Divide as in whole numbers, and point off as many decimals in the quotient as the number of decimals in the dividend exceed those of the divisor; but if the number of those in the divisor exceed that of the dividend, supply the defect by annexing ciphers to the dividend. And if the number of decimals in the quotient and divisor together are not equal to the number in the dividend, supply the defect by prefixing ciphers to the quotient. 9. Divide 780.516 by 2.43. Ans. 321.2. 10. Divide 7.25406 by 9.57. Ans. .758. 11. Divide .21318 by .38. Ans. .561. 12. Divide 7.2091365 by .5201. Ans. 13.861+. 13. Divide 56.8554756 by .0759. Ans. 749.084. 14. Divide 30614.4 by .9567. Ans. 32000. 15. Divide .306144 by 9567. Ans. .000032. 16. Divide four thousand three hundred twenty-two and four thousand five hundred seventy-three ten thousandths, by eight thousand and nine thousandths. Ans. .5403+ 17. Divide thirty-six and six thousand nine hundred fortyseven ten thousandths, by five hundred and eighty-nine. Ans. .0623. 18. Divide three hundred twenty-three thousand seven hundred sixty-five, by five millionths. Ans. 64753000000. SECTION XXI. REDUCTION OF DECIMALS. CASE I. OPERATION. To reduce a vulgar fraction to its decimal. 1. Reduce to its decimal. That the decimal .375 is equal to s may be 83.000 shown by writing it in a vulgar fraction and .375 Ans. reducing it; thus, 375 26=*= Ans. Hence the following 1000 75 200 RULE. Divide the numerator by the denominator, annexing one or more ciphers to the numerator, and the quotient will be the decimal required. NOTE. - It is not usually necessary, that decimals should be carried to more than six places. 2. Reduce to a decimal. Ans. .625. 3. Reduce to a decimal. 1 / Ans. .5. 4. Reduce , à, k, l, in as and I to decimals. Ans. .666+, .75, .833+, 91666+, .1875, .04.125. 5. Reduce ii, î, 5, 1, 11 and 1234 to decimals. Ans. .05882+, .07407+, .1351+ .00696+, .072077, .0008 103+. 3 11 3 49 6, , . CASE II. OPERATION. To reduce compound numbers to decimals. 1. Reduce 15s. 9&d. to the decimal of a £. Ans. .790625. The 3 farthings are of a penny, and 4 3.00 these reduced to a decimal are .75 of a 12 9.75000 penny, which we annex to the pence and 20 | 15.81250 proceed in the same manner with the other .790625 Ans. terms. Hence the following RULE. Write the given numbers perpendicularly under each other for dividends, proceeding orderly from the least to the greatest : opposite to each dividend, on the left hand, place such a number for a divisor, as will bring it to the next superior name, and draw a line between them. Begin at the highest, and write the quotient of each division, as decimal parts, on the right of the dividend next below it, and so on, till they are all divided ; and the last quotient will be the decimal required. 2. Reduce 9s. to the fraction of a pound. Ans. .45. 3. Reduce 15cwt. 3yr. 141b. to the decimal of a ton. Ans. .79375. 4. Reduce 2qr. 21lb. 8oz. 12dr. to the decimal of a cwt. Ans. .6923828125. 5. Reduce lqr. 3na. to the decimal of a yard. Ans. .4375. 6. Reduce 5fur. 35rd. 2yd. 2ft. 9in, to the decima' of a mile. Ans. .73603219+. 7. Reduce 3gal. 2qt. 1pt. of wine to the decimal of a hogshead. Ans. .575396+. 8. Reduce 1pt. to the decimal of a bushel. Ans. .015625. 9. Reduce 2R. 16p. to the decimal of an acre. Ans. .6. CASE III. To find the decimal of any number of shillings, pence, and farthings by inspection. Note.— A demonstration of this case has been given, page 57. RULE. Write half of the greatest number of shillings for the first decimal figure, and if there be an odd shilling, annex a 5 to the half number of shillings, let the farthings in the given pence and farthings, occupy the second and third places, observing to increase their number by 1, if they exceed 12, and by 2, if they exceed 36. EXAMPLES. 1. Find the decimal of 15s. 9 d. by inspection. .7 =) of 14s. .791 2. Find the value of 13s. 64d. by inspection. Ans. .678. 