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SUBTRACTION OF DECIMALS.

RULE.

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

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6, From 480 take 245,0075

Ans. 254.9925 7. From 256 dois. take ,549 dols. Ans. $255,451 8. From ,145 take ,09684

Ans. ,04816 9. From ,0754 take ,2571

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

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

Ans. 106,9995 13. Eroin an unit, or 1, subtract the millionth part of itself,

ins. ,999999

DIULTIPLICATION OF DECIMALS.

RULE.

1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers.

2. Point of so many tigures 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 cyphers to the left hand.

EXAMPLES. 1. Multiply 5,236

2. Multiply 3,024 by 9008

by 2,23 Product ,041888

6,74352 3. Multiply 25,238 by 12,17 stels, 307,14646 4. Multiply 2461 by 9329

130,1869 5. Multiply 7853 by 3,5

27485,5 6. Multiply ,007853 by ,035

,000274855 7. Multiply ,004 by ,004

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

Ans. $14, 4d. Sc. 82.R. 9. Multiply 7,02 dollars, by 5,27 dollars.

Ans. 36,9954dols. or 836 99cts. 57om. 10. Multiply 41 dols. 25 cts. by 120 dollars.

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

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

Ans. $0,0585=5cts. 83mills. 13. Multiply 10 dols. by 10 cts.

Ans. 21 14. Multiply 341,45 dols. by ,007 or 7 mills.

Ans. 82,59+ To multiply by 10, 100, 1000, &c. remove the separa. ting point so many places to the right hand, as the multiplier has cyphers.

Multiplied by 10, makes 4,25 So ,425

by 100, makes 42,5

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

425,

DIVISION OF DECIMALS.

RULE.

1. The places of the decimal parts of the divisor and ayotient countel together, must always be cqual 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 decimal places in the divi. dend exceed those in the divisor.

2. If the places in the quotient are not so many as the rule requires, supply the defect by prefixing cyphers to the left hand of said quotient.

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

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00 S. Divide 780,517 by 24,3 Answers. 52,12 4. Divide 4,18 by ,1812

,23068+ 5. Divide 7,25406' by 957

,00758 6. Divide ,00078759 by ,525

,00150+ 7. Divide 14 by $65

2058356+ 8. Divide $246,1476 by S604,25

,40736+ 9. Divide $186513,239 by 6304,81

611,9 10. Divide $1,28 by $8,51

,154+ 11. Divide 56 cis. by 1 dol. 12 cts.

,5 12. Divide 1 dollar by 12 cents.

8,533+ 13. \ 21 or 21,75 yards of cloth cost 34,317 dollars, what will one yard cost?

$1,577 NOTE. When decimals, or whole numbers, are to be divideil liy 10, 100, 1000, &c. (viz. unity with cyphers)

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it is performed by removing the separatrix in the dividend, so many places towards the left hand as there are cyphers in the divisor.

EXAMPLES.

10, the quotient, is 57,2 572 divided by 100,

5,72 1000,

,572

REDUCTION OF DECIMALS.

CASE I.

To reduce a Vulgar Fraction to its equivalent Decimal

RULE. Annex cyphers to the numerator, and divide by the denominator ; and the quotient will be the decimal ree quired.

NOTE. So many cyphers as you annex to the given Aumerator, so many places must be pointed in the quotient; and if there be not so many places of figures in the quotient, make up the deficiency by placing cyphers to the left hand of the said quotient,

EXAMPLES.

1. Reduce to a decimal.

8)1,000

Ans. ,125 2. What decimal is equal to 1? Answers. S. What decimal is equal to ? 4. Reduce } to a decimal. 5. Reduce to a decimal,

,6875 6. Reduce is to a decimal.

.85 7. Bring to a decimal.

,09375 8. What decimal is equal to ?

,037037 9. Reduce { to a decimal.

,3333334 10. Reduce to its equivalent decimal.

2008 IF Reduce to a decimal.

,192506

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CASE II. to reduce quuntities of several denominations to a

Decimal.

RULE.

Bring the given denominations first to a vulgar fraction by Problem III, page 76; and reduce said vulgar fraction to its equivalent decimal ; or

RULE 2. Place the several denominations above each other, letting the highest denomination stand at the bot tom; then divide each denomination (beginning at the top) by its value in the next denomination, the last quam tient will give the decimal required.

EXAMPLES.

1. Reduce 123. 61. Sqrs. to the decimal of a pound.

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