2. Reduce 15s. 9d. Sqrs. to the decimal of a pound Ans. ,790625 S. 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 39. 4d. New-England Currency, to the de cimal of a dollar. Ans. ,555555+ 6. Reduce 12s. to the decimal of a pound. Ins. ,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 decima's Shillings 1 4 9 16 19 Answers. ,05 ,1 ,45 ,8 ,95 8. What is the decimal expression of 41. 16s. 61d.? Ans. 54,97708+ 9. Bring 34l. 16s. 73d. into a decimal expression. Ans. £34,8322916+ 10. Reduce 251. 19s. 5 d. to-a decimal. Sins. £25,9729164 11. Reduce 3qrs. 2na. to the decimal of a yard. Ans. ,875 12. Reduce 1 gallon to the decimal of a hogshead. Ans. ,0158734 13. Reduce 7oz. 19pwt. to the decimal of a lb. troy. Ans. ,6625 14. Reduce Sqrs. 211b. Avoirųupois, to the decimal of an owt. Ans. ,9375 15. Reduce 2 roods, 16 perches to the decimal of an Ans. ,6 16. Reduce 2 feat 6 inches to the decimal of a yard. Ans. ,833333-4 17. Reduce 5fur. •1Gpo. to the decimal of a mile. Ans..,673 18. Reduce 4 calendar monitiis to the decimal of 1895. ,575 acre. CASE III. To find the value of a decimal in the known parts of the integer. RULE. 1 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 by the next inferior denommation, and cut off a remainder as before, and so on through all the parts of the integer, and the several denominations standing on the left hand, make the answer. EXAMPLES. 1. What is the value of ,5724 of a pound sterling? £. ,5794 20 11,4480 12 5,3760 1,5040 Ans. 11s. 5d. 1,59To. 2. What is the value of ,75 of a pound ? Ans. 15$. 3. What is the value of ,85251 of a pound? Ans. i7s. Od. 2,4qrs 4. What is the value of ,040625 of a pound? Ans. 91d. 5. Find the value of ,8125 of a shilling. Ans. 9 jeho 6. What is the value of ,617 of an cwt. Ans. 2grs. 131b. 1oz. 10,6dr. 7. Find the value of ,76442 of a pound troy. Ans. 90%. 3pwt. 11gr. 8. What is the value of ,875 of a yd. ? Ans. Sgrs. Como 9. What is the value of ,875 of a hhd. of wine : than 55 gol. Oot. int 10. Find the proper quantity of ,089 of mile. Ans. 28po. Qyds. ft. 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. 26ın. 24sec. 13. What is the proper quantity of ,002084 of a pound Ans. 12,00384 r 14. What is the value of ,046875 of a pound avoirdua ois ? Ans. 12dr. 15. What is the value of ,712 of a furlong? Ans. 98po. 2yd, ift. 11.04in. 16. What is the proper quantity of ,142465 of a year? Ins. 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 shil, lings be odd; and the third place by i when the farthings 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 93d. 2 for thc excess of St. 6. ,91=-decimal required 2. Find the decimal expression of 16s. 4 d. and 17 1 8''d. Ans. £. ,819, and £. ,885 3. Write, gown £,47 18 10% in a decimal expression Ans. £47,943 4. Rechtice £1 8s. 2d. to an equivalent deciñal. Ans. £1,408 PROBLEM II. A short and easy method to find the value of any deci mal 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 f. ,679, by inspection. 12$, Edouble of 6 [be deducted out of 7. Add 70.=29 farthings remain to be added. Deduct d. for the excess of 12. Ans. 13s. 7d. Ans, 17s. 61d. 3. Find the value of £. ,842 by inspection. Ans. 16s. 10d. 4. Find the value of £. ,097 by inspection. Ans. 1s. 111, 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 Federal Money. They are North-Carolina. S ROLS. !. When the sun consists of pounds only, annex a cy, pler to the pounds, alid dividle by half the number of shillings in a rollar ; de quotient will be dollars. 9. But if the sum consists of pounds, shillings, pence, Eic. bring the given sum into stillings, 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 a dollar, and the quotient will be dollars, cents, mills, &c. *Formerly the pound was of the same sterling value in all the colonies as in Great-Britain, and a Spanish Dollar worth 450--but the legislatures of the different colonies emitted bills of credit, which afterwards depreciated in their value, ia gome states more, in others less, &c. Tus a dollar is reckoned in New-England, New-Jersey, South Pirginia, Pennsylvania, Carolina, Ss >786 458 Kentucký, and Delaware, and and Tennessee. Maryland. Georgia. New V. Carolina." } 85 jAdding a cypher to the pounds, multiplies the whole loy 19, bringing them into tenths of a pound; then because a olan is just three-tenths of a pound N. E. currency, divising those tenths by 3, brings them into dollars, &e. See Vore, page 85. |