« ΠροηγούμενηΣυνέχεια »
8. What is the decimal expression of 41. 195. 6. d. ?
Ans. £4,97708+ 9. Bring 311. 16s. 73d. into a decimal expression.
Ans. £31,03:22916+ 10. Reduce 251. 195, 5 d. to a decimal.
Ans. £25,972916-+ 11. Reduce 3 qrs. 2 na. toile decimal of a yard. Ans.,875 12. Reduce 1 gallon to this decimal of a hogshead.
Ans. ,0158734 13. Reduce 7 oz 19 pwi. to the decimal of a lb. troy.
Ans. ,6025 14. Reduce 3 qrs. 21'5. avoirdupois, to the decimalofa 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. Ins. ,675 18. Reduce 4., calendar months to the decimal of a year.
CASE III. 2o find the value of a Decimal in the known paris of the In
teger. Rrle.--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 hy 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 lett hand make the answer.
1. What is the value of ,5724 of a pound sterling?
Ans. 11s. 5d. 1,5 grs. 2. What is the value of ,75 of a pound ? Ans. 15s.. 3. What is the value of ,85251 of a pound?
Ans. 17s. Od. 2,4 qrs. 4. What is the value of ,040625 of a pound? Ans. 9;.. 5. Find the value of ,8125 of a shilling.
Ans. 9 d. 6. What is the value of ,617 of a cwt. ?
Ans. 2 qrs. 13 lt. 1 oz. 10,6 dr. 7. Find the value of ,76442 of a pound troy.
Ans. 9 oz. 3 pwt. llgr. 8. What is the value of ,875 of a yd. ? Ans. 3 qrs. 9. What is the value of ,875 of a bhd. of wine?
Ans. 53 gels. Oqt. 1 pt. 10. Find the proper quantity of ,089 of a inile.
Ans. 28 po. 2 yds. I ft. 11,04 in. 11. Find the proper quantity of ,9075 of an acre.
Ans. 3r. 25,2 po. 12. What is the value of ,569 of a year of 365 days?
Ans. 207 d. 16 h. 26 m. 13. What is the proper quantity of,002084 ot'a pound troy?
Ans. 12,00384 gr. 1 1. What is the value of ,046875 of a pound avoirdupois?
Ans, 12 di. 15. What is the value of ,712 of a furlong?
Ans. 28 po. 2 yds. 1 ft. 11,04 in. 16. What is the proper quantity of ,1 +2465 of a year ?
Ans. 51,999725 days.
CONTRACTIONS IN DECIMALS.
PROBLEM 1. 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 nuniber of shillings for tho first decimal figure.
2. Let the farthings in the given pence and farthings possess the second and third places; observing to increase the second placo of
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.
1. Find the decimal of 7s. 9 d. by inspection.
,3 = 6s.
5 for the odd shillings. -39=the farthings in 9 d.
2 for the excess of 36.
£. ,391=decimal required. 2. Find the decimal expression of 16s. 4£d. and 17s. 8 d.
Ans. £ ,819, and £ ,885 3. Write down £47 18 10 in a decimal expression.
Ans. £17,943 4. Reduce £1 8s. 2d. to an equivalent decimal.
PROBLEM II. 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 furthings, 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.
1. Find the value of £. ,679 by inspection,
12s=double of 6
[deducted out of 7
2. Find the value of £.,876 by inspection. Ans. 17s.6jd. 3. Find the value of £.,842 by inspection. Ans, 16s. 10d. 4. Find the value of £.,097 by inspection. Ans. Is. 11 d.
North Carolina. }
REDUCTION OF CURRENCIES. Rules for reducing the Currencies of the several United
States* into Federal Money.
Tennessee. Rule.- 1. When the sum consists of pounds only, annex a cipher to the pounds, and divide by half the number of shillirigs 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 conluined in a dullar, and the quotient will be dollars, cents, mills, &c.
EXAMPLES. 1. Reduce 731. New-England and Virginia currency, to Federal money.
$243-243 33 2. Reduce 451. 15s. 7d. New-England currency, to fede20
d. A dollar=-6)915,625
* Formerly the pound was of the same sterling value in all the colonies as in Great-Britain, and a Spanish Dollar worth 4s. 6..--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
ds. Se Kentucký, and Delaware, and
8.8 North Carolina, # 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 hy 3, brings them into dollars, &c. See Note, page 78.
Note. I farthing is ,25 , which annex to the pence,
,50 divide by 12, you will have the 3
,75 ) decimal required. 3. Reduce 3451. 10s. 11 d. New-Hainpshire, &c. currenja cy, to Spanish milled dollars, or federal money.
£345 10 11
,9375 decimal. 81151,8229+ Ans. 4. Reduce 1051. 14s. 33d. New-York and North-Carolina currercy, to federal money. £105 14 3
12)3,7500 A dollar=8)2114,3125
,3125 decimal. $264,289 06 Ans.
Or $ dcm. 5. Reduce 4311. New-York currency to federal money. This being pounds only,* 4)4310
Ans. $1077 =1077,50 6. Reduce 281. 11s. 6d. New-England and Virginia currency, to federal money.
Ans. $95, 25 cts. 7. Change 4631. 10s. 8d. New England, &c. currency, to federal money.
Ans. $1545, Ilcts. Im. + 8. Reduce 35l. 19s. Virginia, &c. currency, to tederal money.
Ans. $119, 83 tis. 3 m. + 9. Reduce 2141. 10s. 7. New-York, &c. currency, to federal money.
Ans. $536, 32 cls. 8 n. + 10. Reduce 3041. 11s, 5d. North-Carolina, &c. currency, to federal money.
Ans. $761 42 cts. 7 m. + 11. Change 2191. 11s. 77d. New-England and Virginia currency, to federal money. Ans. $731 94 cts.
* A dollar is 8s. in this currency-,4=1-10 of a pound; therefore, multiply hy 10, and divide by 4, brings the pounds into dollars, &c.