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5.

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. ,0625

5. Reduce 3s. 4d. New-England Currency, to the decimal of a dollar. Ans. ,555555+ 6. Reduce 128. to the decimal of a pound. Ans. ,6

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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 exression.

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7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals.
4 9 16 19
,2,45

2

,1

,8 ,95

Shillings 1
Answers. ,05
8. What is the decimal expression of 4l. 19s. 6d. ?
Ans. £4,97708+

9. Bring $41. 16s. 74d. into a decimal expression.
Ans. £34,8322916+
decimal.
Ans. £25,972916+

10. Reduce 251. 19s. 54d. to a

11. Reduce Sqrs. 2na. to the decimal of a yard.
Ans. ,875
12. Reduce 1 gallon to the decimal of a hogshead.
Ans. ,015873+
13. Reduce 7oz. 19pwt. to the decimal of a lb. troy.
Ans. ,6625
the decimal of
Ans. ,9575
decimal of an
Ans. ,6

14. Reduce Sqrs. 21lb. Avoirdupois, to

an cwt.

15. Reduce roods, 16 perches to the

acre.

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 41 calendar months to the decimal of a

Ans. 375

year.

8

CASE III.

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.

To find the value of

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 nominations 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
4

1,5040

Ans. 11s. 5d. 1,5grs.

What is the value of 75 of a pound? Ans. 15s. S. 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. 93d. 5. Find the value of ,8125 of a shilling. Ans. 9id. 6. What is the value of ,617 of an cwt.? Ans. 2grs. 13lb. 1oz. 10,6dr. 7. Find the value of ,76442 of a pound troy.

2na.

Ans. 9oz. spurt. 11gr. 8. What's the value of,875 of a yd.? Ans. Syrs. 9. What the value of „875 of a hhd. of wine ? Ans. 55gal. Out, 1pt.

10. Find the proper quantity of ,089 of a mine. Ans. 28po. 2yds. 1ft. 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 troy ? Ans. 12,00384gr. 14. What is the value of ,046875 of a pound avoirdu pois? Ans. 12dr

15. What is the value of 712 of a furlo..g? Ans. 28po. 2yd. 1ft. 11,04in. 16. What is the proper quantity of ,142465 of a year ? Ans. 51,999725days.

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CONTRACTIONS IN DECIMALS.

PROBLEM I.

A CONCISE and easy method to find the decimal of any number of shillings, pence and farthings, (to thre 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.

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

,3

=

6s.

5

for the odd shllings. 39 the farthings in 94d. 2 for the excess of 36.

891decimal required.

2. Find the decimal expression of 16s. 41d. and 178. 841. Ans. £,819, and £,885 3. Write down £47 18 10 in a decimal expression. Ans. £47,945

4. Reduce £1 88 94. to an equivalent decimal. Ans. £1,408

PROBLEM II. 1

A short and easy method to find the value of any decinial 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. 6d.

3. Find the value of £.,842 by inspection. Ans. 16s. 10d.

4. Find the value of £.,097 by inspection. Ans. 1s. 114

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 Federa! Money.

They are
New-England,
Virginia,
Kentucky, and
Tennessee.

a

RULE

1. When the sum consists of pounds only, annex a cypher to the pounds, and divide by half the number of shillings in a uollar; the quotient will be dollars.†

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

New-York, and
North-Carolina.

*Formerly the pound 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

New-England, |New-Jersey, 7
Virginia,
Kentucky, and
Tennessee.

Pennsylvania,
Delaware, and
Maryland.

6s

7861

South

Carolina,
and
Georgia.

4s8

"New-York, & 2 88

N. Carolina.

Adding a cypher to the pounds, multiplies the whole by 10, bringing them into tenths of a pound lollar is just three-tenths of a pound N. ing those tenths by S, brings them inte

then because a currency, dividollars, &c. See

page 85.

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