CASE II. 76 reduce quantities of severał denomination to a Decimal. Bring the given denominations first to a vulgar frac. tion by Problem III. page 76 ; and reduce said vulgar fraction to its equivalent decimal ; or RULE 2. Place the sereral denominations above each other, letting the highest denomination stand at the bot. tom ; then divide each denomination (beginning at the top) by its value in the next denomination, the last quo tient will give the decimal required. EXAMPLES. 1. Reduce 128. 6d. 3qrs. to the decimal of a pound 12 2. Reduce 159. 9d. 3qrs. to the deciinal of a pound. Ans. ,790625 3. 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 3s. 4d. New England Currency, to the decimal of a dollar. Ans. ,555555+ 6. Reduce 12s. to the decimal of a pound. Ans. ,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 decimals, Shillings 1 2 4 16 19 Answers. ,05 ,1 ,2 ,45 ,8 ,95 8. What is the decimal expression of 4l. 195. 6 d. ? Ans. £4,977008+ 9. Bring 341. 16s. 7 d. into a decimal expression. Ans. £34,8322916+ 10. Reduce 251. 198. 5 d. to a decimal. Ans. £25,972916+ 11. Reduce 3qrs. 2na. to the decimal of a yard. Ans. ,875 12. Reduce l gallon to the decimal of a hogshead. Ans. 0158733 * 13. Reduce Yoz. 19pwt. to the decimal of a lb. troy. Ans. ,6625 14. Reduce 3qrs. 21lb. Avoirdupois, to the decimal of 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 5fur. 16po. to the decimal of a mile. Ang ,675 18. Reduce 4f calendar months to the decimal of Ans. ,375 your 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 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 left hand make the answer. 1. What is the value of ,5724 of a pound sterling? £. ,5724 20 EXAMPLES. 11,4480 12 5,3760 4 1,5C-10 Ans. 113. Bd. 1,5qrs. 2. What is the value of ,75 of a pound? Ans. 168. 8. What is the value of ,85251 of a pound ! Ans. 179. 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. 9 d. 6. What is the value of ,617 of a cwt. Ans. 2qrs. 13lb. loz. 10,6dr. 7. Find the value of ,76442 of a pound troy. Ans. 902. 3prot, 11gr. 8. What is the value of ,875 of a yo. ? Ains. 3qrs, 2na. 9. What is the value of ,875 of a hhd. of wine ? Ans. 55gak. Ogt. Ipt. 10. Find the proper quartity of,089 of a mile. Ans. 28po. 2yds. ift. 11,04in 11. Find the proper quartity of ',9075 of an acre. Ans. 3r. 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. 12,00384gr. 14. What is the value of ,046875 of a pound avoirdu. pois ? Ans. 12dr. 15. What is the value of ,712 of a furlong ? Ans. 28po. 2yd. 11. 11,04in. 16. What is the proper quantity of ,142465 of a year? Ans. 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 whe 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 1 when the farthings exceed 12, and by 2 when they exceed 36. EXAMPLES 1. Find the decimal of 78. 9fd. by inspection, 5 for the odd shillings. £. 391 = decimal required. 2. Find the decimal expression of 16s. 45d. and 178. 8td. Ans. £,819 and ,885. 3. Write down £47 18 101 in a decimal expression. Ans. £47,948. 4. Reduce £1 88, 2d. to an equivalent decimal. Ans. £1°,40. 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 tenth 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. 125.=double of 6. [be deducted out of 7. Add 74d.-29 farthing remain to be added, Deduct d. for the excess of 12. Ans. 13s. 1d. Ans. 175. 64d. 3. Find the value of £. ,842 by inspection. Ans. 15s. 10d. 4. Find the value of £. ,097 by inspection. Ans. 13. 117d. |