10. Find the proper quantity of ,089 of a mile. Ans. 28po. 2yds. 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. 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 avoirdu ois ? 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 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. 93d. by inspection. ,3 5 = 6s. for the odd shillings. 39 the farthings in 93d. £.,591=-decimal required 2. Find the decimal expression of 16s. 44d. and 17 8d. Ans. £.,819, and £.,885 3. Write down £47 18 10 in a decimal expression. Write down 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 decimal 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 résult 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. Add 12s.double of 6 1 for the 5 in the second place which is to Ans. 13s. 7d. Ans. 17s. 6ld. 5. Find the value of £. ,842 by inspection. Ans. 16s. 10d. 4. Find the value of £. ,097 by inspection. Ans. is. 11 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 Kentucky, and RULE. New-York, and 2 1. When the sum consists of pounds only, annex a cy pher 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 456-but the legislatures of the different colonies emitted bills of credit, which afterwards depreciated in their value, in some states more, in others less, &c. Thus a dollar is reckoned in New-York, &7 8s N. Carolina. S Adding a cypher to the pounds, multiplies the whole by 10, bringing them into tenths of a pound; then because a daar is just three-tenths of a pound N. E. currency, dividing those tenths by 8, brings them into dollars, &c. See Note, page 85. EXAMPLES. 1. Reduce 751. New-England and Virginia Currency, to Federal Money. 2. Reduce 451. 15s. 7d. New-England currency, to 8)730 Scts. 2243943 334 federal money. d. 12)7,500 ,625 decimal. 20 A dollar-6)915,C25 $152,604+ Aus. 2 S NOTE. 1 farthing is,257 which annex to the pence, ,50 and divide by 12, you 75 have the decimal required. S. Reduce $45. 10s. 114d. New-Hampshire, &c. cur rency, to Spanish milled dollars, or federal money. £45 10. 11! 20 6)6910,9375 $1151,8229+ Ans. d. 12)11,2500 ,9275 decima. 4. Reduce 105l. 14s. 3 d. New-York and North-Carolina currency, to federal money. 5. Reduce 4311. New-York currency to federal money, This being pounds only.* 4)4310 $ cis. Ans. $1077=1077,50 *A dollar is 8s. in this currency-,44 of a pound therefore, multiply by 10, and divide by 4, brings the pounds into dollars, &c. 6. Reduce 281. 11s. 6d. New-England and Virginia currency, to federal money. Ans. $95, 25cts. 7. Change 4631. 10s. 8d. New-England, &c. currency, to federal money. Ans. $1545, 11cts. 1m.+ 8. Reduce 351. 19s. Virginia, &c. currency, to federal Ans. $119, 83cts. 3m.-+ money. 9. Reduce 2141. 10s. 74d. New-York, &c. currency, Ans. $536, 32cts. 8m.+ to federal money. 10. Reduce 3047. 11s. 5d. North-Carolina, &c. currency, to federal money. Ans. $761, 42cts. 7m.+ 11. Change 219. 11s. 7ąd. New-England and Virginia currency, to federal money. Ans. $731, 94cts.+ 12. Change 2411. New-England, &c. currency, into federal money. Ans. $803, 33cts.+13. Bring 201. 13s. 54d. New-England currency, into dollars. Ans. $69, 74cts. 6m.+ 14. Reduce 4691. New-York currency, to federal mo Ans. $1170 15. Reduce 17s. 93d. New-York, &c. currency, to dollars, &c. Ans. £2, 22cts. 6,5m.+ 16. Borrowed 10 English crowns, at 6s. Ed. each, how many dollars at Gs. each, will pay the debt P Ans. 811, 11cts. 1m. NOTE. There are several short practical methods of reducing New-England and New-York currencies to Federal Money, for whisee the Appendix. CASE H. To reduce the currency of New-Jersey, Pennsylvania, Delaware and Maryland, to Federal Money. RULE. Multiply the given sum by 8, and divide the product by s. and the quotient will be dollars, &c.* EXAMPLES. 1. Reduce 2451. New-Jersey, &c. currency, to federal Ax&=1960, and 1960÷S=80531-8653, 331cts. NOTE. When there are shillings, pence, &c. in the A dollar is 7s. 64. —90d. in this currency of ground; therefore, multiplying by 8, and dividing by res the dollars, cents, &c. |