3. Find the value of 19s. 8 d. by inspection. Ans. .984. 4. Value the following sums by inspection, and find their total — 195. 113d., 16s. 94d., 1s. 11d., 3s. Öfd., 17s. 54d., 18s. 4fd., 18s. 8£d., 19s. 114d., 135. 34d., 16s. 0fd., 17s. 7d. Ans. 7.91£. CASE IV. To find the value of any given decimal in the terms of the integer. 1. What is the value of .790625 £. ? Ans. 19s. 9 d. OPERATION. .790625 20 As a lower denomination consists of more 15.812500 units than the same value in a higher one, 12 therefore to bring pounds to farthings, we must multiply by the same numbers as in common 9.750000 Reduction. 4 3.000000 Hence we deduce the following RULE. Multiply the given decimal by that number which it takes of the next denomination to make one of that greater, and cut off as many places for a REMAINDER on the right, as there are places in the given decimal. Multiply the REMAINDER by the next lower denomination, and cut off for a remainder as before, and 80 proceed, until the decimal is reduced to the denomination required; the several denominations, standing at the left hand, are the answers required. 125 2. What is the value of .625 of a shilling ? Ans. 73d. 3. What is the value of .6725 of a cwt. ? Ans. 2qr. 191b. 5 oz. 4. What is the value of .9375 of a yard ? Ans. Sqr. 3na. 5. What is the value of .7895 of a mile ? Ans. 6p. 12rd. 10ft. 6lfin. 6. What is the value of .9378 of an acre ? Ans. 3R. 30p. 13ft. 9923 in. 7. Reduce .5615 of a hogshead of wine to its value in gallons, &c. Ans. 35 gal. 1qt. Opt. 3131gi. 8. Reduce .367 of a year to its value in days, &c. Ans. 134da. 1h. 7m. 19 sec. 9. What is the value of .6923828125 of a cwt. ? Ans. 2qr. 21lb. 8oz. 12dr. 10. What is the value of .015625 of a bushel ? Ans. 1 pint. 11. What is the value of .55 of an ell English ? Ans. 2qr. 3na. 12. What is the value of .6 of an acre ! Ans. 2R. 16p 1258 SECTION XXII. MISCELLANEOUS EXAMPLES. per cwt. : per yard? 1. What is the value of 7cwt. 2qr. 18lb. of sugar, at $ 11.75 Ans. $ 90.01.31 2. What cost 19cwt. 3qr. 141b. of iron, at $. 9.25 per cwt. ? Ans. $ 193.84.34. 3. What cost 39A. 2R. 15p. of land, at $ 87.37.5 per acre ? Ans. $ 3459.50.32. 4. What would be the expense of making a turnpike 87m. 3fur. 15rds., at $ 578.75 per mile ? Ans. $ 50595.414a. 5. What is the cost of a board 18ft. 9in. long, and 2ft. 3 in. wide, at $.05.3 per foot ? Ans. $ 2.27.73 6. Goliah of Gath was 61 cubits high ; what was his height in feet, the cubit being ift. 7.168in. ? Ans. 10ft. 4.592in. 7. If a man travel 4.316 miles in an hour; how long would he be in travelling from Bradford to Boston, the distance being 294 miles ? Ans. 6h. 50m. 6sec.+ 8. What is the cost of 5yd. 1qr. 2na. of broadcloth, at $ 5.625 Ans. $ 30.23.43. 9. Bought 17 bags of hops, each weighing 4cwt. Sqr. 7lb., at $ 5.87 per cwt. ; what was the cost ? Ans. $ 480.64.876. 10. Purchased a farm, containing 176A. 3R. 25rds., at $ 75.37 per acre : what did it cost ? Ans. $ 13334.30.819. 11. What cost 17625 feet of boards, at $ 12.75 per thousand ? Ans. $ 224.71.94. 12. How many square feet in a floor 19ft. 3in. long, and 15ft. 9in. wide ? Ans. 303ft. 27 in. 13. How many square yards of paper will it take to cover a room 14ft. 6in. long, 12ft. 6in. wide, and 8ft. 9in. high ? Ăns. 523yd. 14. How many solid feet in a pile of wood 10ft. 7in. long, 4ft. wide, and 5ft. 10in. high ? Ans. 2467ft. 15. How many garments, each containing 4yd. 2qr. 3na., can be made from 112yd. 2qr. of cloth ? Ans. 24. 16. Bought Igal. 2qt. 1pt. of wine for $1.82; what would be the price of a hogshead ? Ans. $ 70.56. 17. Bought 125šyd. of lace for $ 15.06; what was the price of 1 yard? Ans. $ 0.12. 18. What cost 17cwt. Sqr. of wool, at $ 35.75 per cwt. ? Ans. $ 634.56.21. 19. What cost 7hhd. 47gal. of wine, at $ 87.25 per hhd. ? Ans. $ 675.845. 20. How many solid feet in a stick of timber 34ft. 9in. long, ift. 3in. wide, and ift. 6in. deep ? Ans. 65.15625ft. |