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Here any figure in the first place, reckoning from right to left, denotes only its simple value; but that in the second place, denotes ten times its simple value; and that in the third place a hundred times its simple value; and so on; the value of any successive place being always ten times its former value.

Thus in the number 1834, the 4 in the first place denotes only four units, or simply 4; 3 in the second place signifies three tens, or thirty; 8 in the third place signifies eighty tens or eight hundred; and the 1, in the fourth place, one thousand ; so that the whole number is read thus,-one thousand eight hundred and thirty-four.

As to the cipher, 0, though it signify nothing of itself, yet being joined to the right hand of other figures, it increases their value in a tenfold proportion; thus 5 signifies only five, but 50 denotes 5 tens or fifty; 500 is five hundred; and so on.

NOTE. The idea of number is the latest and most difficult to form. Before the mind can arrive at such an abstract conception, it must be familiar with that process of classification, by which we successively remount from individuals to species, from species to genera, from genera to orders. The savage is lost in his attempts at numeration, and significantly expresses his inability to proceed, by holding up his expanded fingers or pointing to the hair of his head. See Lacroix.

NUMERATION TABLE.

317,897;431,032; 639,864; 361,316; 461,315; 123,675; 816,131; 123,456; 123,614; 315,131; 398,832; 563,871; 251,615; 123,561.

Thousands.

Tridecillions.

In order to enumerate any number of figures, they must be separated by semicolons into divisions of six figures each, and each division by a comma, as in the annexed table. Each division will be known by a different name. The first three figures in each division will be so many thousands of that name, and the next three will be so many of that name, that is over its unit place. The value of the numbers in the annexed table, expressed in words, Undecillions. is Three hundred and seventeen thousand,

Thousands.

Duodecillions.

Thousands.

Thousands.
Decillions.

Thousands.

Nonillions.

Thousands.

Octillions.

Thousands.

Septillions.

Thousands.

Sextillions.

Thousands.
Quintillions.

Thousands.
Quatrillions.
Thousands.

Trillions.
Thousands.

Billions.
Thousands.

Millions.

Thousands.

Units.

eight hundred and ninety-seven tridecillions; four hundred and thirty-one thousand, thirty-two duodecillions; six hundred thirty-nine thousand, eight hundred sixtyfour undecillions; three hundred sixty-one thousand, three hundred sixteen decillions; four hundred sixty-one thousand, three hundred fifteen nonillions; one hundred twenty-three thousand, six hundred seventy-five octillions; eight hundred sixteen thousand, one hundred thirty-one septillions; one hundred twenty-three thousand, four hundred fifty-six sextillions; one hundred twenty-three thousand, six hundred fourteen quintillions; three hundred fifteen thousand, one hundred thirty-one quatrillions; three hundred ninety-eight thousand, eight hundred thirty-two trillions; five hundred sixty-three thousand, eight hundred seventy-one billions; three hundred fiftyone thousand, six hundred fifteen millions; one hundred twenty-three thousand five hundred sixty-one.

NOTE.-The student must be familiar with the names, from Units to Tridecillions, and from Tridecillions to Units, so that he may repeat them with facility either way.

The following Table is the French method of Enumeration.

Tridecillions.
Duodecillions.

Undecillions.

Decillions.
Nonillions.

Octillions.
Septillions.

Sextillions.
Quintillions.

Quatrillions.

Trillions.

Billions.

Millions.
Thousands

Units.

By the annexed table it will be seen, that every three figures have a different name. Their value would be expressed thus: Eight hundred nine tridecillions, three hundred and seventeen duodecillions, one hundred twenty-three undecillions, five hundred eighty-six decillions, three hundred fifteen nonillions, eight hundred sixty-one octillions, eight hundred thirty-one septillions, five hundred sixty-one sextillions, seven hundred eighty-six quintillions, eight hundred eleven quatrillions, one hundred twenty-three trillions, four hundred fifty-six billions, six hundred seventeen millions, eight hundred thirty-one thousand, five hundred and fifteen.

NOTE. It is very doubtful, whether the French method is so good as that of the English.

Let the following numbers be written in words.

76

809,317,123,586,315,861,831,561,786,811,123,456,617,831,515.

[blocks in formation]

3;469,200;000,000;111,111;100,000;001,101

7;006,437;576,589;081,828;384,859;091,929;394,332

71,326;436,035;769,846;012,131;415,161;718,192;021,223

712,642,976,403;796,411;604,220;404,263;575,068;076,001

170,907;642,376;756,809;000,604;020,760;307,000;100,000

Let the following numbers be written in figures.

1. Twenty-nine.

2. Four hundred and seven.

3. Twenty-three thousand and twenty-seven.

4. Five million two thousand and five.

5. Seventeen trillion two hundred million and six.

6. Fifteen billions twenty-seven thousand million nine thousand two hundred and five.

7. Seven billions, five millions, six thousand, five hundred and twenty-five.

8. Ninety-nine trillions, seventy-nine thousand six hundred billions, one hundred and twenty-four millions, three hundred and twenty-nine.

