CASE III. To find the value of a 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 mairy 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 Dominations standing on the left hand make the answer. EXAMPLES. £. ,5724 20 11,4480 12 5,5760 1,5040 Ans. 11s. 5d. 1,5grs. 3. What is the value of 75 of a pound ? Ans. 15s. 3. What is the value of ,85231 of a pound ? Ans. 175. Od. 2,4qrs. 4. "What is the value of ,040625 of a pound ? Ans. 9 d. 5. Find the value of ,8125 of a shilling. Ans. 9jd. 6. What is the value of ,617 of an cwt. ? Ans. 2grs. 15lb. 1oz. 10,6dr. 7. Find the value of ,76412 of a pound troy. Ans. 9oz. 3pirt. 11gr. 8. What's the value of ,875 of a yo. Ans. 3yrs. 2na. 9 What » ihe value of 875 of a hhd. of wine ? Ang. 55gal. But, I 10. Find the proper quantity of ,089 of a mise. Ans. 28po. 2yds. ift. 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 Ans. 12,0038gr. 14. What is the value of ,046875 of a pound avoirdu. Ans. 12dr 15. What is the value of ,712 of a furlo..g? Ans. 28po. 2yd. ift. 11,04in. 16. What is the proper quantity of ,142463 of a year ? Ans. 51,999725days. troy? pois ? 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 INSPEOTIOX. 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 shil. lings be ocd; and 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. 9fd. by inspection. y = 6s. 5 for the odd shllings. 6,891 medecimal required. 2. Find the decimal expression of 16s.* 4fd, and 178 841. Ans. £,819, and £ ,885 3. Write down 647 18 104 in a decimal expression. Ans. $47,943 4. Reduce £1 85 9d. to an equivalent decimal. Ans. £1,408 PROBLEM II. A short and easy method to find the value of any deci. Hial 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 deducted out of 7. Add 74d.-29 farthings remain to be added. Deduct d. for the excess of 12. Ans. 13s. 7d. Ans. 17s. 6td. 3. Find the value of £. ,849 by inspection. Ans. 16s. 10d. 4. Find the value of £. ,097 by inspection. Ans. 1 S. 111 REDUCTION OF CURRENCIES. RULES, For reducing the Currencies of the several United Status* into Federal Money. CASE I. They are North-Carolina. S RULE 1. When the suin consists of pounds only, annex a cy. pher to the pounds, and divide' by hall the number of shillings in a collar ; the quotient will be dollars. 2. But if the sum consists of pounds, s!iillings, pence, &c. bring the given sum into shillings, and reduce the pelice and farthings to a decimal of a shilling; annes 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, cepts, mills, &c * Forinerly the polind was of the same sterling value in all the colonies as in Great-Britain, and a Spanish Dollar worth 4s6but 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 Nor-England, .NP-Virsey, Southl'irginia, Pennsylvania, >6s Carolina, 1861 488 Kentucky, and Delaiare, and and Maryland. Georgia. Neir-Jork, 82 8s N. Carolina. Adding a cypher to the pounds, multiplies the whole by 10, liringing them into tenths of a pound then because Jollar is just three-tenths of a pound N. I currency, diviing those tenths by , brivgs them intc dollars, &c. See lote, page 85. Sennessve. EXAMPI.F.S. 1. Redlice :31. New-England anıl Virginia Currency, to Federal Money. 3):30 8 cts. $9454523 53 2. Reduce 451. 15s. : 3d. New-England currence, to 20 Trileral money. d. A dollai=6)915,625 12): ,500 81.52,604+ Ans. ,625 decimal. Nore. I farthing is ,25 which annes to the prelice, 2 =,50 Sivil diviile' bv 19. sou will 3 ,75 J have the decimal required. 3. Relice 3151. 10s. 11 fd. New Hampshire, &c. cur. rency, to Spanish inilled dollars, or federal money. £$45 10 11 d. 12)11,2500 6)0910,9375 ,9975 decimal $1151,9229+ Ans. 4. Recluce 1051. 149. 3}d. New-York and Nortn-Caro. lina cuirencv, lv federal money. £ 105 14 31 d. 20 12)3.500 A lollar-m8)2114.3123 ,S125 decimal 8264,289 06 Ans. Or S dim. 26 5. Reduce 4511. New-york currency to federal money This being pounds only.* 4)4310 8 cts. Ans. 8107:1=1077,50 ..4'ollar is Rs. in this currenys4to of a pound, thrrefore, inultiplej by 10, and decide by 4, brings the pounds into duliars, &c. |