32 19. What will 67 pounds of tea cost, at 653 cents per lb. Ans. $4.52 20. How many cubic feet does a box contain, that is 8 feet long, 51 feet wide, and 3 feet high? Ans. 146ft. 21. How many feet of boards will it take to cover a side of a house, which is 46 feet long, and 173 feet high? Ans. 812ft. 22. How many feet of boards will it take to make 7 boxes, that shall be 5 feet long, 2 feet high, 3 feet wide; and how many cubic feet will they contain? Ans. 52758ft. 28625 cub. ft. 23. A certain room is 12 feet long, 111⁄2 feet wide, and 7 feet high; how much will it cost to plaster it, at 2 cents per square foot? Ans. $13.483. 24. A man has a garden that is 143 rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 4 feet deep; what will be the expense if he gives 2 cents per cubic foot? Ans. $223.761. 25. How many bushels of grain will a box contain, which is 147 feet long, 511 feet deep, and 44 feet wide, there being 2150 cubic inches in a bushel? Ans. 2942422bush. 26. Which will contain the most, and by how much,box that is 10 feet long, 8 feet wide, and 6 feet deep; or a cubical one, whose each side measures 8 feet? 3584 Ans. The last contains 32 cubic feet most. 27. Divide $1112 equally between 129 men. 28. Bought 68 barrels of flour at $7 was the amount of the whole? a Ans. $8. per barrel, what Ans. $5381. 29. What cost 83 acres of land at $423 per acre? Ans. $369.20. 30. How shall four 3's be arranged, that their value shall be nothing? 31. From 3 take 11. SECTION XVI. DECIMAL FRACTIONS. A DECIMAL FRACTION is that whose integer is always divided into 10, 100, 1000, &c. equal parts. Its denominator is always an unit, with as many ciphers annexed, as there are places in the given decimal. There is therefore no need of having the denominator expressed; for the value of the fraction is always known by placing a point before it, at the left hand, called the separatrix. Thus, .5 is ‰, .37 is 100, .348 is 1000. 37 348 Ciphers annexed to the right hand of decimals do not increase their value; for .4 or .40 or .400 are decimals having the saine value, each being equal to or ; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus .4 is, or four tenths; but .04 is to, or four hundredths; and .004 is 100, or four thousandths. The figure next the separatrix is reckoned so many tenths; the next at the right, so many hundredths; the third is so many thousandths; and so on, as may be seen by the following 100, TABLE. 7 6 5 3 2 1. 2 3 4 6 7 From this table it is evident, that in decimals, as well as in whole numbers, each figure takes its value by its distance from the place of units NOTE. If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c. NUMERATION OF DECIMAL FRACTIONS. Let the pupil write the following numbers. 1. Three hundred twenty-five, and seven tenths. 4. Twenty-four, and nine millionths. 5. Two hundred twenty-one, and nine hundred thousandths. 6. Forty nine thousand, and forty-nine thousandths. 7. Seventy-nine million two thousand, and one hundred five thousandths. 8. Sixty-nine thousand fifteen, and fifteen hundred thousandths. 9. Eighty thousand, and eighty-three ten thousandths. 10. Nine billion, nineteen thousand nineteen, and nineteen hundredths. 11. Twenty-seven, and nine hundred twenty-seven thousandths. 12. Forty-nine trillion, and one trillionth. 13. Twenty-one, and one ten thousandth. 14. Eighty-seven thousand, and eighty-seven millionths. 15. Ninety-nine thousand ninety-nine, nine thousand nine billionths. 16. Seventeen, and one hundred seventeen ten thousandths. 17. Thirty-three, and thirty-three hundredths. 18. Forty-seven thousand, and twenty-nine ten millionths. 19. Fifteen, and four thousand seven hundred thousandths. 20. Eleven thousand, and eleven hundredths. 21. Seventeen, and eighty-one quatrillionths. 22. Nine, and fifty-seven trillionths. 23. Sixty-nine thousand, and three hundred forty-nine thousandths. SECTION XVII. ADDITION OF DECIMALS. 1. Add 23.61 and 161.5 and 2.6789 and 61.111 and 27.0076 and 116.71 and 6151.7671 together. OPERATION. 23.61 161.5 2.6789 61.111 27.0076 116.71 6151.7671 6544.3846 In this question, it will be perceived, that tenths are written under tenths, hundredths under hundredths, &c.; and that the operation of addition is performed as in addition of whole numbers. We therefore induce the following RULE. Write the numbers under each other according to their value, add as in whole numbers, and point off from the right hand as many places for decimals, as there are in either of the numbers. 2. Add together the following numbers 413.1678956, 35.14671, 3.1671, 314.6. 3. What is the sum of the following 61.87, 46.67, 165.13, 676.167895. -81.61356, 6716.31, Ans. 7564.0052656. numbers - 1121.6116, Ans. 2071.449495. 4. Add 7.61, 637.1, 6516.14, 67.1234, 6.1234, together. Ans. 7234.0968. 5. Add 21.611, 6888.32, 3.6167, together. Ans. 6913.5477. 6. Add seventy-three and twenty-nine hundredths, eightyseven and forty-seven thousandths, three thousand and five and one hundred six ten thousandths, twenty-eight and three hundredths, twenty-nine thousand and five thousandths together. Ans. 32193.3826. 7. Add two hundred nine thousand and forty-six millionths, ninety-eight thousand two hundred and seven and fifteen ten thousandths, fifteen and eight hundredths, and forty-nine ten thousandths, together. Ans. 307222.086446. 8. What is the sum of twenty-three million and ten, and one thousand and five hundred thousandths, twenty-seven and nineteen millionths, seven and five tenths? Ans. 23001044.500069. 9. Add the following numbers; fifty-nine and fifty-nine thousandths, twenty-five thousand and twenty-five ten thousandths, five and five millionths, two hundred five and five hundredths. Ans. 25269.111505. 10. What is the sum of the following numbers; twenty-five and seven millionths, one hundred forty-five, and six hundred forty-three thousandths, one hundred seventy-five and eightynine hundredths, seventeen and three hundred forty-eight hundred thousandths ? Ans. 363.556487. SECTION XVIII. SUBTRACTION OF DECIMALS. RULE. Let the numbers be so written, that the separatrix of the subtrahend be directly under that of the minuend, subtract as in whole numbers, and point off so many places for decimals, as there are in either of the numbers. 8. From 96.71 take 96.709. 9. Take twenty-seven and twenty-eight ninety-seven and seven tenths. Ans. .001. thousandths from Ans. 70.672. 10. Take one hundred fifteen and seven hundredths from three hundred fifteen and twenty-seven ten thousandths. Ans. 199.9827. 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. 12. From one million take one millionth. Ans. 999999.999999. |