9. Fifteen quintillions, thirty-three thousand millions, seventysix thousand and five.

10. Eight thousand five hundred and forty-three septillions, five quintillions, seven hundred twenty-nine thousand three hundred and forty-six quatrillions, three hundred fifty-seven thousand two hundred sixty-one trillions, four hundred and two thousand, twenty-three billions, seven millions and forty-six.

11. Nine nonillions, forty-seven trillions, ten thousand seven billions, two million and seventy-two.

12. Three hundred and twenty-thousand and fifteen duodecillions, two thousand and ten trillions, one hundred and twentyseven billions, twenty-six millions, three hundred and twenty thousand four hundred and twenty-six.

SECTION II.

MENTAL OPERATIONS IN ADDITION.

1. How many are 3 and 4? How many are 3 and 6? How many are 3 and 7? How many are 9, 7 and 3? 4 and 10? 7 and 6? 5 and 11? 3 and 15? 6 and 5? 4 and 8? 10 and 5? 3 and 12? 6 and 6? 6 and 8? 6 and 7? 6 and 3? 6 and 10? 6 and 9? 6 and 12? 6 and 11? 6 and 13? 5 and 3? 5 and 5? 5 and 4? 5 and 7? 5 and 9? 5 and 8? 5 and 6? 5 and 12? 5 and 15? 5 and 13? 7 and 3? 7 and 5? 7 and 7? 7 and 9? 7 and 8? 8 and 2? 8 and 5? 8 and 4? 8 and 8? 8 and 7? 8 and 9? 8 and 12? 8 and 10? 9 and 5? 9 and 2? 9 and 4? 9 and 9? 9 and 7? 9 and 8? 10 and 5? 10 and 7? 10 and 4? 10 and 3? 10 and 10?

2. Bought an orange for 3 cents and some nuts for 6 cents; what did they both cost?

3. Bought a pound of figs for 8 cents and a pint of cherries for 7 cents; what was the price of both?

4. Bought a book for 12 cents and some paper for 9 cents; what did they both cost?

5. Gave 6 dollars for a cow and 9 dollars for a load of hay; what did I give for both?

6. A boy gave 12 cents for a penknife and 10 cents for a bunch of quills; what did he give for both?

7. A boy gave 8 cents for a top and 9 cents for some apples; what was the price of the whole?

8. A lady gave 11 dollars for a silk cloak and 7 dollars for a bonnet; what was the price of both?

9. How many are 3 and 2 and 5? How many are 7 and 8 and 10? How many are 11 and 5 and 2? 6 and 5 and 4? 7 and 5 and 8? 12 and 3 and 9? 15 and 2 and 3? 16 and 8 and 4? 10 and 9 and 3? 12 and 5 and 2? 13 and 10 and 2? 15 and 5 and 10? 25 and 2 and 3? 30 and 2 and 8? 1 and 50 and 2? 50 and 50 and 1? 12 and 12 and 10? 13 and 7 and 5? 30 and 20 and 10? 10 and 60 and 30? 15 and 5 and 50? 100 and 50 and 60? 17 and 9 and 7? 19 and 9 and 8? 99 and 6 and 10? 29 and 8 and 8? 15 and 15 and 15?

10. James gave 30 cents for an arithmetic, 10 cents for a slate, and 15 cents for a writing book; what did he give for the whole?

11. A merchant has due from one creditor 20 dollars, from another 10, from another 25. What is the sum due from the whole?

12. A gentleman gave 17 dollars for a coat, 12 dollars for pantaloons, 5 dollars for a vest, 6 dollars for a hat. What did they all cost him?

13. A drover has three flocks of sheep; the first has 25, the second 35, and the third 50. How many in the whole?

14. William is 12 years old, John is 9, and Thomas is 8. What is the sum of their ages?

15. Samuel has 5 apples, Enoch has 18, and Levi has 20. How many in the whole?

16. A beggar received of one man 14 cents, of another 12, of another 8, and of another 7. How many has he received?

17. Samuel has 12 marbles in one pocket, 12 in another, and 2 in each hand; how many has he in all?

18. John has 7 birds in one cage, and 12 in another; how many has he in both cages?

19. A farmer has 11 calves in one pasture, 6 in another, and 5 in another; how many has he in the whole?

20. Thomas caught one afternoon 7 pickerel, 9 trout, and 10 perch; how many had he in all?

21. A boy at service earned the first week 9 shillings, the second week 11 shillings, and the third week 12 shillings how much money had he?

22. A lady gave 15 dollars for a bonnet, 20 dollars for a silk dress, and 12 dollars for other articles; what was the amount of her bill

23. In one school room are 30 scholars, in another 20, and in another 50; how many in all ?

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