will illustrate the repeating:
11 6___
-6 1.83333...
50
-48
20
-18
20
-18
20
-18
2...
Note that during the division above, we brought down zeroes whenever we wished to continue the process. All these zeroes assumedly come from the places to the right of the decimal point. We note that the quotient 11: 6 = 1.83333... may contain as many repeated 3's as we wish. However, if we decide to stop, less than 5, we merely drop the digits that are beyond the place where we wish to stop.
THE FACULTY OF BIOLOGY
The Cell
All living things are composed of cells. Very simple organisms such as yeast1 and bacteria consist of only one cell. They are one-celled or unicellular organisms. A large organism, such as a human being contains billions upon trillions of cells and is called a multicellular organism. A drop of blood, for instance, contains about forty billion cells. And there are thousands of drops of blood in the average man.
Despite its small size, each cell is a tiny drop of life. Some cells can exist independently, and do, as in the case of bacteria. Human cells however, have lost that ability. They depend on one another and specialise in one function or another. Some cells specialise in photosynthesis, some in digestion, some in excretion and some in reproduction.
Groups of cells of a similar shape, size and function form a tissue. When tissues of different types are grouped together for a common function they form an organ. Groups of cells, taken all together, are more advanced than single cells, even if the latter2 are more independent. The living matter inside a cell is called protoplasm. The protoplasm is divided into parts. Near the center of the cell is a part, which is denser and thicker than the rest of the cell. It is the nucleus. The rest of the cell is cytoplasm.
Like any other living things, cells grow and multiply. Most cells multiply .by dividing down the middle. Then there are two cells where only one existed a moment before. The cell nucleus is in charge of seeing that cell division takes place properly. The cytoplasm takes care of the day-by-day life of the cell. Cells in different parts of the body vary in their shape according to the work they must do. Fat cells are just tiny blobs of fat surrounded by a thin layer of protoplasm. The red cells of the blood are little disks that contain a protein called haemoglobin, which carries oxygen to all other cells of the body. Red blood cells are so simple, they don't even have a nucleus and so cannot grow or divide.
Nerve cells have irregular shapes with long thread-like fibers sticking out5 of them. Impulses and sensations travel along those fibers. Muscle cells are long and thin. They can contract into short, thick cells whenever necessary.
Some cells are so specialised that they have abandoned almost everything but6 their main function. They have even lost the ability to multiply. A baby is born with all the brain cells, for instance, that it will ever have. Still other cells are always growing. The cells of the skin grow and divide throughout life.
Notes
1. yeast [ji:st] – дрожжи
2. the latter – nocледние
3. by dividing – путем деления
4. is in charge of seeing – зд. отвечают за
5. sticking out – выступающий
6. but – кроме
Some Familiar Proteins
The hair on your head is an example of an almost pure protein. So is silk. The protein of hair is called keratin by chemists, and the protein of silk is called fibroin.
Both keratin and fibroin are comparatively simple proteins. Their molecules consist of amino acids strung together in more or less a long straight line. Such lines of amino acids are called polypeptides.
In the 1940’s chemists learned to manufacture quite long polypeptide chains in the laboratory. They used only one or two different amino acids in doing so, however.
Then, in the 1950’s, chemists learned how to put together amino acids of many different varieties, one by one, just in a particular order. By 1960, a protein built up of 23 amino acids, was manufactured in the laboratory. It was found to behave just like a similar small molecule formed by the body. However, 23 amino acids are a long way from the hundreds and thousands of amino acids found in the larger proteins made by the body.
Still, fibroin isn’t much more complex than these laboratory creations. Its molecule contrasts of over 250 amino acids of 14 different kinds. Eighty-five per cent of the molecule is made up of only three different amino acids, and those three happen to be the simplest of all. It is for this reason1 that silk doesn't play a vital role in life. It is just used by the silkworm2 to make a soft cocoon for itself.
Protein such as fibroin and keratin are called fibrous proteins. In general, fibrous proteins are strong, sturdy (крепкий) and tough (прочный). Keratin, for instance, is the chief protein not only of hair, but of skin, nails (ногти), hooves (копыта), scales (чешуя), horns (pora) and feathers (перья). Another important fibrous protein is collagen, which occurs in cartilage (xpящ), ligaments (связки) and tendons (cyxoжилия).
