numbers, and point off as many places for decimals as there are in that number which contains the greatest number of decimals. Ans. .001. 8. From 96.71 take 96.709. 9. Take twenty-seven and twenty-eight ninety-seven and seven tenths. thousandths from Ans. 70.672. 10. Take one hundred fifteen and seven hundredths from three hundred fifteen and twenty-seven ten thousandths. Ans. 199.9327. 11. From twenty-nine million four thousand and five take twenty-nine thousand and three hundred forty-nine thousand two hundred, and twenty-four hundred thousandths. Ans. 28625804.99976. RULE. 245.792 Multiply as in whole numbers, and point off us 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 there are decimals in the multiplicand and multiplier, supply the defect by prefixing ciphers. See Example 12th. 13. Multiply 61.76 by .0071. 14. Multiply .0716 by 1.326. 15. Multiply .61001 by .061. 16. Multiply 71.61 by 365. 17. Multiply .1234 by 1234. 18. Multiply 6.711 by 6543. 19. Multiply .0009 by .0009. Ans. .438496. Ans. .0949416. Ans. .03721061. Ans. 26137.65. Ans. 152.2756. Ans. 43910.073. Ans. .00000081. 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 five thousand and two, multiplied 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. $18.43,75. 27. What will 375.6 pounds of sugar cost, at $0.125 per pound? Ans. $46.95. 28. What will 26.58 cords of wood cost, at $5.625 a cord? Ans. $149.51,22. 29. What will 28.75 tons of potash cost, at $125.78 per Ans. $3616.17,5. ton? 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. RULE. Divide as in whole numbers, and point off as many decrmals 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. 10. Divide 7.25406 by 9.57. 11. Divide .21318 by .38. 12. Divide 7.2091365 by .5201. 13. Divide 56.8554756 by .0759. Ans. 321.2. Ans. .758. Ans. .561. Ans. 13.861+. 14. Divide 30614.4 by .9567. 15. Divide .306144 by 9567. Ans. 32000. 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. 19. Divide 119109094.835 by 38123.45. 20. Divide 1191090.94835 by 3812345. 21. Divide 11910909483.5 by 38.12345. 22. Divide 11.9109094835 by 381234.5. 23. Divide 1191.09094835 by 3.812345. 24. Divide 11910909483.5 by .3812345. 25. Divide 1.19109094835 by 3.812345. 26. Divide .119109094835 by .3812315. Ans. 3124.3. Ans. Ans. Ans. Ans. Ans. Ans. Ans. SECTION XXVII. REDUCTION OF DECIMALS. CASE I. To reduce a vulgar fraction to its decimal. 1. Reduce OPERATION. 8)3.000 That the decimal .375 is equal to 3 may be shown by writing it in a vulgar fraction and reducing it; thus, = 20% = 48=& Ans. 375 1000 75 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. 4. Reduce, 3 5 Ans. .625. Ans. .5. 1, 4, 8, 12, 16, 2', ana to decimals. Ans. .666+, .75, .833+, .91666+, .1875, .04, .125. 8 5. Reduce, 27, 37, 41, 1, and T2 to decimals. Ans. .05882+, .074074-, .1351+, .00696+, .07207+, .0008103+. CASE II. To reduce denominate numbers to decimals. 1. Reduce 15s. 9 d. to the decimal of a £. Ans. .790625. OPERATION. 4 3.00 12 9.75000 20 15.81250 .790625 Ans. 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. 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 denomination, 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. 3qr. 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 decimal of a mile. Ans. .73603219+. 7. Reduce 3gal. 2qt. 1pt. of wine to the decimal of a hogshead. Ans. .0575396+. 8. Reduce 1pt. to the decimal of a bushel. Ans. .015625. 9. Reduce 2R. 16p. to the decimal of an acre. CASE III. Ans..6. To find the decimal of any number of shillings, pence, and farthings, by inspection. RULE. Write half the greatest even number of shillings for the first decimal figure, and if the number of shillings be odd, annex to the decimal the figure 5. Then write underneath the number of farthings contained in the given pence and farthings, setting the left-hand figure in the second place, if there be more than one figure, and the single figure |