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, EXAMPLES. 1. What is the value of ,5724 of a pound sterling? £.,5724 20 11,4480 12 5,3760 4 1,5040 Ans. 11s. 5d. 1,5qrs. 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. 2,4qrs. 4. What is the value of ,040625 of a pound? Ans. 94d. 5. Find the value of ,8125 of a shilling. Ans. 94d. 6. What is the value of ,617 of an cwt. Ans. 2qrs. 13lb. 1oz. 10,6dr. 7. Find the value of ,76442 of a pound troy. Ans. 9ox. 3pwt. 11gr. 8. What is the value of ,875 of a yd.? Ans. 3qrs. 2no 9. What is the value of ,875 of a hhd. of wine? Ans. 56gal. Oqt. 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. 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 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. ? 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 shillings be odd; and the third place by 1 when the farthings exceed 12, and by 2 when they exceed 56. EXAMPLES. 1. Find the decimal of 7s. 9ąd. by inspection. ,3=6s. 2. Find the decimal expression of 16s. 4d. and 17s. Ans. £,819, and £,885 8ad. 3. Write down £47 18 104 in a decimal expression. Ans. £47,943 4. Reduce £1 8s. 2d. to an equivalent decimal. PROBLEM II. Ans. £1,408 A short and easy method to find the value of any deciLal 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, it 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. Add 12s. double of 6 1 for the 5 in the second place which is to be [deducted out of 7. 74d.29 farthings remain to be added. Deduct 4d. for the excess of 12. Ans. 13s. 7d. 2. Find the value of £.,876 by inspection. Ans. 17s. 64d. 3. Find the value of £.,842 by inspection. Ans. 16s, 10d. 4. Find the value of £,097 by inspection. Ans. 1s. 114d. REDUCTION OF CURRENCIES. RULES, FOR reducing the Currencies of the several United States into Federal Money. To reduce the currencies of the different states, where a dollar is an even number of shillings, to Federal Money. They are New-England, Virginia, Kentucky, and Tennessee. RULE. New-York, and 1. When the sum consists of pounds only, annex a cypher to the pounds, and divide by half the number of shillings 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 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 486-but 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 } 8s New-York, & N. Carolina. ך 488 Adding a cypher 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 by 3, brings them into dollars, &c. See Note, page 85. EXAMPLES. 1. Reduce 731. New-England and Virginia Currency, to Federal Money. 2. Reduce 45l. 15s. 7d. New-England currency, to 3)730 cts. $243 243 354 federal money. d. 12)7,500 ,625 decimal. 20 A dollar 6)915,625 $152,604+ Ans. NOTE. 1 farthing is ,25) which annex to the pence, 2 3 50 and divide by 12, you will 75 have the decimal required. 3. Reduce 345l. 10s. 11 d. New-Hampshire, &c. currency, to Spanish milled dollars, or federal money. £345 10 114 20 6)6910,9375 $1151,8229+ Ans. d. 12)11,2500 ,9385 decimal. 4. Reduce 105l. 14s. 34d. New-York and North-Carelina currency, to federal money. 5. Reduce 4317. New-York currency to federal money. This being pounds only.* 4)4310 Ans. $1077 $ cts. 1077,50 4 *A dollar is 8s. in this currency-,4 of a pound; therefore, multiply by 10, and divide by 4, brings the pounds into dollars, &c. |