NOTE. -To change 30ths to 10ths, find how many 10ths there are in as many whole ones as you have 30ths, and then divide them by 30. 5. Change 6. to a decimal fraction. NOTE. First reduce the fraction to its lowest terms. Find then what product of 10 by itself can be divided by the denominator. 7. What decimal fraction is equal to ? To? To 28? 8. What does 0.7 signify? NOTE. The point after the O is called the decimal point; all the figures before it denote whole numbers; all after it decimal fractions. If there is but one figure after the decimal point, it is tenths; if two, they are hundredths; if three, thousandths; and so on. 0.6 is 1; 0.64 is 1; 0.643 is 1603; 1.5 is 11; 22.4 is 221; 365.252 is 3651000. 252 9. What does 1.8 signify? 2.81? 12.892? 10. What does 6.872 signify? 0.97? 5.5? 11. What does $124.54 signify? NOTE. Cents are decimals of a dollar, so dollars and cents are written with the decimal point between them. 12. What does $223.6 signify? $223.60? $223.06? NOTE. We do not often use the decimal expression for dimes, but rather annex a cipher and make cents of dimes, just as we talk of ten cents instead of one dime. 13. What do the figures 0.24 express? The figures 0.46? The figures 3.1? The figures 3.14? 14. What part of a dollar is 48 cents? cents? 34 cents 3 mills? 15. 34 Reduce 1 shilling to the decimal of a pound; 3 shillings; 7 shillings. 16. Reduce 7 shillings 6 pence to shillings and cenths; to the decimal of a pound. NOTE. is equal to no even number of tenths, but it is nearly equal to 0.3; nearer to 0.33; still nearer to 0.333; and so on. If we have of a dime to reduce to cents, we should call it 3 cents; of a dollar, we should call it 33 cents; and of an eagle $3.33; and so on. 18. How many cents in of a dime? NOTE. of 10 cents is nearly 2 cents. 19. How many cents in of a dollar? ? ? 20. Reduce of an eagle to dollars and cents. 21. What decimal to hundredths of a pound avoirdupois is 1 ounce? Is 3 ounces? Is 4 ounces? NOTE. "To hundredths," means that all fractions less than hundredths are not counted—more than 5 thousandths counting as an additional hundredth. 22. How many hundredths of a foot are there in 6 inches? In 7 inches? In 8 inches? 23. How many hundredths of a mile are there in 154 rods? How many thousandths of a mile in 129 rods? NOTE. 320 rods make a mile. 24. Reduce 67 square inches to the decimal of a foot; 79 square inches; 87 square inches. NOTE. If inconvenient to divide by 144, divide by 12, twice, since 12 times 12 are 144. 25. Reduce 85 square rods to thousandths of an acre; 97 square rods? 26. Reduce 85 cubic feet to the decimal of a cord, to hundredths; 77 cubic feet; 44 cubic feet. 27. Reduce 22 hours to the decimal of a day; 16 hours 45 minutes; 15 hours 23 minutes. NOTE. There are 1440 minutes in a day. 28. Reduce 12 ounces to the decimal of a pound; 8 ounces; 10 ounces. LESSON LXII. 1. Add together 0.25, 0.67 and 0.92. 2. Add together $1.26, $1.37 and $0.63. 3. How much are $22.54 and $27.46? 4. Add together 0.9, 0.09, 0.009 and 0.27. 5. How much are $2.65, $3.1 and 1 cent? 6. Add to 2.76; to 2.21; 8 to 4.35; 7 to 4.04. 7. Subtract 0.645 from 3.334. 8. How much is $77.25 less $64.51? 9. Subtract 0.62 from 53. 10. Subtract 2.228 from 31. 11. Subtract 1.58 from 1, to thousandths. 