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

RULE. Annex ci phers to the numerator, and divide by the denominator; and the quotient will be the decimal required.

NOTE. So many ciphers as you annex to the given numerator, 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

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2. What decimalis equal to ? Answers.
3. What decimal is equal to 1 ?
4. Reduce } to a decimal.

,2 5. Reduce it to a decimal.

,6875 6. Reduce 17 to a decimal.

,85 7. Bring to a decimal.

,09375 8. What decimal is equal to ty?

,037037+ 9. Reduce { to a decimal.

,333333 + 10. Reduce it's to its equivalent decimal. - ,008 11, Reduce A to a decimal,

1923076

CASE II.

To reduce quantities 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 bottom; then divide each denomination (beginning at the top) by its value in the next denomination, the last quo tient will give the decimal required.

EXAMPLES.

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

12

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,15

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

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

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

Ans. ,0623 5. Reduce 3s. 4d. New-England Currency, to the decimal of a dollar.

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

Note. When the shillings are even, half the number svith a point prefixed, is their decimal expression ; but if the number beodd, annex a cipher to the shillings alli then by having them, you will have their decimal ex. pression. 7. Reduce 1, 2, 4, 9, 10 and 19 shilings to decimals.

Shillings 1 2 4,9 10 19
Answers. ,05
,1 ,2

,8

9.) 8. What is the decimal expression of 1l. 195.0!1?

ns. -1,9770 9. Bring 341. 16s. 73d. into a decimal expression

Ans. 15-1,83222910+ 10. Reduce 25l. 195. 5.,d. to a decimal.

ins. £21,972016+ 11. Reduce 3qrs. Qna. to the decimal of a yard.

vins. ,575 12. Reduce 1 gallon to the decimal of a houslead.

Ans. ,0158737 13. Reduce 7oz. 19pwt. to the decinal of a lb. troy.

Ans. ,0025 14. Reduce 3qrs. 211b. Avoirdupois, to the decimal of cwt.

ins. ,9373 15. Reduce 2 roods, 16 perches to the decimal of u

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

Ans. ,833333 + 17. Reduce 5fur. 16po. to the decimal of a mile.

Ans. ,675 18. Reduce 4; calendar months to the decimal co year.

H

Ans. ,375

a

acre.

CASE III.

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

the integer

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 denomi. nation, and cut off a remainder as before ; and so on through all the parts of the integer, and the several denomi. nations standing on the left hand make the answer.

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

£. ,5724

20

11,4480

5,3760

1,5040 Ans. 113. 5d. 1,5qrs. 2. What is the value of ,75 of a pound ? Ans. 158. 3. What is the value of ,85231 of a pound?

Ans. 178. Od. 2,4qrs. 4. What is the value of ,040625 of a pound ?

Ans. 9fd 5. Find the value of ,8125 of a shilling.

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

Ans. 2qrs. 1316. 1oz. 10,6dr 7. Find the value of ,76442 of a pound troy.

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

Ans. 55gal. Oqt. Ipf.

10. Find the proper quantity of ,089 of a mile.

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

Ins. 37. 25,2po. 12. What is the value of ,569 of a year of 365 days ?

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

Ins. 12,00384 gr. 14. What is the value of 2046375 of a pound avoirdu

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

Ans. 28po. 2yd. ift. 11,04in. 16. What is the proper quantity of ,142465 of a year?

Ans. 51,999725days.

troy ?

fois ?

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 third places ; observing to increase the second place or place of hundredths, by 5 if the shillings be odd; and the third place by 1 when the farthings exceed 12, and by 2 when they exceed 36.

EXAMPLES.

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1. Find the decimal of 7s. 9 d. by inspection

,3

for the odd shillings. 39=the farthings in 9 d. 2 for the excess of 36.

£. ,391 zdecimal required.

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