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Q. What are they?
A. Simple and local.

Q. Now, as it takes 10 units to make one ten, or one in the next leftband place, and 10 tens to make 100, how do figures appear to increase by being removed one place farther to the left ?

A. In a tenfold proportion, from right to left.

You must have acquired, by this time, some considerable knowledge of figures : let me examine you a little ; and, in the first place, let me see you write down on the slate the figure 4.

Q. What do you call it ?
A. 4 units.
Write at the left of the 4, the figure 3, (thus, 34.)
Q. What do you call them both, and how are they read ?
A. 4 units and 3 tens read thirty-four.
Write at the left of the 31 the figure 8, (thus, 834.)
Q. What do you call the three figures now, and how are they read ?

A. 4 units, 3 tens, and 8 hundreds, read eight hundred and thirty-four.

Write at the left of 831 the figure 1, (thus, 1834.)
Q. What do you call the 4 figures now, and how read ?

A. 4 units, 3 tens, 8 hundreds, and 1 thousand, read one thousand eight hundred and thirty-four.

Q. We have now heen combining, or placing figures iogether, till we have obtained the number 1834, representing the number of years it is since Christ appeared on earth, 10 the present time. We might continue to put ligures together in this way, that would express higher numbers still, up to billions, &c. That you may be able to form some idea of the power of figures, let me tell you that there is not a billion of seconds in thirty thousand years; notwithstanding there are 60 seconds in every minute, 60 minutes in every hour, 24 hours in every «lay, and in a solar year, 365 days, 5 hours, 48 mimies, and about 48 seconds. Should we continue to go on as we began, in combining more figures still, it would be very inconvenient: to avoid this, we have a rule by which we can read almost any number of figures, ever so large. What is this rule called ?

A. Numeration.

Q. What is the reading or 'expressing a number by figures, as now shown, called ?

A. Notation or Numeration.

RULE.

Q. From the above illustrations, how does it appear that you must begin to numerate ?

A. Begin at the right hand.
Q. At which hand would you begin to read ?
A. The left.

Q. What is the first figure at the right hand, or first place, caned ?
A. Units.
Q. What is the second figure, or second place, called ?
A. Tens.
Q. What is the third place called ?
A. Hundreds.
Q. What is the fourth place called ?
A. Thousands.

Q. In reading, what value do you give those figures which were called units in numerating ?

A. Units.
Q. What value do you give tens ?
A. Tens.
Q. What value do you give hundreds, thousands, &c.?
A. Hundreds, thousands, &c.

Q. Will you repeat the Numeration Table, beginning with units, tens, &c.?

NUMERATION TABLE.

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do Hundreds of millions.

BILLIONS.

Hundreds of thousands.
ĆU O O Tens of millions.

o MILLIONS.
oo Tens of thousands.
O THOUSANDS.

Hundreds.
Tens.
UNITS.

Q. A А. Q. A.

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Q. A. Nur

0 0 0 0 0 0 0 0 0 , read-1 Billion.
2 0 0 0 0 0 0 0 0 read-200 Million.
30 0 0 0 0 0 0

read-30 Million.
4,000 0 0 0 read-4 Million.
5 0 0 000, read~500 Thousand.
6 0,000, read-60 Thousand.
7,000 read-7 Thousand.

0 0 read —8 Hundred.
90, read-Ninety.

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Q. A.

1, readOne.

tens,

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Or, more commonly, thus,

Hundreds of millions.
e Hundreds of thousands.
co Tens of millions.

BILLIONS.
MILLIONS.

Tens of thousands.
W THOUSANDS.

Hundreds.
♡ Tens.

Units.

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1, 2 3 4, 5 6 7, 8 9 1, Which, by putting their values together, are read thus : One billion, two hundred and thirty-four million, sle hundred and sixty-seven thousand, eight hundred and ninety-one.

Questions on the Table. Q. What is tne value of 9 with one cipher on the right of it? What the value of 8 with two ciphers ? Of 7 with three cipliers? Of 6 with four ciphers ? Of 5 with five ciphers ? Of 4 with six ciphers? or 3 with seven ciphers ? Of 2 with eight ciphers ? Or 1 with nine ciphers ?

