The periods succeeding those in the table, are Trillions, Quadrillions, Quintillions, Sextillions, Septillions, Octillions, and Nonnillions, and analogical names might be formed for the succeeding higher periods.

From the preceding remarks the pupil will readily understand the reason of the following rule for numerating or expressing figures by words.

RULE.-Commence at the right hand, and separate the given number into periods, then beginning at the left hand, read the figures of each period as if they stood alone, and then add the name of the period.

Thus, the number 8304000508245, when divided into periods, becomes 8,304000,508245, and is read, Eight billion, three hundred and four thousand million, five hundred and eight thousand two hundred and forty-five. The name unit of the right hand period is commonly omitted in reading.

8. 40024 17. 62003005 26. 80000102051003 9. 61304 18. 91010010 27. 50000021375604 28. 4000012000040250014

29. 1000982000375000482000354000271000032561804

600000501

3000400230024

From the preceding tables and remarks, the pupil will likewise readily understand the reason of the following rule for notation, or expressing numbers by figures.

RULE. Make a sufficient number of cyphèrs or dots, and divide them into periods, then underneath these dots write each figure in its proper order and fill the vacant orders with cyphers.

NOTE. The object of the dots or cyphers, being to guide the learner at first, after a little practice he may dispense with them.

Ex. 1. Write down in figures the number twenty millions three hundred and four thousand and forty. Here millions being the highest period named, we write cyphers to correspond with that, and the period. of units, and then underneath these place the significant figures in their proper order, and afterwards fill the vacant orders with cyphers.

0 0 0 0 0 0, 0 0 0 0 0 0

20 30 40 40

The pupil must recollect that cyphers being of no use except to fill vacant orders, are never to be placed to the left of whole numbers.

EXERCISES IN NOTATION.

Express the following numbers in figures.

2. Seventy-five.

3. Ninety.

EXAMPLES.

4. One hundred and five.

5. Three hundred and twenty,

6. Nine hundred and four.

7. Eight hundred and ninety.

8. Two thousand three hundred and five. 9. Six thousand and forty.

10. Seven thousand and four.

11. Eight thousand and ninety-five.

12. Ten thousand five hundred and fifty-six

13. Forty thousand and forty.

14. Ninety-five thousand two hundred and sixty-seven.

15. Eighty thousand one hundred and nine.

16. One hundred and thirty-six thousand two hundred and seventy five.

17. Three hundred and seven thousand and sixty-four. 18. Five hundred thousand and five.

19. One million, two hundred and forty-seven thousand, four hundred and twenty-three.

20. Ten millions, forty thousand and twenty.

21. Sixty millions, seventeen thousand and two. 22. One hundred and four millions two hundred and four thousand and sixty-five.

23. Five hundred and three millions, one hundred and two thousand and nine.

24. Ninety one thousand and two millions, and four. 25. Sixty billions, three millions and forty-one thousand. 26. One billion, one hundred million, one thousand and

one.

The Roman method of representing numbers, is by means of certain capital letters of the Roman alphabet. Thus:

NOTE 1. As often as any letter is repeated, so often is its value repeated.

NOTE 2. A less character before a greater one, diminishes its value NOTE 3. A less character after a greater one, increases its value.

QUESTIONS.

When

What is Arithmetic? When is it a science? is it an art? What are the fundamental rules of arithmetic? What is numeration? What is notation? What does a unit signify? What does two signify? Three, &c.? What is meant by the simple value of a unit? What does the local value of a figure depend on? How do you write the number ten in figures? Why is the one in this case called a unit of the second order? How many units of the first order does it take to make a unit of the second order? How many units of the second order does it require to form a unit of the third order? &c. Repeat the principles of notation and numeration. Repeat the names of each of the first nine orders as expressed in the numeration table. Repeat the name of each of the periods. Repeat the Rule for numeration. Repeat the Rule for notation.

equal; as 20s.

£ 1.

into, with, or multiplied by; as 6 X 2 = 12. by (i. e. divided by ;) as 623; or, 2)6(3. proportionality; as 2:4:: 6:12.

or, Square Root; as

Cube Root; as

Fourth Root; as

64

8.

A vinculum; denoting the several quantities. over which it is drawn, to be considered jointly as a simple quantity.

SIMPLE ADDITION.

SIMPLE ADDITION is the art of collecting several numbers, of the same name, into one sum.

RULE.

Place the numbers with units under units, tens under tens, &c. Begin the addition at the units, or right hand column, and add together all the figures in that column; then, if the amount be less than ten, set down the whole sum: but if greater than ten, see how many tens there are, and set down the number above the even tens, and carry one for each ten to the next column, and proceed with it as in the first.

Proof.-Begin the addition at the top of each column, and proceed as before, and if the result be the same, it is presumed to be right.

(5) 27636 7 9 8 9 2 38941 6 7 8 32 59 244

2 7 3 54 5

Here 4, 2, 1, 2 and 6 make 15. In fifteen there is one ten and five units. Set down the five units under the units column, and carry one for the ten to the next or tens column.

Then 1, 4, 3, 4, 9 and 3 make 24; in 24 there are two tens, and four over: set down the four under the column of tens, and carry two to the next or hundreds column &c., to the last, where the whole amount may be set down.