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5. In the number 111, the 1 at the right denotes some unit, and the 1 next toward the left denotes a unit ten times as great, and the 1 at the left denotes a unit ten times the second unit, or one hundred times the first unit.

may be shown thus:

one hundreds' unit

This

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100

10

1

6. In 236, the 6 represents 6 units; the 3 represents 3 units, each of which is ten times each of the units represented by 6; and the 2 represents 2 units, each of which is ten times each of the units represented by 3, or one hundred times each of the units represented by 6.

7. Tell what each figure represents in 125, 47, 352.

8. In 30, the 0 shows that there are no units of ones; and the 3 represents 3 units of tens. What does each figure represent in 60, 600, 405, 530, 203, 478, 700, 520?

9. In 324, the units represented by 4 are called units of the first order, or of units' order; the units represented by 2 are called units of the second order, or of tens' order; and the units represented by 3 are called units of the third order, or of hundreds' order.

10. Our number system is a decimal system. Decimal means tens. A decimal system is one in which ten units of one order are equal to one unit of the next higher order.

The decimal system is believed to have had its origin in the practice of using the fingers for counting.

11. Beginning at the left of 111, the 1 in the third order represents some unit; the 1 in the second order represents a unit one tenth as great; and the 1 in the first order represents a unit one tenth as great as that represented by a unit of the second order. A unit one tenth as great as that represented by the 1 in the first order may be represented by 1 written to the right of a decimal point (.) placed to the right of units' order, thus: .1 (111.1). A unit one tenth as great as this last unit may be represented by 1 written in the second place to the right of the decimal point, thus: .01 (111.11).

12. 1 is read one tenth; .01 is read one hundredth; .11 is read eleven hundredths; 1.1 is read one and one tenth; .4 is read four tenths. Read 6.7; 8.05; 56.25.

13. The decimal point is placed after the figure that represents whole units. The figures to the right of the decimal point represent decimal parts of units. The parts thus represented are tenths, hundredths, thousandths, etc.; and are called decimals.

14. A whole number is called an integer. Write an integer. On which side of the decimal point are integers written?

15. What is the meaning of the word decimal? Why is our number system called a decimal system?

16. What does each 2 in 222.222 represent?

17. Write the following so that units of the same order are below one another: 45.5, 214.25, 347, 4.315, 17.

18. Compare the value of 2 in 24 with the value of 2 in 240; with the value of 2 in .24.

19. Is the system of United States money a decimal system? Explain your answer.

NOTATION AND NUMERATION OF INTEGERS AND

DECIMALS

2. 1. Numbers are commonly expressed by means of figures (or digits) as 5, 10, etc.; by means of words, as five, ten, etc.; and by means of letters, as V, X, etc. The art of writing numbers by means of symbols is called notation. The word digit means finger. Why were the figures called digits?

2. The figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, are called Arabic numerals, as they were introduced into Europe by the Arabs, who borrowed most of them from the Hindus. The system of denoting numbers by means of figures is called Arabic notation.

3. The figure 0 is called naught, cipher, or zero. It has no value. It is used to fill out places that are not occupied by other figures. Using figures, write six; six tens; six hundreds.

4. The art of reading numbers is called numeration.

5. Integers of more than three places are read more easily when the figures are separated by commas into groups of three each, beginning at the right. The groups are called periods, and each period is named after the order of the right-hand figure in the group.

6. The names of the first four periods, and the orders in each, are as follows:

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3. Reading Integers.

To read an integer of more than three figures, begin at the right of the number and point off periods of three places each. Read the part occupying the left-hand period as though it stood alone, and add the name of the period; then read the part occupying the next period as though it stood alone, and add the name of the period. Continue until units' period is reached; there omit the name of the period.

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5. What is the name of the first period? of the second period? of the third period? of the fourth period?

6. How many periods are there in the numbers in column a? b? c? d?

7. How many places do the numbers in column c occupy? in column d?

8. What is the name of the left-hand period in the numbers in column a?

9. Read the left-hand period of the first number in column d. Read the middle period of the same number. Read the number.

10. Read the third period of the column d. Read the second period.

fourth number in Read the number.

11. When a number consists of three periods, how many places must there be in the first period? in the second? How many places may there be in the third period?

* 625 is read six hundred twenty-five.

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