How we read and write numbers

To make it easier to read¹ large numbers, we separate the figures of the numbers by commas into groups of three, counting from right to left. Each group is called a period and has its own name.

The system of numbers we use, called Arabic system, is a decimal system: that is, it is based on tens. In this system, the value a digit represents is determined by the place² it in the number; if a digit is moved to the left one place, the value it represents becomes ten times as great³.

Zero in the decimal system is a "place-holder"; in the number 30, the zero shows that 3 has been moved to the left one place, thus counting tens instead of ones. The place value in numbers is shown below:

682,000,000,000 847,000,000 136,000 592

Billions Millions Thousands Ones

These numbers are read: six hundred eighty-two billion, eight hundred forty-seven million, one hundred thirty-six thousand, five hundred and ninety-two.

682,000,000,000 847,000,000 136,000 592

Billions Millions Thousands Ones or Units

4 periods 3 periods 2 periods 1 period

Rule to Remember. a) All periods of a number contain three digits, or places (the first period on the left may or may not). b) Zero is used as a place-holder.

Average. When we want to find a single number that will represent all the numbers in a group of unequal numbers or quantities we find the average (or arithmetic mean). To find the average of a group of unequal numbers, we add the numbers and then divide their sum by the number of addends.

Notes:

¹ to make it easier to read - для того, чтобы легче читать

² is determined by the place - определяется местом

³ ten times as great - в десять раз больше

Exercises

I. Read the following words paying attention to the pronunciation:

to separate, period, system, zero, average, digit, unequal.

II. Form nouns of the following verbs:

to read, to count, to move, to place, to contain, to find, to determine, to represent.

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

quantity, unequal, sum, to make it easier to read, to separate the figures of the number, to be determined by, ten times as great, ten times as small.

IV. Answer the following questions:

1. Why do we separate the figures of the numbers by commas? 2. How is each group of three figures called? 3. How is the system of numbers we use called? 4. How many digits does a period of a number contain? 5. How do we find the average of unequal numbers?

V. Translate into Russian:

Our present-day number-symbols are Hindu characters. It is important to notice that no symbols for zero occur in any of this early Hindu number system. They contain symbols for numbers like twenty, forty, and so on. A symbol for zero had been indented in India. The invention of this symbol for zero was very important, because its use enabled the nine Hindu symbols 1, 2, 3, 4, 5, 6, 7, 8 and 9 to suffice for the representation of any number, no matter how great. The work of a zero is to keep the other nine symbols in their proper place.

VI. Translate into English:

Десятичная система нумерации возникла в Индии. Впоследствии ее стали называть «Арабской», потому что она была перенесена в Европу арабами. Цифры, которыми мы теперь пользуемся, тоже называются арабскими.

В этой системе особо важное значение имеет десять, и поэтому система носит называние десятичной системы нумерации.

Чтобы легче читать многозначные числа, мы отделяем (separate) цифры в них запятыми по три в группе. Группу из трех цифр мы называем периодом.

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