Exercises

I Read the following words paying attention to the pronunciation:

hundredth, tenths, arrange, column, subtrahend, annexed.

II Give all possible derivatives of the following words:

to arrange, to start, product, power.

III Form adverbs of the following words by adding suffixes:

power, use, part, equal.

IV. Make up sentences of your own using the words and expressions given below:

in multiplying, in dividing, in subtracting, in the dividend, in the same way, mark off, since, must be written.

V. Answer the following questions:

1. How are decimal fractions added? 2. How do we write decimal fractions when we want to subtract them? 3. How do we check the answer? 4. How do we multiply (divide) decimal fractions? 5. How do we arrange numbers in adding decimal fractions?

VI. Put 5 questions to the text and answer them.

VII. Translate into Russian:

Decimals are fractions which always have a denominator of 10 or some power of 10, such as 100, 1000, etc. The denominator is usually not written down; but a dot or point called the "decimal point" is placed to the right of the digit in the numerator, which is distant from the extreme left of these digits by the number of zeroes in the denominator.

In addition or subtraction of decimals, the decimal points must be placed in a straight one under the other.

In multiplication of decimals, point off as many places in the product as there are decimal places in the multiplier and the multiplicand.

VIII. Translate into English:

При сложении десятичных дробей надо соблюдать следующий порядок: дроби записывают одну под другой так, чтобы во всех слагаемых одинаковые разряды находились друг под другом и все запятые стояли в одном и том же вертикальном столбце; справа от десятичных знаков некоторых слагаемых приписывают такое число нулей, чтобы все слагаемые после запятой имели одинаковое число цифр.

TEXT

What is per cent?

We have already learned two ways of writing fractional parts: common fractions and decimal fractions. Another method is by using per cents.

Per cent tells the number of parts in every hundred. This number is followed by the per cent sign (%). The word "per cent" and sign % actually refer to the denominator of a fraction expressed as hundredths.

When working with per cent, we do not write the word, but use the sign %, 20 per cent is written 20% and so on.

In working with problems involving percentage¹ we must be able to change per cents to decimals and decimals to per cents.

We can change a per cent to a decimal by dropping the per cent sign and moving the decimal point two places to the left. We can change a per cent to a common fraction with the given number as the numerator and 100 as a denominator.

One hundred per cent of quantity is the entire quantity. To find a per cent of a number, change the per cent to the equivalent decimal fraction or common fraction and multiply the number by the fraction. To find the per cent of one number from a second number, form a fraction in which the first number is the numerator and the second number is the denominator. Divide the numerator into the denominator and change the decimal fraction to a per cent. To find a number when a per cent of it is known, change the per cent to an equivalent decimal fraction or common fraction, divide given number by this fraction.

Note:

¹ problems involving percentage — задачи на нахождение процента