36. Find the total length of the edges of a box 31 ft. long, 2 ft. wide, and 13 ft. high. 37. What should 2 lb. of tea cost if 1 lb. cost $1 ? 38. When $233 was paid for 8 months' rent, what rent was charged per year? 39. Find the cost of 83 doz. plants at 3 each. 40. If one stove consumes gal. of oil in a day and another gal., what part of a day will a gallon last both stoves? 41. A and B together purchased 150 acres of land, of which A took 30 acres more than B. How many acres did each take? SUGGESTION. 2 × B's + 30 acres = 150 acres. 42. A man and his son earned $25 in a week. The man earned $5 more than the son. How much did each earn? 43. If 2 in. on a certain drawing represent 10 mi., what should of an inch represent on the same drawing? 44. Two loads of corn contained together 75 bushels. They were sold at $ a bushel. $4 more was received for one load than for the other. How many bushels did each contain? 45. A dealer weighed 3 drafts of lard in a can which weighed 23 lb. The weight of the first draft and can was 21 lb., the weight of the second draft and can was 181 lb., the weight of the third draft and can was 203 lb. What was the weight of the lard in the three drafts? DECIMALS 105. One tenth of a unit is a tenth; one tenth of a tenth is a hundredth; one tenth of a hundredth is a thousandth; one tenth of a thousandth is a ten-thousandth; and so on. 106. A tenth, a hundredth, a thousandth, a ten-thousandth, and so on, are called decimal units. A tenth is a decimal unit of the first order; a hundredth is a decimal unit of the second order; a thousandth is a decimal unit of the third order; and so on. REMARK. In practice a decimal unit less than one ten-thousandth is seldom used. 107. Any number of decimal units of the same order is called a decimal fraction, or simply a decimal. Thus, 7 tenths, 21 hundredths, and 325 thousandths are decimals. 108. If the line of notation in the decimal system is extended to the right from units' place, and a point (.), called the decimal point, is placed after the units' order, a figure standing in the first place to the right of this point, represents a number of tenths; in the second place, a number of hundredths; in the third place, a number of thousandths; in the fourth place, a number of ten-thousandths; and so on. Thus, .375 represents 3 tenths, 7 hundredths, and 5 thousandths. 1000' 109. Since .375=10+100+1000, or 35, which is read three hundred seventy-five thousandths, .375 may be read three hundred seventy-five thousandths. 110. To read a decimal, read the number expressed by the figures of the decimal, and pronounce the name of the place occupied by the right-hand figure. 111. To write a decimal in figures, write the number of decimal units, and so place the decimal point that the right-hand figure will stand in the place that has the same denomination as the decimal. Illustrative Examples I. Read .426. Thus, .426 is read four hundred twenty-six thousandths. 2. Read 3.45. Thus, 3.45 is read three and forty-five hundredths. 3. Read .163. Thus, .163 is read sixteen and two thirds hundredths. 4. Read .01. Thus, .0 is read one third of a tenth. 5. Read 6.257 correct to the nearest hundredth. Thus, 6.257, read correct to the nearest hundredth, is six and twenty-six hundredths. 6. Read 2.783 correct to the nearest hundredth. Thus, 2.783, read correct to the nearest hundredth, is two and seventy-eight hundredths. 7. Write in figures 8 thousandths. Thus, write 8, and so place the decimal point that 8 stands in the thousandths' place; as, .008. 8. Write in figures 75 tenths. Thus, write 75, and so place the decimal point that 5 stands in the tenths' place; as, 7.5. 17. .00 18. .021 19. .031 21. Read 3.68 correct to the nearest tenth. 22. Read 3.52 correct to the nearest tenth. 16. .121 20. 4.66 23. Read 7.651 correct to the nearest hundredth. 24. Read 8.757 correct to the nearest hundredth. 25. Read 4.7321 correct to the nearest thousandth. 26. Read 4.7348 correct to the nearest thousandth. 27. Read $7.8746 correct to the nearest mill; correct to the nearest cent; correct to the nearest dime; correct to the nearest dollar. 29. 45 hundredths 31. 9 thousandths REDUCTION Illustrative Examples 1. Reduce .375 to a common fraction. |