it is performed by removing the separatrix in the dividend, so many places towards the left hand as there are ciphers in the divisor. To reduce a Vulgar Fraction to its equivalent Decimai. RULE. Annex ciphers to the numerator, and divide by the denominator ; and the quotient will be the decimal required. NOTE. So many ciphers 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 ciphers to the left hand of the said quotient. CASE II. To reduce quantities of several denominations to a Decimal. RULE. Bring the given denominations 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. 12 2. Reduce 15s. 9d. 3qrs. to the decimal 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. 5555554 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 cipher to the shillings and then by halving them, you will have their decimal ex. pression. 2 4 9 19 16 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals. Shillings 1 Answers. 05 ,1 ,2,45 8. What is the decimal expression of 4. 19s. 6d.? Ans. £4,97708+ 9. Bring 347. 16s. 73d. into a decimal expression Ans. 434,8322916+ 10. Reduce 25l. 19s. 51d. to a decimal. Ans. £25,972916+ 11. Reduce 3qrs. 2na. to the decimal of a yard. Ans. ,875 12. Reduce 1 gallon to the decimal of a hogshead. Ans. 015873+ 13. Reduce 7oz. 19pwt. to the decimal of a lb. troy. Ans. 6625 14. Reduce 3qrs. 21lb. Avoirdupois, to the decimal of Ans. 9575 a 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. 16po. to the decimal of a mile. Ans. ,675 18. Reduce 4 calendar months to the decimal c year. H 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 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? 11,4480 12 5,3760 4 1,5040 Ans. 11s. 5d. 1,5grs. 2. What is the value of 75 of a pound? Ans. 15s. Ans. 178. Od. 2,4qrs. 4. What is the value of ,040625 of a pound? Ans. 93d 5. Find the value of ,8125 of a shilling. 6. What is the value 7. Find the value of 76442 of a pound troy. Ans. 9oz. 3pwt. 11gr 8. What is the value of ,875 of a yd.? Ans. 3qrs. 2na. 9. What is the value of ,875 of a hhd. of wine? Ans. 55gal. 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. 3r. 25,2po. 12. What is the value of ,569 of a year of 365 days? An.. 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. 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 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. 39 the farthings in 93 d. £.,391 decimal required. |