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When printed, they become,

1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

They have the following names:

1 is called One, or a Unit,
2 is called Two, or two Units,
3 is called Three, or three Units,
4 is called Four, or four Units,
5 is called Five, or five Units,
6 is called Six, or six Units,
7 is called Seven, or seven Units,
8 is called Eight, or eight Units,
9 is called Nine, or nine Units,

0 is called Naught, Cipher, or Zero.

Each of these characters, except the zero, is called a digit*; and the first nine, when taken together, are called the nine digits.

Any digit is called a significant figure.

What is numeration? How is the common method sometimes called? In this method how many characters are employed? What are the names of these char acters? What are called digits? What is a significant figure?

3. The significant figures have unchanging values; that is, they always represent units or ones; but the units which they represent differ in value.

When a significant figure stands disconnected from other figures, the value of its unit is called its simple value. When such figure stands in connection with other figures, the value of its unit will depend upon the place which it occupies, and is therefore called its local value.

Thus, in the number 3456, which consists of four sig.

* From the Latin, digitus, a finger; because the ancients used to do then reckon on their fingers. Originally 10 was also called a digit...

nificant figures standing in connection with each other, each figure expresses units; but units of different values. The right-hand figure, 6, expresses six units, whose value is their simple value; that is, each unit is a single one. The second figure, 5, expresses five units; but each unit is ter times greater than each unit of the first figure; therefore the 5 may be read 5 tens, equal to fifty units of simple value. The units expressed by the third figure, 4, are ten times greater than the units expressed by the second figure, and one hundred times greater than those expressed by the first figure; the third figure is therefore read 4 hundreds. The last figure, 3, expresses units ten times greater than the units in 4, and one thousand times greater than the units in 6, and is read 3 thousands.

Hence this property:

When figures are connected in a line as in the number 3456, the units which they express are said to be of different orders. Thus, 6 occupies the first place, and its units are of the first order, that is, they have their simple value. The 5 occupies the second place, and its units are of the second order, or tens. The 4 occupies the third place, and its units are of the third order, or hundreds The 3 occupies the fourth place, and its units are of the fourth order, or thousands. Hence the above number is three thousand four hundred and fifty-six.

To numerate and read the numbers in the following table, proceed thus: Begin with the upper line 3. The first place only being occupied, you numerate Units. Then read, three units, or simply three. In the second line two places are occupied-then numerate Units, Tens-read fifty-four. In the third line three places are occupied; then numerate Units, Tens, Hundreds-read two hundred and sixty-seven, and so proceed.

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4. In the preceding table no 0 occurs. -ter, 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 significant 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 thou sands, must be read twenty thousand four hundred and six.

Does the value of figures change? What do they always represent ? Do their units 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 make of the zero? What figures do we read?

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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

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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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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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