CASE II. To redu quantities of several denominations to a Decimal RULE Bring the given denommations first to a vulgar fraction by Problem III. page 76; and reduce said vulgar frac tion 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. 3 qrs, to the decimal of a pound 2. Reduce 15s. 9d. 3qrs. to the decimal of a pound. Ans. 790625 3. Reduce 9d. 3qrs. to the decimal of a shisling. Ans. ,8125 4. Reduce 3 farthings to the decimal of a shilling. Ans. ,0625 3. Reduce 3s. 40. New-England Currency, to the deamal of a dollar. Ans. ,555555+ 6. Reduce 12s. to the decimal of a pound. Ans.,6 NOTE. When e shillings are even, half the number with a point prefixed, is their decimal expression; but f the number be odd, annex a cypher to the shillings and then by halving them, you will have their decimal ex. pression. 2 4 19 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals. Shillings 1 16 9 Answers. ,05 ,1 ,2 ,45 ,8 ,95 8. What is the decimal expression of 4l. 19s. 6d.? Ans. £4,977008+ 9. Bring 34. 16s. 7gd. into a decimal expression. Ans. £34,8322916+ 10: Reduce 251. 19s. 54d. to a decimal. Ans. £25,972916+ 11. Reduce 3qrs. 2na. to the decimal of a yard Ans. ,875 12. Reduce 1 gallon to the decimar of a hogshead. Ane. 0158733 13. Reduce 7oz. 19pvt. to the decimal of a lb. troy. an cwt. 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 5fur Topo. to the decimal of a mile 1 Ans. ,675 18. Reduce 44 callendar months to the decimal of a year. Ans,375 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 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 denomi nation, and cut off a remainder as before; and so on through all the parts of the integer, and the several denomi nations standing on the left hand make the answer. EXAMPLES. f. What is the value of ,5724 of a pound sterling? 11,4480 12 5,3760 4 1,5040 Ans. 11s. 5d. 1,5grs. 2. What is the value of 75 of a pound r Ans 158. 3. What is the value of ,85251 of a pound? Ans. 17s. Od. 2,4grs. 4. What is the value of ,040625 of a pound , 5. Find the value of ,8125 of a shilling. 5. What is the vaine of,617 of an cwt. } Ans. 93d Ans. 2qrs. 13lb 1oz. 10,6dr 7. Find the value of ,76442 of a pound troy. Ans. 9oz. 3pwt. 11gr 8. What is the value of ,875 of a yd. 9. What is the value of ,875 of a hhd. of wine? Ans. 55gal. Ogt. 1pt. 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. 2. 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 pouna troy? Ans. 12,00384gr. 14. What is the value of ,046875 of a pound avoirdupois ? Ans. 12dr. 15. What is the value of ,712 of a furlong? Ans. 28po. 2yd. 1ft. 11,04in. 16. What is the proper quantity of ,142465 of a year? Ans. 51,999725days. 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 in rease the second place or 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. 93d. by inspection ,3 5 6s. for the odd shillings. 59the farthings in 93d. 2 for the excess of 36. £,391 decimal required. 2. Find the decimal expression of 16s. 44d and 17 8fd. Ans. £,819, and £,895 3. Write down £ 47 18 101 in a decimal expression. Ans. £47,948 4. Reduce £1 8s. 2d. to an equivalent decimal. PROBLEM []. Ans. £1,40 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, vr more than 5, reckon another shilling; then, after this 5 .s 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 Add 1 for the 5 in the second place which is to be [deducted out of 7. 74d. 23 farthings remain to be added. Deduct 4d. for the excess of 12. Ans. 13s. 7d. 2. Find the value of .,876 by inspection. Ans. 178. Ôtd. 3. Find the value of £.,842 by inspection. Ans. 16s. 10d. 4. Find the value of £.,097 by mspecun Ans. 13. 1112 |