12. How wide must a piece of land be that is 17 rod.: long to make an acre ? 13. How many square inches in a square foot; that is, in a figure that is 12 inches long and 12 wide ? 14. How much in length, that is 8 inches wide, will mako a square foot ? 15. How many square feet in a square yard ? 16. How many square yards in a square rod ? 17. How many square inches in a square yard ? 18. A piece of land 20 rods long and 2 rods wide, or in any other form which contains the same surface, is called a rood. How many square rods in a rood ? 19. How many roods make an acre ? 21. How many square inches in a square rod ? inches ? 29. The whole surface of the globe is estimated at about 199,000,000 square miles. How many acres on the surface of the globe ? 30. Ilow many square inches in a board 15 inches wide and 11 feet long? How many square feet? 31. How many acres in a piece of land 183 rods long and 97 rods wide ? 32. How many square inches in a yard of carpeting that is 2 ft. 3 in. wide? How many yards of such carpeting will it take to cover a floor 19 ft. 4 in. long and 17 ft. 2 in. wide ? a To measure solid bodies, such as timber, wood, &c., it is necessary to use measure that has three dimensions, length, breadth, and depth, height, or thickness. For this a measure is used in which all these dimensions are alike. Take a block, for example, and make it an inch long, an inch wide, and an inch thick, and all its corners or angles alike; this is called a solid or cubic inch ; so a block made in the same way, having each of its dimensions one foot, is called a solid or cubic foot. 33. If a block 1 inch wide and 1 inch thick and 1 inch long contains 1 solid inch, how many solid inches does such a block that is 2 inches long contain ? 3 inches long ? 4 inches long ? 5 inches long ? 8 inches long? 34. How many solid inches does a block that is 1 foot long, 1 inch thick, and 1 inch wide contain ! How many inches does such a block that is 2 inches wide contain ? 3 inches wide ? 4 inches wide ? 5 inches wide ? .8 inches wide ? 35. How many solid inches does a block 2 inches long, 2 inches wide, and 1 inch thick contain ? 2 inches thick ? 36. How many solid inches does a block 4 inches long, 3 inches wide, and 1 inch thick contain ? 2 inches thick ? 3 inches thick ? 37. How many cubic inches in a block 10 inches long, 8 inches wide, and 1 inch thick ? 2 inches thick ? 3 inches thick ? 5 inches thick ? 17 inches thick ? 38. How many cubic inches in a block 18 inches long, 13 inches wide, and 1 inch thick ? 5 inches thick ? 11 inches thick ? In the above examples supply feet instead of inches, and do them over again. 39. What rule can you make for finding the number of solid inches or feet in any regular solid body? 40. How many solid inches in a block 12 inches long, 12 inches wide, and 12 inches thick ; that is, in a solid foot ? 41. A pile of wood 8 feet long, 4 feet wide, and 4 feet high, or in any other form containing an equal quantity, is called a cord of wood. How many solid feet in a cord? 42. Find the numbers for the following table. SOLID OR CUBIC MEASURE. solid inches solid feet 40 solid feet of round timber, or 50 solid feet of hewn timber make 1 solid foot 1 cord of wood 1 ton or load , } 43. How many solid inches in a cord ? 44. How many solid inches in a ton of hewn timber? 45. In 468,374 solid inches, how many solid feet ? 46. How many feet of timber in a stick 28 feet long and 11 inches square ? 47. How many tons of timber in 2 sticks, each 25 feet long, 15 inches wide, and 11 inches thick ? 48. A pile of wood 4 feet square and 1 foot long, or a pile containing 16 solid feet is called 1 foot of wood. How many such feet in a cord ? 