Учебно-методическое пособие для студентов I-II курсов заочного отделения неязыковых факультетов



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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.



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