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9th Period. 7th Period. 6th Period. 5th Period. 4th Period. 3d Period. 2d Period. 1st Period. Seitil- Quintil- duadril- Trillion*. Billion*. Millions. Thousands. Units. lions. lion*. lioni.

The value of the number represented in the table is, seven hundred eighty-nine sextillions, one hundred twenty-three quintillions, four hundred fifty-six quadrillions, seven hundred eighty-nine trillions, one hundred twenty-three billions, four hundred fifty-six millions, seven hundred eighty-nine thousands, one hundred twenty-three.

38. The unit of the first period, or right-hand group, is 1; of the second, 1 thousand; of the third, 1 million; of the fourth, 1 billion; of the fifth, 1 trillion; of the sixth, 1 quadrillion; of the seventh, 1 quintillion; of the eighth, 1 sextillion, etc.

The periods above sextillions, in their order, are, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novemdecillions, Vigintillions, etc.

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 ascend 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. It is, indeed, difficult for any mind to form an adequate idea of the larger numbers. To count a million, at the rate of one in a second, would require upward of twenty-three days of twelve hours each A billion is equal to a million a thousand times repeated, or a number so great, as to exceed all the seconds of time that would elapse in thirty-two years.

39. To read numbers represented by figures according to the French method; —

Begin at the right hand, and point off the figures into as many periods as possible of three places each.

Then, commencing at the left hand, read the figures of each period, giving the name of each period excepting that of units.

Exercises.

Read orally, or write in words, the numbers represented by the following figures, according to the French method: —

[table]

19. 407000010703801 I 21. 478127815016666060707

20. 200070007801000 | 22. 800800800800800800800800

23. 127081061071081010009007007

24. 407144140070060700007101800808

40. To write numbers in figures according to the French method; —

Begin at the left hand, and write in each successive order the figuri belonging to it.

If any intervening order would otherwise be vacant, fill the place by a cipher.

Exercises.

Represent by figures, and read, the following numbers, according to the French method: —

1. Twenty-nine.

2. Four hundred and seven.

3. Twenty-three thousand and seven.

4. Five millions and twenty-seven.

5. Seven millions, two hundred five thousand and five.

6. Two billions, two hundred seven millions, six hundred four thousand and nine.

7. One hundred five billions, nine hundred nine millions, three hundred eight thousand two hundred and one.

8. Nine quintillions, eight billions and forty-six.

9. Fifteen quintillions, thirty-one millions and seventeen.

10. Five hundred seven septillions, two hundred three trillions, fifty-seven millions and eighteen.

11. Nine nonillions, forty-seven trillions, seven billions, two millions, three hundred ninety-two.

12. Fifteen duodecillions, ten trillions, one hundred twentyseven billions, twenty-six millions, three hundred twenty thousand four hundred twenty-six.

English Numeration.

41. The English method of numeration is that generally used in Great Britain, and in the British Provinces. It divides numbers into periods of six figures, and gives a distinct name to each.

ENGLISH NUMERATION TABLE.

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The value of the figures in the above table, expressed in words according to the English method, is, Three hundred ninety-eight thousand, eight hundred thirty-two trillions; five hundred sixty-three thousand, eight hundred seventy-one billions; three hundred fifty-one thousand, six hundred fifteen millions; one hundred twenty-three thousand five hundred sixty-one.

42. To read numbers represented by figures according to the English method; —

Begin at the right hand, and point off the figures irito periods of six places each.

Then, commencing at the left hand, read the figures of each period, giving the name of each period except that of units.

Exercises.

Read orally, or write in words, the numbers represented by the following figures, according to the English method: —

1. 23457896 4. 98765421910311

2. 325487691 5. 5632411132321300012

3. 1678912161 6. 6961771889133201443345567

13. To write numbers in figures according to the English method; —

Begin at the left hand, and write in each successive order the figure belonging to it.

If any intervening order would otherwise be vacant, fill the place by a cipher.

Exercises.

Represent by figures, and read, the following numbers, according to the English method: —

1. Thirty-two million three hundred.

2. Seven billion seventeen thousand.

3. Five hundred sixty thousand one hundred two million, nine hundred twenty-nine thousand four hundred eleven.

4. One trillion, seven hundred forty-eight thousand nine hun• dred fifty-five billion.

ADDITION.

44. Addition is the. process of finding the sum of two or more numbers. The result obtained is called the amount.

Numbers can be added together only when their units are ot the same kind. When the numbers added are simple, the pro tess is termed Addition of Simple Numbers.

45 i To add simple numbers.

Ex. 1. A man has three farms; the first contains 378 acres, the second 586 acres, and the third 168 acres. How many acres are there in the three farms. Ans. 1132.

Operation. Having arranged the numbers so that all the units Acres. 0f the same order shall stand in the same column, o 7 8 we first add the column of units; thus, 8 and 6 are 5 8 6 14, and 8 are 22 units, = 2 tens and 2 units. We 16 8 write the two units under the column of units, and

carry or add the 2 tens to the column of teas; thus,

Ans. 1 1 3 2 2 added to 6 make 8, and 8 are 16, and 7 are 23 tens, 2 hundred and 3 tens. We write the 3 tens under the column of tens, and add the 2 hundred to the column of hundreds; thus, 2 added to one make 3, and 5 are 8, and 3 are 11 hundred, = 1 thousand and 1 hundred. We write the 1 hundred under the column of hundreds; and there being no other column to be added, we set down the 1 thousand in the thousands' place, and find the amount of the several numbers to be 1132.

In practice, it is better not to name each figure added, but only the results, thus, 8, 14, 22 units, = 2 tens and 2 units, etc.

Rule. Write the numbers so that all the figures of the same order shall stand in the same column.

Add, upward, all the figures in the column of units, and, if the amount be less than ten, write it underneath. But if Ike amount be ten or more, write down the unit figure only, and add in the figure denoting the ten or tens with the next column.

Proceed in this way with each column, until all are added, observing to write under the last column its whole amount.

46. First Method of Proof. — Begin at the top and add the columns downward in the same manner as they were before added upward; and if the two sums agree, the work is presumed to be right.

The reason of this proof is, that, by adding downward, the order of the figures is inverted; and, therefore, any error made in the first addition would probably be detected in the second. Note. — This method of proof is generally used in business.

47 i Second Method of Proof. -— Separate the numbers to be added into two parts, by drawing a horizontal line between them. Add the numbers below the line, and set down their sum. Then add this sum and the number or numbers above the line together; and if their sum is equal to the first amount, the work is presumed to be right.

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