In the number four hundred and six, there are 4 units of the 3d order, O of the 2d, and 6

of the 1st.

It is written

huns.

O tens

406

§ 10. To express ten units of the 3d order, or one thousand, we form a new combination by writing three ciphers on the right of 1; thus 1000

Now, although this thousand expresses one thousand units of the 1st order, it is, nevertheless, but one single thousand, and may be regarded as a unit of the 4th order.

Proceeding in this way, we may place as many figures in a row as we please. When so placed, we conclude:

1st. That the same figure has different values according to the place which it occupies.

2d. That counting from the right hand towards the left, the first place is the place of units; the second, the place of tens; the third, the place of hundreds; the fourth, the place of thousands, &c.

3d. That ten units of the first place are equal to one unit of the second place; that ten units of the second place are equal to one unit of the third place; that ten units of the third place are equal to one unit of the fourth place; and so on, for places farther to the left.

11. Expressing numbers by figures is called NOTATION. Reading the order of their places, correctly, when written, is called NUMERATION.

16

17

6,

57,

18 920,

9 12, 761, 257,

84, 912, 87 6,

410, 285

327, 826

87 6, 541

541, 297, 313

407, 212, 93 6,
289, 678,

323, 842, 76 8, 319,

*NOTE.-This Table is formed according to method of numeration. The English method g to thousands, &c.

2

J

counting from the right hand.

The different lines of the table are thus read. ten separated into periods of three figures each, To make the reading of figures easy, they are of

ry, after which, the pupil may read the Table. ble to all numbers, and must be committed to memotable, units, tens, hundreds, &c. are equally applica12. The words at the head of the numeration

1st line

23

5

6

8

9

10

11

12

13

14

15

Eight hundred, and seventy-nine.

Six thousand and twenty-three.
Eighty-two thousand, 3 hundred and one.
123 Thousand and eighty-seven.

7 Millions, 628 thousand, 735.

43 Millions, 210 thousand, 460.
548 Millions, 721 thousand, and 87.

6 Billions, 245 millions, 289 thousand, 421.
72 Billions, 549 millions, 136 thousand, 822.
894 Billions, 602 millions, 43 thousand, 288.

7 Trillions, 641 billions, 248 millions, 907 thousand, 456.
84 Trillions, 912 billions, 876 millions, 410 thousand, 285.
912 Trillions, 761 billions, 257 millions, 327 thousand, 826.
6 Quadrillions, 407 trillions, 212 billions, 936 millions, 876 thousand, 541.
57 Quadrillions, 289 trillions, 678 billions, 541 millions, 297 thousand, 313.
18 920 Quadrillions, 323 trillions, 842 billions, 768 millions, 319 thousand, 675.

16

17

EXAMPLES.

1. Write four, in figures.

2. Write four tens, or forty.
3. Write four hundred.
4. Write four thousand.

5. Write forty thousand.

6. Write four hundred thousand.

7. Write four millions.

Ans. 4.

Ans. 40.

Ans. 400. Ans. 4000.

Ans. 40,000.

Ans. 400,000.

Ans. 4,000,000.

These examples show us very clearly that the same significant figure will express different numbers according to the place which it occupies.

8. Write six hundred and seventy-nine.

Ans. 679.

9. Write six thousand and twenty-one. 10. Write two thousand and forty. 11. Write one hundred and five thousand, and

seven.

12. Write three billions.

13. Write ninety-five quadrillions.

14. Write one hundred and six trillions, four thousand and two.

15. Write fifty-nine trillions, fifty-nine billions, fifty-nine millions, fifty-nine thousands, fifty-nine hundreds, and fifty-nine.

16. Write eleven thousand, eleven hundred and eleven.

After writing each of the examples let the pupil numerate it.

QUESTIONS.

1. Of what does Arithmetic treat? When is it a science? When an art?

§ 2. How are numbers expressed? How many figures there? Name them. Is there any other way of repre ing numbers? What stands for one, two, three, &

are

§ 3. What does 0 express? What are the nine other fig.

ures called?

§ 4. Have we a separate character for ten? express ten?

How do we

To how many units 1 is it equal? May we consider it a single unit? Of what order?

§ 5. When two figures are written by the side of each other, what is the place on the right called? The place on the left?

§ 6. When units simply are named what units are meant? 7. Of what is the number 12 made up? Also, 18, 25, 37, 54, 89, 99.

§ 8. How do you express one hundred? To how many units of the 2d order is it equal? To how many of the first order? May it be considered a single unit? Of what order is it?

§ 9. With these combinations what numbers can be expressed? Of what is the number three hundred and seventy-five composed? The number eight hundred and ninetynine?

§ 10. To what are ten units of the 3d order equal? How do you express them? May this be considered a single unit? Of what order? May any number of figures be written in a row? When so placed what do you conclude ?

Which

§ 11. What is Notation? What Numeration? way do you numerate? What is the first place called? What the 2d? What the 3d: 4th, &c.

ADDITION OF SIMPLE NUMBERS.

§ 13. John has three apples and Charles has two; how many apples have they between them? Every boy will answer, five.

a2*

Here, the single apple is the unit, and the number five contains as many units as the two numbers three and two. The operation by which this result is obtained is called addition.

Addition is the uniting together of several numbers, in such a way, that all the units which they contain may be expressed by a single number.

single number is called the sum, or sum total numbers. Thus 5 is the sum of the sed by John and Charles.