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. Ans. ,375 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. EXAMPLES. 1. What is the value of ,5724 of a pound sterling? £ ,5724 20 11,4480 12 5,3760 [Carried up.; 2 na. 5,3760 4 1,5040 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. 24 sec. 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. EXAMPLES. 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. Ans. £1,40 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. EXAMPLES. 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. CASE I. York 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. 3)730 cls. $243-243 33 2. Reduce 451. 15s. 7d. New-England currency, to fede20 [ral money. d. A dollar=-6)915,625 12)7,500 * 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 South- Carolina, ds. Se Kentucký, and Delaware, and and Georgia, 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. 78. 6. Note. I farthing is ,25 , which annex to the pence, and 2 ,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 d. 12)11,2500 6)6910,9375 ,9375 decimal. 81151,8229+ Ans. 4. Reduce 1051. 14s. 33d. New-York and North-Carolina currercy, to federal money. £105 14 3 d 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. cis. * 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. |