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T'he following is the manner of writing the numbers from nine to ninety-nine, inclusive.

The first column contains thy figures, the second shows tiie

proper mode of expressing them in words and the way in which they are always to be understood, and the third contains the names which are comronly applied. The common names are expressive of their signification, but not 80 much so as those in the second column. Figures.

Proper mode of expressing Common Names.

them in words.
10.
One Ten or simply Ten.

Ten.
11.
Ten and one.

Eleven.
Ten and two.

Twelve.
13.
Ten and three.

Thirteen.
14.
Ten and four.

Fourteen.
15.
Ten and five.

Fifteen.
16.
Ten and six.

Sixteen.
17.
Ten and seven.

Seventeen.
18.
Ten and eight.

Eighteen.
19.
Ten and nine.

Nineteen.
20.
Two tens.

T'wenty.
21.
Two tens and one.

Twenty-one.
22.
Two tens and two.

Twenty-two.
23.

Two tenis and three. Twenty-three. 24.

Two tens and four. Twenty-four.
25.

Two tens and five. Twenty-five.
26.
Two teus and six.

T'wenty-six.
27.

Two tens and seven. Twenty-seven. 29.

Two tens and eight. Twenty-eight. 29.

Two tens and nine. 'I'wenty-nine.
30.
Three tens.

Thirty
31.

Three tens and one. Thirty-one.
32, &c. Three tens and two. Thirty-two.
40.
Four rens.

Forty.
41, &c,
Four tens and one.

Forty-one.
50.
Five tens.

Fifty.
&c
Five tens and one.

Fifty-one.
60.
Six tens.

Sixty.
61, &c.
Six tens and one.

Sixty-one.
0.
Seven tens.

Seventy.
71, &c.

Seven tens and one, Seventy-one.
80.
Eight tens.

Eighty
81, &c.

Eight tens and one. Eighty-one.

51,

Figures

Proper mode of expressing Common Names.

them in words. 90. Nine tens.

Ninety. 91, &c. Nine tens and one.

Ninety-one. 19.

Nine tens and nine. Ninety-nine. Nine tens and nine or ninety-nine is the largest number that can be expressed by two figures. If one be added to nine tens and nine, it makes ten tens, or one hundred. To express one hundred we use the first figure again ; but in order to show that it has a new value, it is put in another place, which is called the hundreds' place. The hundreds' place is the third place counting from the right. One hundred is written, 100; two hundred is written, 200; three hundred is written, 300. The zeros on the right have no value; their only purpose is to occupy the two first places, so that the figures 1, 2, 3, &c. may stand in the third place.

The figures in the second place, we observe, have the same value whether the first place bc occupied by a zero or by a figure : for exanıple, in 20 and in 23 the 2 has precisely the same value; it is two tens or twenty in both. In the first there is nothing added to the twenty, and in the second three is added to it.

It is the same with figures in the third place. They have the same value, whether the two first places are occu pied by zeros or figures. In 400, 403, 420, and 435, the 4 has the same value in each, that is four hundred. The value of every figure, therefore, depends upon its place as counted from the right towards the left

. A figure standing in the first place signifies so many units; the same figure standing in the second place signifies so many tens; and the same figure standing in the third place signifies so many hundreds. For example, 333, the three on the right signifies three units, the three in the second place signifies three tens or thirty, and the 3 in the third place signies three hundreds. The number is read three hundreds, three tens, and three, or three hundred and thirty-three. We have seen that all the numbers from ten to twenty, from twenty to thirty, &c. are expressed by adding units to the tens ; m the same manner all the numbers from one hundred to two hundred, from two hundred to three hundred, &c. are expressed by addmg tens and units to the hundreds. For example, to express live hundred and eighty-two, we write five hundreds, eight tens, and two units thus, 582.

