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Ciphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure continues to possess the same place : so ,5 ,50 and ,500 are all the same value, and equal to voor

But ciphers placed at the left hand of decimals, de crease their value in a tenfold proportion, by removing them further from the decimal point. Thus, ,5 ,05 ,005, &c. are five tenth parts, five hundredth parts, five thousandth parts, &c. respectively. It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure : for inštance, a fraction beginning with any figure less than ,9 such as ,899229, &c. if extended to an infinite number of figures, will not equal ,9.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers wliether mixed or pure decimals, under each other, according to the value of their places.

2. Find their sum as in whole numbers, and point off so many places for the decimals, as are equal to the great, est number of decimal parts in any of the given numbers.

EXAMPLES.

1: Find the sum of 41,653 +36,05+24,009 +-1,6

41,653

36,05 Thus,

24,009
1,6

Sum, 103,312 which is 103 integers, and parts of

unit. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of a unit, or 1.

Hen“, we may observe, that decimais, and FEDERAL M'.£y, are subject to one, and the same law of notation, and consequently of operation.

For since dollar is the money unit ; and a dime being the tenth, a cent the hundreth, and a mill the thousandth part of a dollar, or unit, it is evident that any number of doliars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar : Thus, 11 dollars, 6 dimes, 5 cents, = 11,65 or 11145 dol. &c.

2. Add the following mixed numbers together.
(2)
(3)

(4)
Yards.

Ounces. Dollars. 46,23456 12,3456 48,9108 24,90400 7,891

1,8191 17,00411 2,34

3,1030 3,01111 5,6

.7012

5. Add the following sums of Dollars together, viz. $12,34565+7,891+2,34+14,+,0011

Ans. $36,57775, or $36, 5di. 7cts. 710 mills. 6. Add the following parts of an acre together, viz. ,7569+,25+,654+,199

Ans. 1,8599 acres. 7. Add 72,5+32,071 +2,1574+371,4+2,75

Ans. 480,8784 8. Add 30,07 +200,71 +59,4+3207,1

Ans. 3497,28 9. Add 71,467+27,947 16,084+98,009+86,5

Ans. 300 19. Add ,7509+,0074+,69+,8408+,6109

Ans. 2,9 11. Add ,6+,099+,37+,905+,026

Ans. 2 12. To 9,999999 add one millionth part of a unit, and the sum will be 10.

13. Find the sum of
Twenty-five hundredths,
Three hundred and sixty-five thousandths,
Six tenths, and nine millionths

Answer, 1,215009

SUBTRACTION OF DECIMALS.

RULE.

Place the numbers according to their value ; then subu tract as in whole numbers, and point off the decimals as in Addition.

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6. From 480 take 245,0075

Ans. 234,9925 7. From 236 dols. take ,549 dols.

Ans. $235,451 8. From ,145 take ,09684

Ans. ,04816 9. From ,2754 take ,2371

Ans. ,0383 10. From 271 take 215,7

Ans. 55,3 11. From 270,2 take 75,4075 Ans. 194,7925 12. From 107 take ,0007

Ans. 106,9993 13. From a unit, or 1, subtract the milliónth part of itself.

Ans. ,999999

MULTIPLICATION OF DECIMALS

ROLE. 1. Whether they be mixed rumbers, or prre decinals, place the factors and niultiply them as in whole numbers.

2. Point off so many figures from the product as there are decimal places in both the factors; and if there be not so many places in the product, supply the defect by prefixing ciphers to the left hand.

EXAMPLES

1. Multiply 5,236

by

,008

2. Multiply 3,024

by

2,73

Product, ,041888

6,74352

3. Multiply 25,238 by 12,17 Answers, 307,14646 4. Multiply 2461 by ,0529

130,1369 5. Multiply 7853 by 3,5

27485,5 6. Multiply ,007853 by 2035

,000274855 7. Mültiply 004 by 2004

,000016 8. Whạt cost 6,21 yards of cloth, at 2 dols. 32 cents, 5 mills per yard ?

Ans. $14, 4d. 3c. 83m. 9. Multiply 7,02 dollars by 5,27 dollars.

Ans: 36,9954dols. or $36 99cts. 514 m. 10. Multiply 41 dols. 25 cts. by 120 dollars.

Ans. $4950 11. Multiply 3 dols. 45 cts. by 16 cts.

Ans. $0,5520=55ets. 2mills. 12. Multiply 65 cents, by ,09 or 9 cents.

Ans. $0,0585=5cts. 8£mills. 13. Multiply 10 dols. by 10 cts.

Ans. $1 14. Multiply 341,45 dols. by ,007 or 7 mills.

Ans. $2,39+ To multiply by 10, 100, 1000, &c. remove the separating point so many places to the right hand, as the multiplier has cựphers.

Multiplied by 10, nakes 4,25
So ,425

by..100, makes 42,5

by 1000, is ,425 Por ,425 X10 is 4,250,&c.

DIVISION OF DECIMALS.

RULE. 1. The places of the decimal parts of the divisor and quotient counted together, must always be equal to those

in the dividend, therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decirnal places in the dividend exceed those in the divisor.

2. If the places in the quotient be not so many as the rule requires, supply the defect by prefixing ciphers to the Heft hand of said quotient. Note.-If the decimal places in the divisor be more

those in the dividend, annex as many ciphers to the dividend as you please, so as to make it equal, (at least) to the divisor. Or, if there be a remainder, you may annex ciphers to it, and carry on the quotient to any de gree of exactness.

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00

00 8. Divide 780,517 by 24,3 Answers. 32,12 4. Divide 4,18 by 1812

,23068+ 5. Divide 7,25406 by 957

,00758 6. Divide ,00078759 by ,525

,00150+ 7. Divide 14 by 365

,038356+ 8. Divide $246,1476 by $604,25

,40786+ 9. Divide $186513,239 by $304,81

611,9+ 10. Divide $1,28 by $8,31

,1547 11. Divide 56 cts. by 1 dol. 12 cts.

,5 12. Divide 1 dollar by 12 cents.

8,333+ 13. If 21 or 21,75 yards of cloth cost 34,917 dollars, what will one yard cost ?

$1,577+ Note.---When decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with ciphers,

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