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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 mairy 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 de Dominations 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

5,5760

4

1,5040 Ans. 11s. 5d. 1,5grs. 3. What is the value of 75 of a pound ? Ans. 15s. 3. What is the value of ,85231 of a pound ?

Ans. 175. 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. 9jd. 6. What is the value of ,617 of an cwt. ?

Ans. 2grs. 15lb. 1oz. 10,6dr. 7. Find the value of ,76412 of a pound troy.

Ans. 9oz. 3pirt. 11gr. 8. What's the value of ,875 of a yo. Ans. 3yrs. 2na. 9 What » ihe value of 875 of a hhd. of wine ?

Ang. 55gal. But, I

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

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

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

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

Ans. 12,0038gr. 14. What is the value of ,046875 of a pound avoirdu.

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

Ans. 28po. 2yd. ift. 11,04in. 16. What is the proper quantity of ,142463 of a year ?

Ans. 51,999725days.

troy?

pois ?

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 INSPEOTIOX.

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 shil. lings be ocd; and the third place by 1 when the far. things exceed 12, and by 2 when they exceed 36.

EXAMPLES.

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

y = 6s.

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

6,891 medecimal required.

2. Find the decimal expression of 16s.* 4fd, and 178 841.

Ans. £,819, and £ ,885 3. Write down 647 18 104 in a decimal expression.

Ans. $47,943 4. Reduce £1 85 9d. to an equivalent decimal.

Ans. £1,408

PROBLEM II.

A short and easy method to find the value of any

deci. Hial of a pound by inspection.

RULE.

Double the first figure, or place of tenths for shillings, and if the second figure be 5, or more than 5, reckon another shilling; then, after this 5 is deducted, call the figures in the second and third places so many farthings, abating 1 when they are above 12, and 2 when above 36, and the result will be the answer.

NOTE. When the decimal has but 2 figures, if any thing remains after the shillings are taken out, a cypher must be annexed to the left hand, or supposed to be so.

EXAMPLES.

1. Find the value of £. ,679, by inspection.

12s, double of 6
1 for the 5 in the second place which is to be

deducted out of 7. Add 74d.-29 farthings remain to be added. Deduct d. for the excess of 12.

Ans. 13s. 7d.
2. Find the value of £. ,876 by inspection.

Ans. 17s. 6td. 3. Find the value of £. ,849 by inspection.

Ans. 16s. 10d. 4. Find the value of £. ,097 by inspection.

Ans. 1 S. 111

REDUCTION OF CURRENCIES..

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RULES,
For reducing the Currencies of the several United
Status* into Federal Money.

CASE 1.
To reduce the currencies of the different states, where
a dollar is an even number of shillings, tu Federa! Money.

They are
Nric-England, Nere-York, and
Virginia,

North-Carolina.
Kentucky, and
Tennysore.

RULE
1. When the suin consists of pends only, annex a cy.
ipher to the pounds, and divide' by hall the number of
shillings in a wollar ; the quotient will be dollars.t

2. But if the sum consists of pounds, shillings, pence, &c. bring the given sum into shillings, and reduce the pelice and farthings to a decimal of a shilling; annes said decimal to the shillings, with a decimal point between, then divide the whole by the number of shillings contained in

dollar, and the quotient will be dollars, cents, mills, &ic.

* Forinerly the pogind was of the same sterling value in all the colonies as in Great-Britain, and a Spanish Dollar worth 486-but the legislatures of the different colonies emitted bills of credit, which afterwards depreciated in their value, ir some states more, in others less, &c.

Thus a dollar is reckoned in
Nor-England, 1. Wpre-Jirseys

South-
l'irginia, Pennsylvania, Carolina,
6s

s6

a

488 Kentucky, and Delairare, and

and Tennessee. Maryland. Georgia. Nir-Jork, 82

88 N. Carolina.

fAdding a cypher to the pounds, multiplies the whole by 10, bringing them into tenths of a pound then because a Jollar is just three-tenths of a pound N. I currency, divi'ing those tenths by 5, brings them intc dollars, &c. See

nage 85.

EXAMPI.F.S.

1. Redlice :31. New-England anıl Virginia Currency, to Federal Money. 3):30

8 cts.

$9454523 53 2. Reduce 451. 15s. : 3d. New-England currence, to 20

Trileral money.

d. A dollai=6)915,625

12): ,500

81.52,604+ Ans.

,625 decimal. Nore. I farthing is ,25

which annes to the prelice, 2

=,50 Sivil diviile' bv 19. sou will 3

,75 J have the decimal required. 3. Relice 3151. 10s. 11 fd. New Hampshire, &c. cur. rency, to Spanish inilled dollars, or federal money. £$45 10 11

d.

12)11,2500 6)0910,9375

,9975 decimal $1151,9229+ Ans. 4. Recluce 1051. 149. 3}d. New-York and Nortn-Caro. lina cuirencv, lv federal money. £ 105 14 31

d. 20

12)3.500

A lollar-m8)2114.3123

,S125 decimal

8264,289 06 Ans.

Or S dim. 26 5. Reduce 4511. New-york currency to federal money This being pounds only.* 4)4310

8 cts. Ans. 8107:1=1077,50

..4'ollar is Rs. in this currenys4to of a pound, thrrefore, inultiplej by 10, and decide by 4, brings the pounds into duliars, &c.

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