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As huns.
o tens
o units

In the number four hundred and six, there are 4 units of the 3d order, 0 of the 2d, and 6 of the 1st. It is written

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 thou. sand 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 ac. cording 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 hun. dreds; the fourth, the place of thousands, fc.

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, corroctly, when written, is called NUMERATION.

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Hundreds of Trillions
Tens of Trillions
Trillions

· Hundreds of Billions
Tens of Billions
Billions

· Hundreds of Millions

Tens of Millions
Millions

· Hundreds of Thousands
Tens of Thousands
Thousands

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Tens

coco ar os Units

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1

75 3

879 4

6, 02 5

82, 301 6

1 2 3, 08

7, 62 8, 7 3 5 8

43, 210, 460 9

5 48, 72 1, 087 10

6, 2 4 5, 289, 42 1 11

72, 5 4 9, 136, 8 2 2 12

8 94, 6 0 2, 043, 288 13

7, 641, 2 4 8, 90 7, 4 5 6 14

84, 912, 876,:41 0,2 8 5 15

912, 761, 2 57, 32 7, 8 2 6

6, 407, 212, 936, 876,5 4 1 17 57, 289, 678, 541, 297, 313 18 920, 323, 8 42, 768, 31 9, 675

* NOTE.—This Table is formed according to the French method of numoration. The English method gives six place to thousands, &c.

2

16

1st line

Six. 2

Seventy-five.
3

Eight hundred, and seventy-nine.
4

Six thousand and twenty-three.
5

Eighty-two thousand, 3 hundred and one. 6

123 Thousand and eighty-seven.
7

7 Millions, 628 thousand, 735.
8

43 Millions, 210 thousand, 460.
9

548 Millions, 721 thousand, and 87.
10

6 Billions, 245 millions, 289 thousand, 421.
11

72 Billions, 549 millions, 136 thousand, 822.
12

894 Billions, 602 millions, 43 thousand, 288. 13

7 Trillions, 641 billions, 248 millions, 907 thousand, 456. 14

84 Trillions, 912 billions, 876 niillions, 410 thousand, 285.
15

912 Trillions, 761 billions, 257 millions, 327 thousand, 820.
16 6 Quadrillions, 407 trillions, 212 billions, 936 millions, 876 thousand, 541.
17 57 Quadrillions, 289 trillions, 678 billions, 541 millions, 297 thousand, 313.
18 920 Quadrillions, 323 trillions, 842 billions, 708 millions, 319 thousand, 675.

The different lines of the table are thus read. counting from the right hand. ten separated into periods of three figures each,

To make the reading of figures easy, they are ofry, after which, the pupil may read the Table. ble to all numbers, and must be committed to memotable, units, tens, hundreds, &c. are equally applica

Ø 12. The words at the head of the numeration

EXAMPLES.

1. Write four, in figures.

Ans. 4. 2. Write four tens, or forty.

Ans. 40. 3. Write four hundred.

Ans. 400. 4. Write four thousand.

Ans. 4000. 5. Write forty thousand.

Ans. 40,000. 6. Write four hundred thousand. Ans. 400,000. 7. Write four millions.

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 thou. sand 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 ?

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

$ 3. What does 0 express ? What are the nine other fig. ures called ?

$ 4. Have we a separate character for ten? How do we express ten? To how many units 1 is it equal ? May we consider it a single unit ? Of what order?

$ 3. 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 ?

8 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 or. der is it?.

$ 9. With these combinations what numbers can be expressed? Of what is the number three hundred and seven. ty-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 ?

11. What is Notation ? What Numeration ? Which 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.

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 conmain may be expressed by a single number.

single number is called the sum, or sum total op numbers. Thus 5 is the sum of the

sed by John and Charles.

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