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NUMERATION TABLE.

| Ninth. Hund. of Mill.
Eighth. | Tens of Mill.

Hund. of Th’s.
Seventh. Millions.
Fifth. | Tens of Th’s.

Hundreds.

Units.
· Fourth. Thousands.

Second. Tens.
Sixth.

Third.
w First.
·
·

PLACE OR ORDER.

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..... 3 Units—three.
.... 5 4. Units, Tens-fifty-four.

2 6 7 Units, Tens, Hundreds
.. 7 4 38 -two hundred and

9 1 2 sixty-seven ; and so
4 3 2 6 5 4 proceed.
.. 6 3 5 7 4 2 1
in 6 8 2 4 6 9 8

6 8 5 7 3 1 9 7 5 4. In the preceding table no O occurs. This character, unlike the digits, represents the absence of number. It is used to fill places where no value is to be expressed, and thus to cause the significant figures to occupy those places in which they will express the intended values Thus, 2, standing alone, means 2 units of the first order or of simple value; but 20 means 2 units of the second order, and no units of the first order; that is, 20 is the ex pression for 2 tens, or twenty. In the same way, 200 means 2 units of the third order, no units of the second order, and no units of the first order; that is, 200 is the expression for two hundred.

Hence, a zero placed at the right-hand of a significanı figure, increases the simple value of its units tenfold. Two zeros placed at the right-hand of a significant figure in

crease the simple value of its units ten times tenfold, or a hundred-fold. Three zeros a thousand-fold, and so on; every additional zero increases the preceding value tenfold.

In reading numbers containing zeros, we read only the significant figures. Thus the number 20406, consisting of 6 units, no tens, 4 hundreds, no thousands, 2 ten thouBands, must be read twenty thousand four hundred and six.

Does the value of figures change? What do they always represent ? Do their nnits differ in value? What is the local value of a unit? When significant figures are connected together, what value has the unit of the right-hand figure? What the unit of the second figure, &c. ? Give an illustration. When a figure occupies the first place, of what order are its units, &c. ? Repeat the Numeration Table. What do you mean by the place of a figure? What by the order of its units ? What does the zero represent ? For what purpose is it used ? What effect has it on the units of the significant figures with which it is connected? What effect have two zeros ? What effect has every additional zero? In reading numbers, what use do we mako of the zero? What figures do we read ?

EXAMPLES.

Numerate and read the annexed numbers : Also, write down the following

205

1 2 3 7 numbers under each other, so

29 8 3 5 that units may stand under

1 0 2007 units, tens under tens, hundreds 6 3 0 0 0 6 9 under hundreds, &c.

5 4 1 2 8 9 0 0

1 6 5 1 2 3 4 5 6 y Seventy-three. Three hundred and thirty-seven. Eight thousand six hundred and one. Ninety-seven thousand three hundred and forty-three. Three hundred thousand, five hundred and eleven. Six millions, one thousand and twenty-five. Forty-three millions and seventeen. Two hundred and thirty-three millions and ten thousand.

5. Thus far we have shown how to numerate and read numbers which do not contain more than nine places

of figures. When there are more than nine places of figures, it will be convenient to divide them into periods of three figures each, as in the following

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Hundreds of Septillions.
Tens of Septillions.
Hundreds of Sextillions.
Tens of Sextillions.
Hundreds of Quintillions.
Hundreds of Quadrillions.
Tens of Quintillions.
Septillions.
Tens of Quadrillions.
Quintillions.
Sextillions.
Quadrillions.
Hundreds of Trillions.
Tens of Trillions.
Hundreds of Billions.
Hundreds of Thousands.
Tens of Billions.
Hundreds of Millions.
Tens of Millions.

&c.
Trillions.
Tens of Thousands.
Billions.
Millions.
Thousands.
Hundreds.

Tens.
il Units.
&c.

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By this table we discover that each period, or group of three figures, takes a new name, by which means the numeration of all numbers is made to depend upon that of three figures.

6. The above method of numerating, by giving to each period of three figures an independent name, is due to the French. There is another method, sometimes used, called the English method. It consists in giving a new name to each period of six figures. The French way is the sim

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467743486921785412123456489

45654213400100205437
633456267489136545
75456278327005717
3478567321752005

1347835674116

periods of three figures, the following numbers : et him be required to numerate and read, by dividing into

7. After the pupil has carefully examined this table,

How many do the English connect in a period? Which method is to be preferred ?

By the French method of numerating, how many figures are connected in a period !

ENGLISH METHOD.

FRENCH METHOD.
Hunds. of Thous. of Quadrillions. ( Hundreds of Octillions.
Tens of Thous. of Quadrillions.

Tens of Octillions.
Thousands of Quadrillions. . . Octillions.
Hundreds of Quadrillions...

Hundreds of Septillions.
Tens of Quadrillions. . . W Tens of Septillions.
Quadrillions. . . : :...

W ) Septillions.
Hunds. of Thous. of Trillions.

Hundreds of Sextillione
Tens of Thousands of Trillions.

Tens of Sextillions.
Thousands of Trillions. . . . w ) Sextillions.
Hundreds of Trillions. . . .

Hundreds of Quintillions.
Tens of Trillions. . . . . . . W Tens of Quintillions.
Trillions. . . . . . . . . . ) Quintillions.
Hunds. of Thous. of Billions. . . ) Hundreds of Quadrillions.
Tens of Thous. of Billions... W Tens of Quadrillions.
Thousands of Billions . ..

Quadrillions.
Hundreds of Billions. ...

| Hundreds of Trillions.
Tens of Billions. . . .

w Tens of Trillions.
Billions. . i

w Trillions.
Hunds. of Thous. of Millions. w Hundreds of Billions.
Tens of Thousands of Millions.

Tens of Billions.
Thousands of Millions. . . . w Billions.
Hundreds of Millions. . . .

Hundreds of Millions.
Tens of Millions. . . . . .

Tens of Millions.
Millions..

W Millions.
Hundreds of Thousands. . . . Hundreds of Thousands.
Tens of Thousands. . . . . .

Tens of Thousands.
Thousands.

Thousands.
Hundreds. . . . . . . . . ) Hundreds.
Tens. . . . . . . . . . . > Tens.
Units. . . . . . . . . ( Units

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TABLE.

methods at one view in the following pler, and is generally adopted. We will exhibit the two

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Let him also separate them into periods of six figures, According to the English method, and then numerate and ead them.

It will be seen, by reference to the foregoing tables, nat the French and English methods of numeration agrce as far as nine places of figures, which is as far as we generally wish to extend numbers in the ordinary business operations of life. Numbers could be chosen which should be widely different, and still would be read precisely the same by the two methods. For instance, the French method of reading 103900000000000 is the same as the English method of reading 103000900000000000000, each reading being one hundred and three trillions, nine hundred billions.

The same is the case with infinite other numbers which might be selected. Hence the importance of knowing which system of numeration is employed. Twenty billions in the English system is a tho' sand times twenty billions in the French system.

ROMAN NOTATION.

8. The Romans, as well as many other nations, expressed numbers by certain letters of the alphabet. The Romans made use of only seven capital letters, viz. : I foi one ; V for five ; X for ten; L for fifty ; C for one hundred , D for five hundred ; M for one thousand. The other num bers they expressed by various repetitions and combinations of these letters, as in the following

TABLE.

1 expressed by I. 2 6 6 II.

As often as any character is repeated, so many

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