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The value of the number represented in the table is, One hundred twenty-seven sextillions, eight hundred ninety-four quintillions, two hundred thirty-seven quadrillions, eight hundred sixty-seven trillions, one hundred twenty-three billions, six hundred seventy-eight millions, four hundred seventy-eight thousand, six hundred thirty-eight.

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

11. The successive places occupied by figures are often called Orders. A figure in the right-hand or units' place is called a figure of the first order, or of the order of units ; a figure in the second place is a figure of the second order, or of the order of tens ; in the third place, of the order of hundreds, and so on.

Thus, in 1847, the 7 is of the order of units, 4 of the order of tens, 8 of the order of hundreds, and 1 of the order of thousands, so that we read the whole, one thousand eight hundred and forty

seven.

12. To numerate and read figures according to the French method.

RULE. Begin at the right, and point off the figures into periods of THREE places each.

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

EXERCISES IN FRENCH NUMERATION.

Read or write in words the numbers represented by the following figures : 1. 152 5. 2254 9. 84093 | 13.

610711 2. 276 6. 4384 | 10. 98612 | 14. 3031671 3. 998 7. 7932 11. 592614 15. 4869021 4. 1057 8. 42198 12. 40061916. 637313789

10. What is the value of the number represented in the table expressed in words? What are the names of the periods above sextillions ?-11. What are the successive places of the figures in the table called? Of what order is the first or right-hand figure? The second ? The third ? &c. 12. The rule for numerating and reading numbers according to the French method ?

17. 18. 19. 20. 21. 22. 23.

39461928 427143271 6301706716 143776700333 20463162486135 63821024711802 44770630147671

24. 25. 26. 27. 28. 29. 30.

3761700137706717

242173562357421 870037637471078635

8216243812706381

2403172914376931

3761706137706167138 610167637896430607761607

13. To write numbers by figures according to the French method.

RULE. Begin at the left, and write in each successive order the fig. ure belonging to it.

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

EXERCISES IN FRENCH NOTATION AND NUMERATION. Represent by figures, and read, the following numbers :1. Forty-seven. 2. Three hundred fifty-nine. 3. Six thousand five hundred seventy-five. 4. Nine hundred and eight. 5. Nineteen thousand. 6. Fifteen hundred and four. 7. Twenty-seven millions five hundred. 8. Ninety-nine thousand ninety-nine. 9. Forty-two millions two thousand and five. 10. Four hundred eight thousand ninety-six. 11. Five thousand four hundred and two.

12. Nine hundred seven millions eight hundred five thousand and seventy-four.

13. Three hundred forty-seven thousand nine hundred and fifteen.

14. Eighty-nine thousand forty-seven.
15. Fifty-one thousand eighty-one.
16. Seven thousand three hundred ninety-five..

17. Fifty-seven billions fifty-nine millions ninety-nine thousand and forty-seven.

13. The rule for writing numbers according to the French method ? At which hand do you begin to numerate ? Where do you begin to read ? At which hand do you begin to write numbers? Why?

14. The English Method of numeration separates figures into periods of six figures each. The first or right-hand period is regarded as units and thousands of units ; the second, as millions and thousands of millions ; and so on, six places being assigned to each period designated by a distinct name.

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The value of the figures in the table, according to the English method, is, One hundred thirty-seven thousand eight hundred ninety trillions, seven hundred eleven thousand seven hundred sixteen billions, three hundred seventy-one thousand seven hundred twelve millions, four hundred fifty-six thousand seven hundred eleven.

NOTE. — Although there is the same number of figures in the English and in the French table, yet it will be observed that in the French table we have the names of three periods other than in the English. It will also be observed that the variation commences after the ninth place, or the place of hundreds of millions. If, therefore, we would know the value of numbers higher than

14. How many figures in each period by the English method of numeration ? What orders are found in the English" method that are not in the French ? Give the names of the periods in the table, beginning with units. Repeat the table. What is the value of the numbers in the table? How do the figures in the English and French table compare as to numbers ? How as to periods? Why is this difference? Has a million the same value reckoned by the French table as when reckoned by the English ?

hundreds of millions, when we see them written in words, or hear them read, we need to know whether they are expressed according to the French or the English method of numeration.

The English method of numeration is that generally used in Great Britain, and in the British Provinces.

15. To numerate and read figures according to the English method.

Rule. Begin at the right, and point off the figures into periods of sıx 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 IN ENGLISH NUMERATION.

Read orally, or write in words, the numbers represented by the following figures :1. 125 5.

27306387903 2. 1063 6.

531470983712 3. 25842 7.

4230578032765038 4.

904357 8. 716756378807370767086389706473

16. To write numbers in figures according to the English method.

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

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

EXERCISES IN ENGLISH NOTATION AND NUMERATION.

Write in figures, and read, the following numbers :

1. Three hundred twenty-five thousand four hundred and twelve.

2. Two hundred fourteen thousand, one hundred sixty-five millions, seventy-eight thousand and fifty-six.

3. Forty-two billions, six hundred seventeen thousand thirtyone millions, forty-one thousand three hundred forty-two.

4. Two thousand eight billions, nine thousand eighty-two millions, seven hundred one thousand, nine hundred and eight.

14. Has the billion the same value as that by the French table? Why not? By which table has it the greater value? Where is the English method of numerating in use ? — 15. What is the rule for numerating and reading numbers by the English method ?- 16. The rule for writing numbers according to the English method ?

ADDITION.

17. When it is required to find a single number to express the sum of the units contained in several smaller numbers of the same kind, the process is called Addition.

Ex. 1. James has 3 pears, and his younger brother has 4; how many have both ?

ILLUSTRATION. — The 3 pears and 4 pears must be added; thus, 3 pears added to 4 pears make 7 pears. Therefore both have 7 pears.

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17. What is the process called by which we find the sum of several numbers?

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