The largest number that can be expressed by three figures is 999, nine hundreds, nine tens, and nine units, or nine hundred and ninety-nine. If to this we add one unit more, we have a collection of ten hundreds, which is called one thousand. To express this, the 1 is used again ; but to show that it expresses I thousand it is written one place farther to the left, that is, in the fourth place, thus 1000. Two thousand is written 2000, and so on, to nine thousand, which is written 9000. The intermediate numbers are expressed by adding hundreds, tens, and units to the thousands.

It is easy to see that this manner of expressing numbers may be continued to any extent. Every time a figure is removed one place to the left its value is increased ten-fold, and since nothing limits the number of places which we may use, there can be no number conceived, however large, which cannot be expressed with these nine characters.

We sometimes call the figures in the first place or right hand place, units of the first orilor ; those in the second place, or the collection of tens, units of the second order ; those in the third place, or the collection of hundreds, units of the third order, &c.

The following table exhibits the first nine places or orders, with their names, and contains a few examples to illustrate them.

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116

ARITHMETIC.

Part 2

9th or hdrs. of mills'. place.
8th or tens of mills'. place.
7th or millions' place
6th or hdrs, rif thous'. place.
5th or tens of thous'. place.
Ath or thousands' place.
3rd or hundreds' place.

2d or tens' place. si Ist or units' place.

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Seven nnits or sevon
Three tens, or thirty

3 Four tens and six units, or forty-six

46 Eight hundreds

800 Seven hundreds and three units, or seven hundred and three

703 Five hundreds and four tens, or five hundred and forty

5410 Six hundreds, five tens, and eight units, or six I undred and fiiy-eight

6 518 Six thousands

6101010 Six thousands and five units

60 Six thousands and four tens, or six thousand and forty

610140 Six thousands and four tens and five units, or six thoue',nd and forty-five

6045 Six thouseads and seven hundreds

6700 Six thousand, seven hundred, and five

67 Six thousund, seven hundred, and forty

67 Six thousand, seven hundred, and forty-five

67 Four tens of thousands, or forty thousand Forty thousand and three

4,010 03 Forty thousand, five hundred and three

401503 Forty-seven thousand, five hundred, and eighty three

4 75 8/3 Four hundred and twenty-six thousand, eight hundred and fifty-three

4261853 Ihree hundred and twenty-eight millions,

four hundred and thirty-five thousand, six hundred and eighty-seven

32814 51687 Three liundred millions

30

0 0 0 Twenty millions

0010010 Eight millions Four hundred thousand Thirty thousand

30101010 Five tho'isand

010 Six hundred Eighty Seven

In looking orer the above examples it will be observed, that the three first places on the right have distinct names,

iz. units, tens, hundreds; and that the three next places are all called thousands, the first being called simply tłuusands ; the second, tens of thousands; the third, hundreds of thousands. In the same manner there are three places appropriated to millions, and distinguished in the same way, viz. millions, tens of millions, hundreds of millions. The same is true of all the other names, three places being appropriated to each name. From this circumstance it is usual to divide the figures into periods of three figures each. This division very much facilitates the reading and writing of large numbers. Indeed it enables us to read a number consisting of any number of figures, as easily as we can read three figures. This is illustrated in the following example.

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Co Hundreds

Tens
er Units
o Hundreds
v Tens
co Units
u Hundreds

Hundreds
or Tens
© Units
- Hundreds
az Tens
co Units
HA Hundreds
o Tens

Units
Tens

Units
o Hundreds
i Tens

Units

3 8 5, 6 9 9,2 5 8,6 7 3,4 6 2,9 2 7,6 4 8 We have only to make ourselves familiar with reading and writing the figures of one period, and we shall then be able to read or write as many periods as we please, if we know the names of the periods.

It is to be observed that the unit of the first period is simply one; the unit of the second period is a collection of a thousand simple units; the unit of the third period is a collection of a thousand units of the second period, or a mil lion of simple units; and so on as we proceed towards the left, each period contains a thousand units of the period next preceding it.

The figures of each period are to be read in precisely the same manner as the figures of the rig.c hand period. At the end of each period, except the right hand period, the name of the period is to be pronounced. The right hand

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