ciation of two figures—thus, twenty, 20; thirty, 30; eightyfive, 85; ninety-nine, 99. These are called decimal numbers, from decem, Latin for ten. The numbers between a hundred and nine hundred and ninety-nine inclusive are, in like manner, expressed by three figures—thus, a hundred, 100; five hundred, 500; eight hundred and eighty-five, 885; nine hundred and ninety-nine, 999. Four figures express thousands; five, tens of thousands; six, hundreds of thousands; seven, millions; and so forth. Each figure, in short, put to the left hand of another, or of several others, multiplies that one or more numbers by ten. Or if to any set of figures a nought (0) be added towards the right hand, that addition multiplies the number by ten; thus 999, with 0 added, becomes 9990, nine thousand nine hundred and ninety. Thus it will be seen that, in notation, the rank or place of any figure in a number is what determines the value which it bears. The figure third from the right hand is always one of the hundreds; that which stands seventh always expresses millions; and so on. And whenever a new figure is added towards the right, each of the former set obtains, as it were, a promotion, or is made to express ten times its former value.
A large number is thus expressed in the Arabic numerals, every set of three from the right to the left hand being divided by a comma for the sake of distinctness.
The above number is therefore one thousand two hundred and thirty-four millions, five hundred and sixty-seven thousands, eight hundred and ninety. Higher numbers are expressed differently in France and England. In the former country, the tenth figure expresses billions, from which there is an advance to tens of billions, hundreds of billions, trillions, etc. In our country, the eleventh figure expresses ten thousands of millions, the next hundreds of thousands of millions, the next billions, etc. The two plans will be clearly apprehended from the following arrangement:—
| ENGLISH METHOD, | FRENCH METHOD, |
| Units. | Units. |
| Tens. | Tens. |
| Hundreds. | Hundreds. |
| Thousands. | Thousands. |
| Tens of thousands. | Tens of thousands, |
| Hundreds of thousands. | Hundreds of thousands, |
| Millions. | Millions. |
| Tens of millions. | Tens of millions. |
| Hundreds of millions. | |
| Thousands of millions. | Billions. |
| Ten thousands of millions. | Tens of billions. |
| Hundreds of thousands of millions. | Hundreds of billions. |
| Billions. | Trillions. |
| Tens of billions. | Tens of trillions. |
| Hundreds of billions, etc. | Hundreds of trillions, etc. |
SIMPLE OR ABSTRACT NUMBERS.
There are four elementary departments in arithmetic—Addition, Multiplication, Subtraction, and Division.
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| 27 |
| 5 |
| 536 |
| 352 |
| 275 |
| 1195 |
ADDITION is the adding or summing up of several numbers, for the purpose of finding out their united amount. We add numbers together when we say, 1 and 1 make 2; 2 and 2 make 4; and so on. The method of writing numbers in addition, is to place the figures under one another so that units will stand under units, tens under tens, hundreds under hundreds, etc. Suppose we wish to add together the following numbers— 27, 5, 536, 352,and 275; we range them in columns one under the other, as in the margin, and draw a line under the whole, Beginning at the lowest figure of the right-hand column, we say 5 and 2 are 7—7 and 6 are 13—13 and 5 are 18—18 and 7 are 25; that is, 2 tens and 5 units. We now write the five below the line of units, and carry or add the 2 tens, or 20, to the lowest figure of the next a column. In carrying this 20, we let the cipher go, it being implied by the position or rank of the first figure, and take only the 2; we therefore proceed thus—2 and 7 are 9—9 and 5 are 14—14 and 3 are 17—17 and 2 are 19, Writing down the 9, we proceed with the third column, carrying 1, thus—1 and 2 are 3—3 and 3 are 6—6 and 5 are 19. No more figures remaining to be added, both these figures are now put down, and the amount or sum of them all is found to be 1195. Following this plan, any quantity of numbers. may be summed up. Should the amount of any column be in three figures, still only the last or right-hand figure is to be put down, and the other two carried to the next column. For example, if the amount of a column be 127, put down the 7 and carry the other two figures, which are 12; if it be 234, put down the 4 and carry 23.
For the sake of brevity in literature, addition is often 'denoted by the figure of a cross, of this shape +. Thus, 7+6 means 7 added to 6; and in order to express the sum resulting, the sign =, which means equal to, is employed, as 7+6 =13; that is, 7 and 6 are equal to 13.
The Sign of Dollars is $. It is read dollars. Thus, $64 dollars is read 64 dollars; $5 is read 5 dollars. When dollars and cents are written, a period or point (.) is placed before the cents, or between the dollars and cents. Thus, $4.25 is read 4 dollars and 25 cents. Since 100 cents make $1.00, cents always occupy two places, and never more than two.
If the number of cents is less than 10 and expressed by a single figure, a cipher must occupy the first place at the right of the point. Thus, 3 dollars 6 cents are written $3.06; 1 dollar 5 cents are written $1.05. When cents alone are written, and their number is less than 100, either write the word cents after the number, or place the dollar sign and the before the number. Thus 75 cents may be expressed, $.75. In arranging for addition, dollars should be written dol-