Q. What is the meaning of annex ?
A. To place after.
Q. What is the meaning of prefix ?
A. To place before.
kr Let the scholar write down, in figures, the answers to the following
questions on his slate at recitation.

Q. How much does 1, with 1 cipher annexed, stand for?
A. Ten.
Q. Why?
A. Because the 1 is tens, when I numerate.
Numerate the 10, and see.
Q. What does l' with 3 ciphers stand for?
A. One thousand.
Q. Why?

A. Because, when I numerate, by saying 'Units, tens, hundreds, thousands,' the 1 comes thousands.

Q. What does 5 with five cipliers stand for?
A. Five hundred thousand.

e Hundreds of

Q. Why?

A. Because, when I numerate, the 5 comes hundreds of thousands.

Numerate and see.
Q. What does & with 6 cipliers stand for?
A. 8 millions.
Q. Why?
A. In numerating, the 8 comes millions.
Numerate and see.
Q. How do you read the figures 624 ?
A. Six hundred and twenty-four.
Q. Why do you say 6 hundred ?
Q. What do the figures 6278 stand for?
A. Six thousand two hundred and seventy-cight.
Q. How do you know that the 6 is 6 thousand ?

Q. How do you read the figures 56768 ? How do you read the figures 27365? How do you read the figures 654212 ?

Express in words the following numbers.
Note. The pupil may learn the value of each succeeding number by a

8 Eight.
9
30 - Thirty.
70
239=Two hundred and thirty-nine.
029
5005=Five thousand and five.
7007
30002=Thirty thousand and two.
50009

[nine.
623029=Six hundred twenty-three thousand and twenty.
928028
6000066 Six million and sixty-six.
8000099
75000100=Seventy-five million and one hundred.
83000800

former one.

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Express in figures the following numbers.
Sixty.-One hundred and twenty-five.
Three thousand three hundred and thirty-three.

Three million, three hundred thirty-three thousand, Wiree hundred and thirty-liree.

Thirty million.
Three hundred million and twenty-five.

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Q. Will you repeat the following

NUMERATION TABLE?

et Hundreds of quintillions.*

Tens of quintillions.
et QUINTILLIONS.
c7 Hundreds of quadrillions.
C Tens of quadrillions.
OF QUADRILLIONS.
er Hundreds of trillions.
er Tens of trulions.

TRILLIONS.
er Hundreds of 2.lions.
or Tens of billions.
er lundreds of millions.
co BILLIONS.
e Tens of milions.
o Hundreds of thousands.
6 MILIONS.
er Tens of thousands.
CT THOUSANDS.
er Hundreds.
er Tens.

UNITS.

5 5 5,5 5 5,5 5 5, 5, 5,555, 5 5 5.

Q. Will you now repeat the combined value of each figure 5 which is prefixed to the foregoing Table?

A. Five hundred and fifty-five quintillion, five hundred and fifty-five quadrillion. five hundred and fifty-five trillion, five hundred and fifty-five billion, five hundred and fifty-five million, five hundred and fifty-five thousand, five hundred and fifty-five.

SIMPLE ADDITION, 1 VII. 1. You bought an orange for 9 cents, and a melon for 15 cents; what did you pay for both ?

2. James bought a top for 6 cents, a knife for 12 cents, and an irkstand for 8 cents; how much did they all come to

3. Harry and James lost some money ; James lost 20 cents, and Harry 12; how much did both lose?

4. A bry laid out 10 cents in marbles, 8 cents in quills, and 6 cents for a slate pencil; how much did he lay out in all ?

5. You give 40 cents for a Practical Arithmetic, 8 cents for a ruler, 9 cents for an inkstand, and lose 6 cents, how much money has gone from you?

6. A man gave his children money in the following mander; to his oldest 3 dollars, to James 5 dollars, to Thomas 9 dollars, and to his two daughters 4 dollars apiece; how much did he give away? * In like runner we may go from uintillions to sectillions, septillioni, ucendo tions, norillions, decillions, uriccillions, duodecillions, &c.

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