49. How many solid feet of wood in a pile 5 feet wide, 3 feet high, and 23 feet long? How many feet of wood ? How many cords? * A few more examples of this kind will be found in deciinals. DECIMAL FRACTIONS. XXV. In the following numbers, write the fractional part in the form of decimals. 1. Twenty-seven and six tenths, 27.10. Ans. 27.6. 2. Fourteen and seven hundredths. 1417. Ans. 14.07. 3. One hundred twenty-three, and eight thousandths. 123-8 Ans. 123.008. T007 4. One hundred and eight, and five tenths. 108, 5. Seventy-three, and nine hundredths. 7310 6. Four, and six thousandths. 4106 7. Sixteen, and one thousandth. 167dbo 8. Six tenths. 6 9. Five hundredths. Tóc: 10. Seven thousandths. Too 11. Two ten thousandths. Tooth 5 2 8 To 17. 3 10 6 12. Three, and four tenths and two hundredths. 316 and 1o7 13. are how many hundredths ? are how thousandths ? many 16. are how many thousandths ? and So and 10 oo are how many thousandths ? 18. Write 7 385 in the form of a decimal. 19. to are how many ten-thousandths ? 20. To are how many ten-thousandths ? 21. 1777 are how many ten-thousandths ? 22. 7, 76, Too, and totoo are how many ten-thousandths ? 23. Write 25.677 in the form of a decimal ? Write the fractions in the following numbers in the form of decimals. 24. 13106 30. 193,47 31. 87 106 32. 95,406 27. 142 38746 33. 98-6004 10000 Change the decimals in the following numbers to com mon fractions and reduce then to their lowest terms. 36. 42.5. 45. 4.00025. 37. 84.25.. 46. 13.0060058. 38. 9.8. 47. 0.75. 39. 137.16. 48. 0.3125. 40. 25.125. 49. .075. 41. 18.625. 50. .00128. 42. 11.8642. 51. .00015. 43. 163.90064. 52. .000106. 44. 72.0065. 53. ,1500685. 10000 100000* 100000 1000000 28. limit 29. 1775700 107000 XXVI. 1. A man purchased a barrel of flour for $7.43.; 5 gallons of molasses for $1.625; 3 gallons of wine for $4.87 ; 4 gallons of brandy for $7; 7 lbs. of sugar for $0.95; and 3 gallons of vinegar for $0.42. What did the whole amount to ? 2. How many bushels of corn in 4 bags, the first containing 24 bushels ; the second, 37; the third, 31780; and the fourth, 42%? Notc. Write the fractions in the form of decimals. 3. A man bought four loads of bay, the first containing 17 cwt.; the second, 191 cwt. ; the third, 24 cwl.; and the fourth, 141 cwt. How many cwt. in the whole ? Note. In all the examples under the head of decimals, change the fractions and parts to decimals. 4. A man raised wheat in five fields, in the first, 47% bushels ; in the second, 94, ? in the third, 871; in the fourth, 14316; and in the fifth 387 bushels. How many bushels in the whole ? 5. A man bought a load of hay for 6.45€. ; a load of oats for 77.£. ; 3 bushels of corn for 37£.; and a load of wood for 23. How much did the whole come to ? 6. Add together the following numbers, 3844; 1386, ; 7006; 17; 24083; 8; and 46013. 7. From a piece of cloth conic ning 473 yards, a merchant sold 23,95. How much reru' ined unsold ? A man owing $253 paid $187.375, how much did he then owe ? 9. A man owing 342,244. paid 187 £. How much did he then owe ? 10.. A merchant sold a barrel of flour for 25£.; 5 galTons of molasses for 1;£.; and 6 gallons of wine for 24. In pay he received a load of wood worth 21.£. and 2 bushels of wheat, worth it. and the rest in money ; how much money did he receive ? 11. From 1832£. take 875£. Multiplication of Decimals. XXVII. 1. A man bought 5 barrels of pork, at $17.43 per barrel ; how much did it come to ? 2. What cost 8 yards of cloth, at $7.875 per yard ? 3. How many bushels of meal in 14 sacks, containing 1.37 bushels each ! 4. How much hay in 8 loads, containing 24.35 cwt. each? 5. How much cotton in 17 bales, containing 4 cwt. each 6. How many cwt. of hay in 14 loads, containing 23.25 cpt. each? |