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therefore divide as in whole numbers, and from the right hand of thn quotient, point off so many places for decimals, as the decimal 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 left hand of said quotient.

Note.—If the decimal places in the divisor be inore than 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 degree of exactness,

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00 3. Divide 780,517 by 24,3.

Answers. 32,13 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.

,40736+ 9. Divide $186513,239 by $304,81.

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

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

,5 12. Divide 1 dollar by 12 cents.

8,333+ 13. If 211 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 di vided by 10, 100, 1000, &c. (viz. unity with ciphers,) it is performed by removing the separatrix in the dividend, so many places towards the left hand as there are ciphers in the divisor

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REDUCTION OF DECIMALS.

CASE I. To 1. luce a Vulgar Fraction to its equivalent Decimal.

RULE..-Annex ciphers to the numerator, and divide by the denominator; and the quotient will be the decimal required. Noth.So

many ciphers as you annex to the given nu. merator, 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 ciphers 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 į?

Answers. ,5 3. What decimal is equal to ?

,75 4. Reduce } to a decimal.

,2 5. Reduce it to a decimal.

,0875 6. Reduce jí to a decimal.

,85 7. Bring to a decimal.

,09375 8. What decimal is equal to zt?

,037037+ 9. Reduce } to a decimal.

333333+ 10. Reduce is to its equivalent decimal. - 0,008 11. Reduce to a decimal.

,1923076+

CASE I To reduce quantities of several denominations to a Decimai.

RULE.-1. Bring the given denominations first to a vulgar fraction by Problem III. page 71 ; and reduce said vulgar fraction to its equivalent decimal; or,

2. Place the several denominations above each other, letting the highest denomination stand at the bottom; then dirigy auch denomination (beginning at the top) by its value in the man last quotient will give the decimal required.

EXAMPLES.

1. Reducc 12 s. 6d. 3 qrs. to the decimal of a pound

12

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4800

4800 2. Reduce 15s. 9d. 3 qrs. to the decimal of a pound.

Ans. ,790625 3. Reduce 9d. 3 qrs. to the decimal of a shilling.

Ans. ,8125 4. Reduce 3 farthings to the decimal of a shilling,

Ans. ,0625 6. Reduce 3s. 4d. New-England currency, to the deci mal of a dollar.

Ans. ,555555+ 6. Reduce 12s. to the decimal of a pound. Ans. ,6 NOTE.-When the shillings are even, half the number with a point prefixed, is their decimal expression; but if the number be odd, annex a cipher to the shillings, and then by halving them, you will have their decimal expression. 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals. Shillings 1 2 4 9 16

19 Answers. ,05 ,1 ,2

,8

45

,95

8. What is the decimal expression of 41. 19s. 6 d.?

Ans. £4,97708+ 9. Bring 341. 16s. 73d. into a decimal expression.

Ans. £34,8322916+ 10. Reduce 251. 19s. 5 d. to a decimal.

Ans. £25,972916+ 11. Reduce 3 qrs. 2 na. to the decimal of a yard. Ans.,875 12. Reduce 1 gallon to the decimal of a hogshead.

Ans. ,015873+ 13. Reduce 7 07. 19 pwt. to the decimal of a lb. troy.

Ans. ,6625 14. Reduce 3 qrs. 21 lb. avoirdupois, to the decimal of a cwt.

Ans. ,9375 15. Reduce 2 roods, 16 perches, to the decimal of an acre.

Ans. ,6 16. Reduce 2 feet 6 inches to the decimal of a yard.

Ans. ,833333+ 17. Reduce 5 fur. 16 po. to the decimal of a mile. Ans. ,675 18. Reduce 4; calendar months to the decimal of a year.

Ans. ,375

CASE III. To find the value of a Decimal in the known parts of the In

teger. RULE.—1. Multiply the decimal by the number of parts in the next loss denomination, and cut off so many places for a remainder, to the right hand, as there are places in the given decimal.

2. Multiply the remainder by the next inferior denomination, and cut off a remainder as before; and so on through all the parts of the integer, and the several denominations standing on the left hand make the answer.

EXAMPLES. 1. What is the value of ,5724 of a pound sterling?

£ ,5724

20

11,4480

12

5,3760

(Carried up.)

5,3760

4

1,5040

Ans. 11s. 5d. 1,5 grs 2. What is the value of ,75 of a pound? Ans. 158 3. What is the value of ,85251 of a pound?

Ans. 17s. Od. 2,4 qrs. 4. What is the value of ,040625 of a pound? Ans. 9 d. 5. nd the value of ,8125 of a shilling.

Ans. 9 d. 6. What is the value of ,617 of a cwt. ?

Ans. 2 qrs. 13 lb. 1 oz. 10,6 dr. 7. Find the value of ,76442 of a pound troy.

Ans. 9 oz. 3 pwt. 11gr. 8. What is the value of ,875 of a yd. ? Ans. 3 qrs. 2 na. 9. What is the value of ,875 of a hhd. of wine?

Ans. 55 gals. Oqt. 1 pt. 10. Find the proper quantity of ,089 of a mile.

Ans. 28 po. 2 yds. 1 ft. 11,04 in. 11. Find the proper quantity of ,9075 of an acre.

Ans. 3r. 25,2 po. 12. What is the value of ,569 of a year of 365 days?

Ans. 207 d. 16 h. 26 m. 24 sec. 13. What is the proper quantity of ,002084 of a pound troy!

Ans. 12,00384 gr. 14. What is the value of ,046875 of a pound avoirdupois ?

Ans. 12 dr. 15. What is the value of ,712 of a furlong?

Ans. 28 po. 2 yds. 1 ft. 11,04 in. 16. What is the proper quantity of ,142465 of a year

? Ans. 51,999725 days.

CONTRACTIONS IN DECIMALS.

PROBLEM I.

A CONCISE and easy method to find the decimal of any number of shillings, pence and farthings, (to three places) by INSPECTION.

Rule.-1. Write half the greatest even number of shillings for the first decimal figure.

2. Let the farthings in the given pence and farthings possess the second and find plucos; observing të intcreme tho second place är

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