in the dividend, therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor. 2. If the places in the quotient are not so many as the rule requires, supply the defect by prefixing cyphers to the left hand of said quotient. NOTE. If the decimal places in the divisor be more than those in the dividend, annex as many cyphers to the dividend as you please, so as to make it equal, (at least) to the divisor. Or, if there be a remainder, you may annex cyphers to it, and carry on the quotient to any degree of exactness. 12. Divide 1 dellar by 12 cents. 8,533+ 13.21 or 21,75 yards of cloth cost 34,317 dollars, what will one yard cost? $1,577 NOTE. When decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with cyphers) it is performed by removing the separatrix in the dividend, so many places towards the left hand as there are cyphers in the divisor. Annex cyphers to the numerator, and divide by the denominator; and the quotient will be the decimal required. NOTE. So many cyphers as you annex to the given numerator, so many places must be pointed in the quotient; and if there be not so many places of figures in the quotient, make up the deficiency by placing cyphers to the left hand of the said quotient. CASE II. To reduce quantities of several denominations to RULE. Bring the given denominations first to a vulgar fraction by Problem III. page 76; and reduce said vulgar fraction to its equivalent decimal; or RULE 2. Place the several 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 quotient will give the decimal required. EXAMPLES. 1. Reduce 12s. 6d. Sqrs. to the decimal of a pound. 4800 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 3s. 4d. New-England Currency, to the de cimal 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 9 16 19 Answers. ,05 ,1 ,2 ,45 ,8 ,95 8. What is the decimal expression of 4l. 19s. 6d. ? Ans. £4,97708+ 9. Bring 34l. 16s. 7ąd. into a decimal expression. Ans. £34,8322916+ 10. Reduce 25l. 19s. 5ąd. to a decimal. Ans. £25,972916+ 11. Reduce Sqrs. 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 3qrs. 21lb. Avoirdupois, to the decimal of an owt. 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. Ans..,675 18. Reduce 45 calendar months to the decimal of Tear. CASE III. To find the value of a decimal in the known parts of the integer. 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 denom❤ mation, 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?. £.,574 20 11,4480 12 5,3760 1,5040 Ans. 11s. 5d. 1,5grs. 2. What is the value of 75 of a pound? Ans. 15s. 5. 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. 6. What is the value of ,617 of an cwt. Ans. 94d. Ans. 2qrs. 13lb. 1oz. 10,6dr. 7. Find the value of ,76442 of a pound troy. Ans. 9ox. Spit. 11gr. 8. What is the value of ,875 of a yd.? Ans. 3grs. Ina 9. What is the value of ,875 of a hhd. of wine? na 55 gal. Oct. 1pt. |