12. What is the sum of 3.12, 5 and 6.38, less 21? 13. From 32 added to 2.72, subtract 2 added to 31. 14. Multiply 24 by 0.008; 45 by 0.9. 15. Multiply 1.27 by 11; 2.35 by 8; 3.27 by 9. 16. What is the product of 346 by 0.02; 154 by 1.3? 17. What will 28 tons of coal cost, at $7.80 a ton? 18. Multiply 0.1 by 0.1; 0.1 by 0.01; 0.01 by 0.01. NOTE. When the multiplicand has one decimal place, and the multiplier one, how many will the product have? When the multiplicand has one decimal place, and the multiplier two, how many will the product have? When the multiplicand has two decimal places, and the multiplier two, how many will the product have? 19. Multiply 0.0009 by 10; by 100; by 1000. NOTE.-Multiplying any decimal by 10 is equivalent to removing the decimal point one place nearer the end; and multiplying by 100 removes the decimal point two places nearer the end; and so on. 20. Multiply 0.007 by 10; by 100; by 1000. 21. What is the profit on 900 yards of cotton cloth, at $0.009 a yard? 22. What cost 10 barrels of flour, at $8.375 a barrel? 100 barrels? 1000 barrels? 23. Multiply $959 by 0.01; by 0.06; by 0.12. 24. How much is 1 per cent. of $959? 6 per cent.? 12 per cent.? 25. How much is 3 per cent. of $150? cent.? 26. How much is 3,3 27. How much is 5 per per cent. of $240? per cent. of $262? NOTE. per cent. of $262 is $2.096; as 0.006 is more than of a cent, 0.096 is nearer 10 cents than 9 cents. $2.10 is sufficiently exact for per cent. of $262. 28. What is 8 per cent. of $536? 29. What is 6 per cent. of $424? 18 per cent.? 30. What is 7 per cent. of $216.40? 28 per cent.? 31. Required 33 per cent. of $200. 66 per cent. NOTE. 33 per cent. is of 99 per cent 32. If 100 tons of hay cost $20.27, how much costs 1 ton? How much cost 2.5 tons, leaving out fractions of a cent? NOTE. In leaving out fractions of a cent, call everything over 5 mills, 1 cent. 33. Required 16 per cent. of $212.54. = NOTE. 16 per cent. of $200 is $32; of $12 is $1.92; of $0.54 is $0.09; and $32+$1.92 $0.09 $34.01, or 16 per cent. of $212.54. per cent. of $200 is $0.54; of $12 is $0.03; of $0.54 is $0.00, less than of a cent; and $0.54 +$0.03=$0.57, or 16 per cent. of $212.54. $34.01+ $0.57 $34.58, the answer. = 27 100 34. What is 8 per cent. of $67.33? 18, per cent. of $243.50? 35. What is the value of 306 pounds of tea, at 58 cents a pound? NOTE. At $1.00 a pound, it would be worth $306.40; so we must find 581 per cent. of $306.40. 36. What cost 86 cords of wood, at $6.43 a cord? 37. At $1.62 a day, how much can a man earn in 8.74 days? 38. How much will 262 pounds of beef cost, at $7.83 per hundred pounds? LESSON LXIII. 1. Divide 8.96 by 7; 8.54 by 7; 9.80 by 8. NOTE. 8 divided by 7 gives 1, and 1 over; .96 and 1 are 188; 186 divided by 7 gives f, or .28. 10 28 2. Divide 2.60 by 4; 3.4 by 8 ; 5.4 by 12. 3. Divide 21 by 0.7; by 0.07; by 0.007. 4. Divide 28.4 by 16; 63.24 by 15; 48.45 by 11, to hundredths. 5. Divide 36.3 by 9, to thousandths. 6. How many times is 16 contained in 256? In 2560 ? 7. How many times is 1.6 contained in 25.6? In 256 ? 8. How many times is 7 contained in 63.7? In 6.37? 9. Divide 1 to thousandths, by 6; by 7; by 8; by 9. 10. How many times is 1.4 contained in 2.24? NOTE. is contained in 24 16 times; how many times in To of 22? |