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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 frac. tíon 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 quotient will give the decimal required.

EXAMPLES.

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

12

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

Ans. ,790625 3. Reduce 9d. Sqrs. 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. eimal of a dollar.

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

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 decimals, Shillings 1 2 4 9 16

19 Answers. ,05

,1 ,2 ,45 ,8 ,95 8. What is the decimal expression of 41. 195. 6}d.?

Ans. £4,97708+ 9. Bring S4l. 16s, 7d. into a decimal expression.

Ans. 434,8522916+ 10. Reduce 251. 19s. 51d. to a decimal.

Ans. £25,97291611. 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 14. Reduce Sqrs. 211b. Avoirdupois, to the decimal of an cwt.

Ans. ,5375 15. Reduce 2 roods, 16 perches to the decimal of an

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. Reduco 41 calendar months to the decimal of a year.

Ans. ,375

acre.

CASE III.

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

the integer.

RULE.

1. Multiply the deciinal 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 de nominations standing on the left hand make the answer.

EXAMPLES.

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

f. ,5724

20

11,4480

12

5,3760

4

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1,5040 Aizs. 11s. 5d. 1,5grs. 2. What is the value of ,75 of a pound ? Ans. 158. 3. What is the value of ,85251 of a pound?

Ans. 17s. Od. 2,49rs. 4. What is the value of ,040625 of a pound?

Ans. 910 5. Find thie value of ,3125 of a sitting Ans. 9fd. 6. What is the value of ,617 of an Cit..

Bus. 2ers. Islo. 1oz. 10,6dr. 7. Find the value of ,76442 of a pound troy:

Ans. Soz. Sput. 11gr. 8. What is the value of ,875 of a yd. ? Ans. 3grs. 2na, 9. What is the value of ,875 of a hhd. of wine?

9 ns. 35gal. Oct. Ipt.

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

Ans. 28po. 2yds. 1ft. 11,04in. 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. 207d. 16h. 26m. 24sec. 13. What is the proper quantity of ,002084 of a pound

Ans. 12,00384 r. 14. What is the value of 2046875 of a pound avoirdupois ?

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

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

Ans. 51,999725days.

troy?

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 ; aud 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. 9 d. by inspection.

,3
5 for the odd shillings.
39=the farthings in 9 d.
2 for the excess of $6.

= 69.

L. 391 decimal required.

2. Find the decimal expression of 16s. 41d. and 17s. 83d.

Ans. £,819, and £ ,885 3. Write down £47 18 101 in a decimal expression,

Ans. 647,943 4. Reduce £1 8s. 2d. to an equivalent decimal.

Ans. £1,408

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PROBLEM II.

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A short and easy method to find the value of any deci

nial of a pound by inspection.

RULE.

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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,

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EXAMPLES.

the 46

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

714.-29 farthings remain to be added. Deduct d. for the excess of 12.

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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 £6,097 by inspection.

Ans. 1s. 114d.

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