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30. Sixteen thousand, six hundred and six. 31. Twenty-four thousand and three.

In order to read and write large numbers more conve. niently, they are divided into periods of three figures each, by means of commas, thus :

876,469,764,256,622,895,946,852. The first right hand period is called the unit period; and contains the orders called units, tens, and hundreds.

The second period, is called the thousand period; and contains the orders called thousands, tens of thousands, and hundreds of thousands.

The third period is called the million period, and con. tains the orders called millions, tens of millions, and hun. dreds of millions.

The fourth period is called the billion period; and contains the orders called billions, tens of billions, and hun. dreds of billions.

The fifth period is called the trillion period; and con. tains the orders called trillions, tens of trillions, and hun. dreds of trillions.

The sixth period is called the quadrillion period; and contains the orders called quadrillions, tens of quadrillions, and hundreds of quadrillions.

The seventh period is called the quintillion period; and contains the orders called quintillions, tens of quintillions, and hundreds of quintillions.

The eighth period is the sextillion.

The following are the periods which must be learned in succession, beginning with the highest, as well as with the lowest ; thus, First Period, Unit. Eighth Period, Sextillion. Second Period, Thousand. Seventh Period, Quintillion. Third Period, Million. Sixth Period, Quadrillion. Fourth Period, Billion. Fifth Period, Trillion. Fifth Period, Trillion. Fourth Period, Billion. Sixth Period, Quadrillion. Third Period, Million. Seventh Period, Quintillion. Second Period, Thousand. Eighth Period, Sextilljon. First period, Unit.

What are the names of the eight periods, and what orders does each pe. riod contain ? Repeat the periods beginning at the lowest or unit period. Repeat them beginning at the highest. Read the above number in the two different ways.

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What is the first period ? the third ? the fifth ? the second ? the fourth ? the seventh ? the sixth ? the eighth ?

The pupil may write the names over the periods until accustomed to reading them; thus,

Tril. Bil. Mil. Thous. Units.
32 427

983

254 693 The above may be read in the following manner :

The first left hand period is read, 3 tens of trillions ; 2 units of trillions ; or thirty-two trillions.

The next period is read, 4 hundreds of billions ; 2 tens of billions ; 7 units of billions ; or four hundred and twenty seven billions.

The next period is read, 9 hundreds of millions ; 8 tens of millions ; 3 units of millions ; or nine hundred and eighty-three millions.

The next period is read, 2 hundreds of thousands ; 5 tens of thousands ; 4 units of thousands; or two hundred and fifty-four thousand.

The next period is read, 6 hundreds ; 9 tens ; 3 units ; or six hundred and ninety-three.

The following is a number in which several orders are omitted, having ciphers in place of numbers. Quin. Quad. Tril. Bil. Mil. Th. U. 33

067 004 803 064 000 400 Let the pupil first tell what periods and what orders are omitted, having ciphers instead of numbers.

The above number may be read thus :

Begin at the left and read; 3 tens of quintillions, and 3 units of quintillions; or thirty-three quintillions.

The next period is, no hundreds of quadrillions ; 6 tens of quadrillions; and seven units of quadrillions ; or sixtyseven quadrillions.

The next period is, no hundreds of trillions ; no tens of trillions; 4 units of trillions; or four trillions.

The next period is, 8 hundreds of billions; no tens of billions ; 3 units of billions; or eight hundred and three billions.

The next period is, no hundreds of millions ; 6 tens of millions ; 4 units of millions; or sixty-four millions.

The next period, as it has no hundreds, tens, or units of thousands, may be omitted entirely, when reading.

The next period is, 4 hundreds; no tens; no units; or four hundred.

The best and most common way of reading, is that in the italics, and then all together, it reads thus:

Thirty-three quintillion; sixty seven quadrillion; four trillion; eight hundred and three billion; sixty-four milfour hundred.

lion;

Let the pupil read the following sum in both ways:

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RULE FOR READING WHOLE NUMBERS.

Point off into periods of three figures each, beginning at the right. Read each period as if it stood alone, and then add the name of the period.

NOTE.-When a period or order is omitted, it is not necessary to mention it at all.

Before reading, let the pupil tell what periods and orders are omitted, and represented by ciphers.

Let the pupil point off, and read the following figures :

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Read the above numbers in the two different ways. What is the rule for reading whole numbers? In the above numbers what periods and orders are omitted?

227034293

9623000062 200004900

10043259054 3690200000

43600078609 30006340200

459643723007 602030004296 612942004000040367

40000643209437 3907650060042300000 237600096430060000 | 396770000543965000076 It is necessary for the pupil to understand, that the French and English arithmeticians use different methods of numeration.

The English have their periods contain six orders, and the French only three.

This makes no difference till we come to hundreds of millions. After that, it makes a great difference, as will be seen by the following comparison.

It must be noticed, that the same figures are used in both.

ENGLISH METHOD.
Trillions. Billions. Millions. Units.
579364, 028635,

419763, 215468.

FRENCH METHOD. Sext. Quin. Qua. Trill. Bill. Mill. Th. Units.

364, 028, 635, 419, 763, 215, 468. From the above it can be seen, that all the orders above hundreds of millions, in both methods, give the same name, to a very different value.

Thus, the orders of thousands of millions, tens of thou. sands of millions, and hundreds of thousands of millions, in the English method, would be read as billions, tens of bil. lions, and hundreds of billions, in the French method.

Billions, tens of billions, and hundreds of billions, in the English method, are equivalent to trillions, tens of tril. lions, and hundreds of trillions, in the French method.

579,

What is the difference between the English and French method of numerating? Where does it make a difference, and where does it not ? How would a billion, in the English method, be read in the French ? How would one hundred billion, in the English method, be read in the French? How would one billion, in the French method, be read in the English ?

Five trillion, in the French method, would be read five billion, in the English ; and five trillian, in the English method, would be read five quadrillion in the French.

The French method is adopted in this work, because it is both the most convenient, and the most common. But the pupil needs to understand the difference be. tween the two modes, and the teacher should make the class point off and read numbers by both.

Point off and read the following numbers, first by the French, and then by the English method.

765432176500431 9870000654321765432 32698000000040000360093

436789643645964379629364 In order to write numbers correctly, the pupil must learn thoroughly, the succession of the periods beginning at the left. Thus, Sextillion, Quintillion, Quadrillion, Trillion, Billion, Thousand and Unit.

RULE FOR WRITING WHOLE NUMBERS.

Begin with the highest period, and write first the hundreds, then the tens, and then the units of that period. Proceed thus, until all the periods are written. Place a comma between each period. If any period or order is omitted, place ciphers in its place.

NOTE.-Ciphers prefixed to a whole number, have no effect

upon the value. A number, therefore, should never be begun with a cipher.

EXERCISES. Write two thousands and two. What orders are omitted?

Write two millions, two thousands, and four. What or. ders are omitted ?

How would six hundred billion in the French method, be read in the English? Which method is adopted in this work? What is the succession of the periods beginning at the left ? What is the rule for writing whole numbers? Why should not any whole number, begin with a cipher ?

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