Multiply as in whole numbers, and point off as many figures for decimals in the product, as there are decimals in the multiplicand and multiplier; but, if there should not be so many figures in the product as in the multiplicand and multiplier, supply the defect by prefixing ciphers. See Example 12th. 13. Multiply 61.76 by 18 Multiply 6.711 by 6543. .061. Ans. .0949416. Ans. .03721061. Ans. 26137.65. Ans. 152.2756. Ans. 43910.073. Ans. .00000081. 19. Multiply .0009 by .0009. 20. Multiply forty-nine thousand by forty-nine thousandths. Ans. 2401. 21. What is the product of one thousand and twenty-five, multiplied by three hundred and twenty-seven ten thousandths ? Ans. 33.5175. 22. What is the product of seventy-eight million two hundred and five thousand and two by fifty-three hundredths? Ans. 41448651.06. 23. Multiply one hundred and fifty-three thousandths by one hundred twenty-nine millionths. Ans. .000019737. 24. What is the product of fifteen thousand, multiplied by fifteen thousandths? Ans. 225. 25. What will 26.7 yards of cloth cost, at $ 5.75 a yard ? Ans. $153.52.5. 26. What will 14.75 bushels of wheat cost, at $1.25 a bushel ? Ans. $18.43.7.5. 27. What will 375.6 pounds of sugar cost, at $0.125 per lb. ? Ans. $46.95. 28. What will 26.58 cords of wood cost, at $5.625 a cord? Ans. $149.51.23. 29. What will 28.75 tons of potash cost, at $ 125.78 per ton? Ans. $3616.17.5. 30. What will 369 gallons of molasses cost, at $0.375 a gallon ? Ans. $138.37.5. 31. What will 97.48cwt. of hay cost, at $1.125 per cwt. ? Ans. $109.66.5. 32. What will 63.5 bushels of corn be worth, at $0.78 per bushel? Ans. $49.53. 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. 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. To reduce a vulgar fraction to its decimal. may be Ans. That the decimal .375 is equal to shown by writing it in a vulgar fraction and reducing it; thus, 375 75 2001 1. Reduce OPERATION. 8)3.000 .375 Ans. Hence the following 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. 3. Reduce to a decimal. 5 4. Reduce,, §, 1, &, and to decimals. Ans. .625. Ans. .5. Ans. .666, .75, .833+, 91666+, .1875, .04.125. 5. Reduce, 27, 37, 431, 11 and 12 to decimals. 5 1234 Ans. .05882+, .07407+, .1351+, .00696+; .07207, .0008 103+. CASE II. To reduce compound numbers to decimals. 1. Reduce 15s. 94d. to the decimal of a £. Ans. .790625. The 3 farthings are of a penny, and these reduced to a decimal are .75 of a penny, which we annex to the pence and proceed in the same manner with the other 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. 3чr. 14lb. to the decimal of a ton. Ans. .79375. 4. Reduce 2qr. 21lb. 8oz. 12dr. to the decimal of a cwt. Ans. .6923828125. 5. Reduce 1qr. 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. 93d. by inspection. 2. Find the value of 13s. 63d. by inspection. 3. Find the value of 19s. 84d. by inspection. Ans. .678. Ans. .984. 4. Value the following sums by inspection, and find their total-19s. 11 d., 16s. 94d., 1s. 11d., 3s. Ò§d., 17s. 54d., 13s. 44d., 18s. 8d., 19s. 11ąd., 13s. 34d., 16s. 0дd., 17s. 7 d. Ans. 7.91£. |