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it expresses by having other figures placed on its right. Hence the local value of a figure depends on its locality, or the place which it occupies in relation to other numbers with which it is connected. (Art. 8.)

Obs. 1. This system of notation is called Arabic, because it is supposed to have been invented by the Arabs.

2. It is also called the decimal system, because numbers increase in a tenfold ratio. The term decimal is derived from the Latin word decem, which signifies ten.

11. The art of reading numbers when expressed by figures, is called NUMERATION.

The pupil has already become acquainted with the names of numbers, from one to a thousand. He will now easily learn to read and express the higher numbers in common use, from the following scheme, called the

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12. The different orders of numbers are divided into periods of three figures each, beginning at the right hand. The first, which is occupied by units, tens and hundreds,

Quest.--11. What is numeration ? Repeat the Numeration Table, beginning at the right hand. What is the first place on the right called ? The second place? The third ? Fourth? Fifth ? Sixth ? Seventh ? Eighth ? Ninth? Tenth, &c.? 12. How are the orders of numbers divided? What is the first period called? By what is it occupied ? What is the second called? By what occupied ? What is the third called ? By what occupied? What is the fourth called ? By what occupied ? What is the fifth called ? By what occupied ?

is called units' period; the second is occupied by thousands, tens of thousands and hundreds of thousands, and is called thousands' period, &c.

The figures in the table are read thus : Three hundred and forty-two trillions, nine hundred and seventy-five billions, eight hundred and ninety-seven millions, six hundred and forty-five thousand, four hundred and thirty-two.

13. To read numbers which are expressed by figures.

Point them off into periods of three figures each ; then, beginning at the left hand, read the figures of each period in the same manner as those of the right hand period are read, and at the end of each period, pronounce its name.

Obs. 1. The learner must be careful, in pointing off figures, always to begin at the right hand; and in reading them, to begin at the left hand.

2. Since the figures in the first or right hand period always denote units, the name of the period is not pronounced. Hence, in reading figures, when no period is mentioned, it is always understood to be the right hand, or units' period.

EXERCISES IN NUMERATION. Note. At first the pupil should be required to apply to each figure the name of the place which it occupies. Thus, beginning at the right hand, he should say, “ Units, tens, hundreds,” &c., and point at the same time to the figures standing in the place which he mentions. It will be a profitable exercise for young scholars to write the examples upon their slates or paper, then point them off into periods, and read them.

Quest.–13. How do you read numbers expressed by figures ? Obs. Where begin to point them off? Where to read them ? Do you pronounce the name of the right hand period ? When no period is named, what is understood ?

Read the following numbers : Ex. 1.

127 11. 75407 21. 5604700 2. 172 12. 125242 22. 2020105 3. 721 13. 240251 23. 45001003 4. 520

14. 407203 24. 30407045 5. 603 15. 300200

25.

145560800 6. 4506 16. 1255673 26. 8900401 7. 7045 17. 5704086 27. 250708590 8. 8700 18. 207047 28. 803068003 9. 25008 19. 2605401 29. 2175240670 10. 40625 20. 4040680 30. 7240305060 31.

45290100300 36. 13657240129698 32. 160000050000 37. 98609006006906 33.

7005003007 38. 80079401697000 34. 101279200361 39. 167540000000465

1143206000675 40. 504069470300400 14. The method of dividing numbers into periods of three figures, is the French Nurneration. The English divide numbers into periods of six figures. The French method is the more simple and convenient. It is generally used throughout the continent of Europe, as well as in America, and has been recently adopted by some English authors.

EXERCISES IN NOTATION.

35.

Write the following numbers in figures :
1. Twenty-seven. Ans. 27.
2. Seventy-two. Ans. 72.
3. One hundred and twenty-five.
4. Three hundred and fifty-two.
5. Two hundred and four. Ans. 204.
6. One thousand and forty-two. Ans. 1042.
7. Thirty thousand nine hundred and seven.

Ans. 30907. OBs. It will be observed, that in the 5th example no tens are men. tioned ; no hundreds in the 6th, &c.; and that these places in the answers are filled by ciphers. In all cases when any intervening order is omitted in the given example, the place of that order in the answer must be filled by a cipher. Hence,

15. To express numbers by figures.

Begin at the left hand, and write in each order the figure which denotes the given number in that order.

If any intervening orders are omitted in the proposed number, write ciphers in their places.

8. Forty-six thousand and four hundred. 9. Ninety-two thousand, one hundred and eight. 10. Sixty-eight thousand and seventy.

11. One hundred and twenty-four thousand, six hundred and thirty.

12. Two hundred thousand, one hundred and sixty. 13. Four hundred and five thousand and forty-five. 14. Three hundred and forty thousand. 15. Nine hundred thousand, seven hundred and twenty. 16. One million and seven hundred thousand.

17. Thirty-six millions, twenty thousand, one hundred and fifty

18. One hundred millions and forty-five. 19. Mercury is thirty-seven millions of miles from the

sun.

20. Venus, sixty-nine millions.
21. The Earth, ninety-five millions.
22. Mars, one hundred and forty-five millions.
23. Jupiter, four hundred and ninety-four millions.
24. Saturn, nine hundred and seven millions.

25. Herschel, one billion, eight hundred and ten millions.

26. Seven billions, nine hundred millions and forty thousand.

27. Sixty billions, seven millions and four hundred.

28. One hundred and thirteen billions, six hundred and fifty thousand

29. Four hundred and six billions, eighty millions and seven hundred.

30. Twenty-five trillions and ten thousand.

QUEST.-15. How are numbers expressed by figures? If any intervening order is omitted in the example, how is its place supplied ?

SECTION II.

ADDITION.

MENTAL EXERCISES.

more :

Art. 16. Ex. 1. George bought a slate for 9 cents, a sponge for 6 cents, and a pencil for 1 cent : how many cents did he pay for all ?

Obs. To solve this example, we must add together the number of cents which he paid for the several articles. Thus, 9 cents and 6 cents are 15 cents, and 1 cent more makes 16 cents. Ans. He paid 16 cents.

2. Henry gave 8 cents for a writing-book, 6 cents for an inkstand, and 4 cents for some quills : how many cents did he give for all ?

3. Sarah obtained 4 credit marks yesterday, 3 the day before, and 5 to-day: how many credit marks has she in all ? 4. John had 6 peaches, and his mother gave him 10 how

many peaches had he then ? 5. Harriet has 7 pins ; she has given away 4, and lost 2 : how many pins had she at first ?

6. If a quart of cherries is worth 5 cents, a pound of figs 9 cents, and a lemon 4 cents : how much are they all worth?

7. Joseph paid 6 cents for some raisins, 7 cents for a top, and 3 cents for some fish-hooks: how many cents did he pay

for all ? 8. Mary has 9 white roses and 8 red ones : how many roses has she in all ?

9. A beggar met four men, one of whom gave him 3 shillings, another 2, another 1, and the last 5 shillings: how many shillings did the beggar receive ?

10. A farmer sold 4 bushels of apples to one customer, 6 to another, 5 to a third, and 2 to a fourth : how many bushels did he sell ?

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