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9. 37000005830.0000870654
10. 2908540002.000000000000001
11. 1.000000800000070000000000000000001
12. 26501.00000000000080567809120566
13. 9003075200000854212.0000000005001376
14. 116840000000000000000000000000000,05
15. 641000000873004000500926050387000.596
16. 5000000000000000000005000000005000005.0005

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Refer to the table of decimals, and observe that

3 decimal places represent thousandths.
6

millionths.
9

billionths.
12

trillionths.
15

quadrillionths.
18

quintillionths.
21

sextillionths.
24

septillionths.
27

octillionths.
30

nonillionths.
33

decillionths.
36

undecillionths.
39

duodecillionths.

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If it were required to write five thousand and eight
hundred billionths, we should first write 5008. Billionths
requiring nine decimal places, hundred billionths will re-
quire two more, or eleven. As 5008 has but four figures,
seven zeroes must be prefixed to make the required num.
ber of places, thus, .00000005008. If this be numerated
it will be found to express hundred billionths, as required.

RULE FOR WRITING DECIMALS. Write first the whole
numbers, (if any,) and put the decimal point at their right.
Then write the decimals like whole numbers, and, if ne-
cessary, prefix zeroes to make up the required number of
decimal places.

EXAMPLES FOR THE BOARD.

115 Septillion, 2 trillion, 97 thousand and 5-and 49 thousand
and 3 hundred thousandths,

Change the decimal in the above example successively to trillionths, hundred quadrillionths, and ten sextillionths.

19 billion 3 million 1 thousand and 16 ten millionths is equivalent to what whole number?

EXAMPLES TO BE WRITTEN BY THE PUPIL, AND PROVED

BY NUMERATING, 1. Ten thousand and three,—and fifty-six thousandths.

2. Two hundred and nine,—and fifteen million and seven trillionths.

3. Six quadrillion seventeen billion and twenty-four, and six quadrillion seventeen billion and twenty-four hundred sextillionths.

4. Seventy-five septillion three quadrillion four hundred and one thousand, -and four octillion eleven thousand and six ten decillionths.

5. Two quadrillion thirty trillion four hundred million and five,-and six decillion and seven duodecillionths.

6. One hundred duodecillion,--and one hundred duodecillionth.

7. One hundred and fifty sextillion fifty one quintillion and thirty-six trillion,--and six hundred and thirty billion and five sextillionths.

8. Twenty-eight nonillion forty-six octillion seven sextillion and nine hundred thousand,—and five hundred and twenty quintillion forty thousand and seven hundred and eight ten septillionths.

9. Seventeen undecillion thirty-one trillion two hundred and fifty billion,--and ninety-five thousand and thirteen hundred quintillionths.

10. Nine hundred and ninety-nine undecillionths. 11. Nine hundred, -and ninety-nine undecillionths.

12. Five hundred and five undecillion seventy-six nonillion and three quintillion,--and fourteen million and fifty-nine ten octillionths.

13. Six duodecillion twenty two quadrillion seven hun. dred and seventy seven hundred duodecillionths.

It has already been stated that zeroes have no value of themselves, their only use being to supply the place of

denominations that are wanting. We may therefore place as many zeroes as we please at the right of decimals, without altering their value. This is a truth of great import

ance.

CHAPTER II.

ADDITION.

ADDITION is the process by which we join two or more numbers together to find their sum, or amount.

The sign + (plus,) signifies that two or more numbers are to be added together. The sign (equal to,) denotes that one number or series of numbers is equal to another. Thus 2+3+5=10, signifies that the sum of 2, 3, and 5 is equal to 10.

RULE. Write units under units, tenths under tenths, foc. Find the sum of each column, (commencing at the right hand,) and write the units' figure of the sum underneath, carrying the tens to the next column.

PROOF.

Perform the addition anew, commencing at the top and adding downwards.

FEDERAL MONEY, or the currency of the United States, is written like decimals, the dollar $ being regarded as the unit, the cents as hundredths, and the mills as thousandths.

1. Add five thousand and thirty-one dollars ; two thousand eight hundred dollars and six cents; nine hundred dollars and eleven cents; five dollars sixty-two cents and five mills; and three hundred and fifty dollars and five mills.

2. Find the sum of 960840.276 +28890037.0009 +5613 .02 +2988135.921 +60.

3. Find the sum of 285,9; 14.283 ; 1390.0025 ; 268; 7412.09; 3.846 ; 176 ; 506.000007; 87.281003; 441.929; and 3765.0761.

4. A steamer on the first nine days of her voyage

sailed K as follows : 308.02 miles ; 295.0009 miles; 315.769 miles;

301.0035 miles; 256 miles ; 261.4 miles ; 279.0908 miles; 300.96 miles; and 298.239 miles. How far had she gone at the end of the ninth day?

5. Ten men entered into partnership, contributing as follows: $1487.638; $1960.00; $1276.45; $1195.10; $2004.375; $1703.199; $751.25; $3475.871; 11240.50; and $989.112. What amount was invested in the firm ?

6. 448.771 +2297.08 + 13596 + 67.0954 +.008876+ 14.32094 + 1559.198874 + 420+ 5995682 +.4830611 + 25700+619.098+477122.6003=?

7. Add together 197446.00887932; 466108.4434097; 331165; 97061588.4003; 5425980.4991844; 761716604 .00491883; 26915224.20211; 8112907690080; 5176448 .037165222; and 9084129765.

CHAPTER III.

SUBTRACTION.

SUBTRACTION is the process by which we take one number from another, to find their difference.

When one number is subtracted from another, the larger number is said to be diminished by the smaller. The number to be diminished, is the minuend. The number to be subtracted, is the subtrahend. The number obtained by subtraction is the difference, the remainder, or the excess of the larger over the smaller number. The sign

(minus,) signifies that the latter of two numbers is to be taken from the former. Thus 7—5=2, signifies that if 5 be taken from 7, the remainder will be 2.

RULE. Write the less number under the greater, units under units, tenths under tenths, fc. If the subtrahend has more decimal places than the minuend, annex zeroes to the latter, to supply the deficiency. Commence at the right hand and subtract each figure from the one above it. When this cannot be done, increuse the upper figure by 10 and carry 1 to the next figure you subtract.

PROOF.

The sum of the remainder and the subtrahend will be equal to the minuend.

1. What is the difference between $88463.11 and $79521.097 ?

2. The population of the United States in 1830 was 12858670. In 1840 it was 17068666. What was the increase in ten years ?

3. A gentleman has invested $140768.25 in two estates, one of which is worth $89329.184. What is the value of the other?

4. A. said to B., I ain worth $116205.393. B. said, I am not worth as much, by $49164.42. What was B. worth?

5. 8843900269517-2988143675.0087906=?

6. What is the excess of $14943870.01 over $9568841 .095 ?

7. A broker purchased stock for which he paid $259084 .638. Did he gain or lose, by selling the same stock for $290451.00 ? How much?

8. In a certain factory there were made 916482.7 yards of satinet, and 895267.594207 yards of broadcloth. How many yards were there of satinet more than of broadcloth ?

CHAPTER IV.

MULTIPLICATION.

MULTIPLICATION is the process by which we find the sum of a number or part of a number, when repeated a given number of times.

The number to be multiplied or repeated, is the multiplicand. The number to multiply by, or the number of

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