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Art. 10. There are two methods of numeration in common use; the French and the English. The former is more generally used on the continent of Europe and in the United States. In the French method, a new name is given to every third figure above millions, and in the English, to every sixth figure above millions.

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FRENCH NUMERATION TABLE.

Hundreds of Sextillions.

Tens of Sextillions.
o Hundreds of Quintillions.
c Tens of Quintillions.
- Sextillions.
o Hundreds of Quadrillions.

Quintillions.
W Tens of Quadrillions.
o Quadrillions.
o Hundreds of Trillions.

Tens of Trillions.
Hundreds of Billions.
Hundreds of Millions.
Tens of Billions.
Hundreds of Thousands.
Trillions.
Tens of Millions.
Tens of Thousands.

Billions.
CO Millions.

Thousands.
o Hundreds.
cu Tens.
. Units.

867,

1 2 3,

47 8,

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The value of the numbers in this table, expressed in words, is, One hundred twenty-seven sextillions, eight hundred ninetyfour 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 preceding table may be extended to any number of figures by supplying the names of the periods above sextillions, in their order; viz. Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecil. lions, Quindecillions, Sexdecillions, Septendecillions, Octode. cillions, Novemdecillions, Vigintillions, &c.

QUESTIONS.- Art. 10. What are the two methods of numeration in common use ? Where is the French method more generally used ? How does the French method differ from the English ? Repeat the French Numeration Table, giving the names of all the places or orders, beginning at the right. What are the names of the different periods in the table ? What is the value of the numbers in the table expressed in words ? Repeat the names of the periods above sextillions.

Art. 11. The successive places occupied by figures are often called orders. Hence, 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 the number 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, each figure expressing so many units of that order to which it belongs; so that we read the whole number one thousand eight hundred and forty

seven.

Art. 12. From the preceding table and explanation, we deduce the following rule for numerating and reading numbers according to the French method.

Rule. - Begin at the right hand, and divide the number into periods of THREE figures each, remembering the name of each period. Then, commencing at the left hand, read the figures of each period in the same manner as the period of units, giving the name of each period excepting the last.

EXERCISES IN FRENCH NUMERATION. The learner may read orally, or write in words, the following numbers : 1. 152|11. 592614|21.

20463162486135 2. 276 12. 40061922.

63821024711802 3. 998 13. 610711 23.

44770630147671 4. 1057 14. 303167124.

3761700137706717 5. 2254 15. 4869021 25.

242173562357421 6. 4384 16. 63731378926. 870037637471078635 7. 7932 17. 3946192827.

8216243812706381 8. 42198 18. 427143271 28.

2403172914376931 9. 84093 19. 630170671629. 3761706137706167138 10.98612|20. 143776700333 30. 610167637896430607761607

QUESTIONS. – Art. 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. - Art. 12. What is the rule for numerating and reading numbers according to the French method ?

Art. 13. To write numbers according to the French method, we have the following

Rule. Begin at the left, and write the figure of the highest order to be written, and place in each successive order the figures belonging to it, observing to fill the place by a cipher, when no number is mentioned to be written.

EXERCISES IN FRENCH NOTATION AND NUMERATION. The learner may write in 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 thou. sand and forty-seven.

Art. 14. The following table exhibits the English method of numeration, in which it will be observed that the figures are separated by commas into divisions or 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 division designated by a distinct name.

QUESTIONS. - Art. 13. What is the rule for writing numbers according to the French method ? At which hand do you begin to numerate figures ? Where do you begin to read them ? At which hand do you begin to write numbers? Why? – Art. 14. How many figures in each period in the Eng. lish method of numeration? What orders are found in the English method that are not in the French ?

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The value of the figures in the above table, expressed in words according to the English method, is, One hundred thirtyseven 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 higher divisions 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 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.

Art. 15. To numerate and read numbers according to the English method we have the following

Rule. - Begin at the right hand and divide the number into periods QUESTIONS. — Give the names of the periods in the English Numeration Table, beginning with the period of units. Repeat the table, giving the names of all the orders or places. What is the value of the numbers in the table expressed in words ? 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? Has a billion the same value? Why not? By which table has it the greater value ? - Art. 15. What is the rule for numerating and reading numbers according to the English method ?

of sıx figures each, remembering the name of each period. Then, commencing at the left hand, read the figures of each period in the same manner as the period of units, giving the name of each period excepting the last.

EXERCISES IN ENGLISH NUMERATION.

The learner may read orally, or write in words, the following numbers : 125 1 5.

27306387903 2. 1063 6.

531470983712 3. 25842 7.

4230578032765038 4.

904357 8. 716756378807370767086389706473

Art. 16. To write numbers according to the English method, we have the following

RULE. Begin at the left, and write the figure of the highest order to be written, and place in each successive order of the periods the figure belonging to it, observing to fill the place by a cipher, when no number is mentioned to be written.

EXERCISES IN ENGLISH NOTATION AND NUMERATION. The learner may 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.

5. One hundred sixty-eight thousand two hundred fortyseven trillions, three hundred twenty-four thousand three hundred forty-one billions, four hundred seventy-two thousand three hundred nineteen millions, eight hundred sixteen thousand four hundred and twenty-one.

QUESTION.- Art 16. What is the rule for writing numbers according to the English method ?

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