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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 dividend 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 mare 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 Ansiers. S2,12 4. Divide 4,18 by ,1812

,23068+ 5. Divide 7,25406 by 957

,00758 6. Divide ,00078759 by ,525

,00150+ 7. Divide 14 by S65

2038356+ 8. Divide $246,1476 by S604,25

,40736+ 9. Divide 8186515,239 by $504,81

611,9+ 10. Divide $1,28 by 88,5i

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

,5 12. Divide 1 dollar by 12 cents.

8,5334 13. 91or 21,75 yards of cloth cost 34,917 dollars, wliat will one yard cost?

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

it is performed by removing the separatrix in the divi. dend, 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 re. quired.

Note. So many cyphers as you annex to the giver pumerator, 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 t to a decimal.

,6875 6. Reduce it to a decimal. 7. Bring to a decimal.

,09575 8. What decimal is equal to ?

,037037 9. Reduce ļ to a decimal.

,333333 19. Reduce in to its equivalent decimal. - 2009 16 Reduce to a decimal.

1923076

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CASE II.

to reduce quantities of several denominations to a

Deciinal.

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

RUIE 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 quotient will give the decimal required.

EXAMPLES.

1. Reduce 123. 6. Sqrs. to the decimal of a pound.

12

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2. Reduce 15s. 9d. Sqrs. to the decimal of a pound.

Ans. ,7906.25 3. Reduce 9d. 3qrs. to the decimal of a shilling.

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

Ans. ,0625 5. Reduce 3s. 4d. New-England Currency, to the de cimal of a dollar.

Ans. ,555555+ 6. Reduce 12s. to the decimal of a pound. Ins. ,6

a

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 cypher 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 decima's Shillings 1

4 9 16 19 Answers. ,05 ,1 ,2 945 ,8 ,95 8. What is the decimal expression of 41. 195. 61d.?

Ans. $4,97708+ 9. Bring 341. 16s. 71d. into a decimal expression.

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

Ans. £25,9729164 11. Reduce 3qrs. 2na. to the decimal of a yard.

Ars. ,875 12. Reduce 1 gallon to the decimal of a hogshead.

ns. ,015873 13. Reduce 7oz. 19pwt. to the decimal of a lb. troy.

Ans. ,6625 14. Reduce Sqrs. 21lb. Avoirąupois, to the decimal of

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

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

Ans. ,8333334 17. Reluce 5fur. •1 Gpo. to the decimal of a mile.

Ans..,675 18. Reduce 4s calendar months to the decimal of

895. ,575

an owt.

acre.

3

CASE III.

To find the value of a decimal in the known parts of the

integer.

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RULE. 1. Multiply the decimal by the number of parts in the next less 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 denom. mation, 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.

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EXAMPLES.

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

£. ,5794

20

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11,4480

12

5,3760

4

1,5040

Ans. 11s. 5d. 1,59To. 2. What is the value of ,75 of a pound ? Ans. 15$. 3. What is the value of ,85251 of a pound !

Ans. 17s. Od. 2,4qrs 4. What is the value of ,040625 of a pound?

Ans. 9 d. 5. Find the value of ,8125 of a shilling. Ans. Joh. 6. What is the value of ,617 of an cwt.

Ans. 2grs. 13lb. 10z. 10,6dr. 7. Find the value of ,76442 of a pound troy.

Ano. 90%. 3pwt. 11gr. 8. What is the value of,875 of a yd. ? Ans. Sars. Suria 9. What is the value of ,875 of a hhd. of wine ?

As 55 gol. Ont, et

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