The really important proteins, however, are the globular proteins. In these, the polypeptide chains are not merely straight lines, but existing complicated loops (петля) and twists (изгиб) which are never quite the same in any two different proteins.
Notes
1. it is for this reason – именно по этой причине
2. silkworm – шелковичный червь
Enzymes and Genes
The nucleus of the cell is in charge of cell division. Unfortunately, most of the details of the process are as yet unknown. Still we can describe some of them.
Inside the nucleus are small patches that can react with certain dyes to become strongly coloured. Biologists noticed them for that reason and called the material in the patches chromatin from the Greek word for colour.
In the process of cell division, the chromatin collects into little rods of varying size. The rods are called chromosomes. In the nuclei of human cells are forty-six such chromosomes, existing in pairs. There are twenty-three pairs of chromosomes, in other words. Each kind of creature has its own fixed number of chromosomes. A rat (крыса) has thirty-eight chromosomes, a grasshopper (кузнечик) twenty-four and a housefly (муха) only twelve. A crayfish (рак) on the other hand, has over two hundred chromosomes.
Before a cell divides, every chromosome lines up in the centre of the cell and splits in two. The two halves of each chromosome move apart and when the cell divides, each new cell has a duplicate of all the original chromosomes.
It is these chromosomes that control a cell’s characteristics. A cell’s nature is determined by the kind of chromosomes it has. Every chromosome is actually a chain of protein molecules which are called genes. Genes are strung along a chromosome as beads are in in a necklace. The genes have a certain chemical resemblance to viruses.
Each gene is thought to control a single characteristic of an organism. For instance, there is a gene for blue eyes and one for brown eyes; one for straight hair and one for wavy hair. Every human being has thousands of different genes scattered through1 his various chromosomes. Whenever a chromosome splits in two, during cell division, each gene duplicates itself exactly and both daughter cells get one apiece.How does a gene control a particular characteristic? Many people now think that each gene is in charge of manufacturing one particular enzyme in the cell.
But how does a gene manufacture an enzyme? For that matter, how does a gene duplicate itself? This is probably the most important unanswered question in biochemistry today. There are theories, of course. There are enzymes that take proteins apart and separate them into amino acids. These protein splitters can also put amino acids back together again.
Apparently, then, the beef (мясо) protein we eat or milk protein, or wheat (пшеница) protein is separated into amino acids and then put together in a different arrangement to make human protein. But how is the arrangement figured out2, when there are so many possibilities?
Here is where the gene comes in3. Genes are nucleo-proteins. The non-protein part of the molecule is the nucleic acid. Each gene contains its own variety of nucleic acid. Each different nucleic acid somehow acts as a model for the formation of a particular enzyme. Nucleic acids, therefore, control amino acid arrangements.
How? Chemists just began working out the method in the 1950’s. The nucleic acid of the chromosomes forms a "messenger"4 molecule which leaves the nucleus and joins particles in the cytoplasm which are called ribosomes.
In the ribosomes are tiny fragments of nucleic acid molecules. There are a number of kinds of these fragments and each will attach its own particular type of amino acid. These nucleic acid fragments carry their amino acids to the "messenger" molecule and use its structure as a guide. They line up to match the structure and each transfers its amino acid. In this way, an entire protein molecule is formed with an exact structure according to the original design of the chromosome’s nucleic acid.
You may wonder how enzymes can control characteristics. How can they decide blue or brown eyes, for instance? Well, eyecolour is due to a pigment called melanin. When the eyes contain very little melanin, they appear blue. With more melanin, they are brown. Melanin is formed in the body as a result of a chemical reaction which is catalysed by the enzyme, tyrosinase. The amount of the formed melanin depends upon the amount of tyrosinase present. Possession of a gene producing much tyrosinase will result in brown eyes. A gene that produces less tyrosinase makes for blue eyes.
What happens when a cell splits in two without proper duplication of genes? Sometimes the daughter cells just can’t live. At other times, the cells survive, but with a changed chemistry. Some biochemists think that cancer (рак) cells may originate as the result of such imperfect duplications.
Notes
1. scattered through – разбросанный
2. figure out – вычислять
3. Here is where the gene comes in. – И вот к этому ген имеет прямое отношение.