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8. What is the decimal expression of 47. 19s. 6d. ?

Ans. £4,97708+

9. Bring 347. 16s. 73d. into a decimal expression.

Ans. £34,6322916+

10. Reduce 257. 19s, 54d. 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 oz. 19 pw. to the decimal of a lb. troy.

Ans. ,6625 14. Reduce 3 qrs. 21 b. 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 45 calendar months to the decimal of a year. Ans. ,375

CASE III.

To find the value of a Decimal in the known paris of the Integer.

ROLE. 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 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?

3. What is the value of ,85251 of a pound?

Ans. 15s.

Ans. 17s. Od. 2,4 grs.

4. What is the value of,040625 of a pound? Ans. 93d.

5. Find the value of ,8125 of a shilling. 6. What is the value of ,617 of a cwt.?

Ans. 93d.

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. O qt. 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. 25,2po.

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?

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

Ans. 12 dr.

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 third places; observing to increase the second place or

place of hundredths, by 5, if the shillings be odd; and the third place when the farthings exceed 12, and by 2 when they exceed 36.

by

EXAMPLES.

1. Find the decimal of 7s. 93d. by inspection.

‚3 =1 ̄6s.

5

for the odd shillings.

.39 the farthings in 93d.

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2. Find the decimal expression of 16s. 41d. and 17s. 8d.

Ans. £,819, and £,885

3. Write down £47 18 10 in a decimal expression.

Ans. £47,943

4. Reduce £1 8s. 2d. to an equivalent decimal.

PROBLEM II.

Ans. £1,40

A short and easy method to find the value of any decimal 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 cipher must be annexed to the left hand, or supposed to be so.

EXAMPLES.

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

12s

1

Add

Deduct

double of 6

for the 5 in the second place which is to be [deducted out of 7 74d. 29 farthings remain to be added.

d. for the excess of 12.

Ans. 13s. 7d.

2. Find the value of £. ,876 by inspection. Ans. 17s. 61d. 3. Find the value of £.,842 by inspection. Ans, 16s. 10d. 4. Find the value of £.,097 by inspection. Ans. Is. 11ļd.

REDUCTION OF CURRENCIES.

RULES for reducing the Currencies of the several United States into Federal Money.

CASE I.

To reduce the currencies of the different states, where a dollar is an even number of shillings, to Federal Money.

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RULE. 1. When the sum consists of pounds only, annex a cipher to the pounds, and divide by half the number of shillings in a dollar; 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 pence and farthings to a decimal of a shilling; annex said decimal to the shillings, with a decimal point between, then divide the whole by the number of shillings contained in a dollar, and the quotient will be dollars, cents, mills, &c.

EXAMPLES.

1. Reduce 731. New-England and Virginia currency, to Federal money.

$

cis.

3)730
$2431-243 33

2. Reduce 45l. 15s. 7d. New-England currency, to fede

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[ral money.

d.

12)7,500

,525 dccima?.

Formerly the pound was of the same sterling value in all the colonies as in Great-Britain, and a Spanish Dollar worth 4s. €4.-but the legisla tures of the different colonies emitted bills of credit, which afterwards depreciated in their value, in some states more, in otheis less, &c.

Thus a doilar is reckoned in

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Adding a cipher to the pounds, multiplies the whole by 10, bringing them into tenths of a pound, then because a dollar is just three tenths of a pound, N. E. currency, dividing those tenths by 3, brings them into dollars, &c. See Note, page 78.

NOTE. 1 farthing is,25

2

3.

=

=

which annex to the pence, and ,50 divide by 12, you will have the ,75) decimal required.

3. Reduce 345l. 10s. 111d. New-Hampshire, &c. curren cy, to Spanish milled dollars, or federal money.

£345 10 11
20

6)6910,9375

d.
12)11,2500

$1151,8229+ Ans.

,9375 decimal.

4. Reduce 1957. 14s. 33d. New-York and North-Carolina currency, to federal money.

£105 14 33
20

A dollar-8)2114,3125

$264,289 06 Ans.

Or $ dem.

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d
12)3,7500

,3125 decimal.

5. Reduce 4317. New-York currency to federal money. This being pounds only,*—

4)4310

cts.

Ans. $10771077,50

6. Reduce 287. 11s. 6d. New-England and Virginia cur

rency, to federal money.
7. Change 4637. 10s. 8d.
to federal money.
8. Reduce 351. 19s.

money.

9. Reduce 2147. 10s.

federal money.

Ans. $95, 25 cts. New-England, &c. currency, Ans. $1545, 11cts. Im. + Virginia, &c. currency, to federal Ans. $119, 83 its. 3 m. + New-York, &c. currency, to Ans. $536, 32 cts. 8 m. +

7d.

10. Reduce 3047. 11s, 5d. North-Carolina, &c. currency,

to federal money.

11. Change 2197. 11s. 73d.

currency, to federal money.

Ans. $761 42 cts. 7 m.+ New-England and Virginia Ans. $731 94 cts.

A dollar is 8s. in this currency-4-4-10 of a pound; therefore, multiply by 10, and divide by 4, brings the pounds into dollars, &c.

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