1. Dimensional Analysis Lecture 2 Chapter 2

2. Review Question Which of the following decimal numbers are NOT written correctly for nursing charting? A.1.2 B..12 C.12.0 D.0.012

3. Calculators!! Bring a calculator to class You may not use cell phones during tests You may not borrow a calculator from another student until they have turned in their test

4. Multiplication of Decimals – Without a calculator The decimal point in the product of decimal fractions is placed the same number of places to the left in the product, as the total number after the decimal points in the fractions multiplied. – 0.42 x 0.6 = 0.42 (2 places to the left) x 0.6 (1 place to the left) 252 (count 3 places to left) .252  0.252

5. Multiplication of Decimals – with a calculator – 0.42 x 0.6 = Enter the number 0.42 Press the multiplication function (x) Enter the number 0.6 Press the equal function (=) Write down the answer

6. Multiplication of Decimals – Without a calculator If the product contains insufficient numbers for correct placement of the decimal point, add as many zeros as necessary to the left of the product to correct this – 1.3 x 0.07 1.3 (1 place to the left) x 0.07 (2 places to the left) 91 (count 3 places to the left) .091  0.091

7. Multiplication of Decimals – With a calculator – 1.3 x 0.07 Enter 1.3 Press the (x) button Enter 0.07 Press the (=) button Write down the answer

8. Multiplication of Decimals Example – 1.08 x 0.05 1.08 (count 2 places) x 0.05 (count 2 places) 540 (count 4 places) .0540  0.0540 (add a zero in front)  0.054 (drop extra zero)

9. Multiplication of Decimals Example – 1.08 x 0.05 – Enter 1.08 – Enter x – Enter 0.05 – Press = – Write down the answer

10. Calculate: 0.55 x 0.2 = A.11 B.1.1 C.0.11 D.0.011 E.None of the above

11. Calculate: 0.34 x 0.08 = A.0.0272 B.0.272 C.2.72 D.27.2 E.None of the above

12. Calculate: 1.16 x 0.05 = A.0.58 B.5.8 C.58 D.580 E.None of the above

13. Need more practice? 1.0.55 x 0.2 2.0.34 x 0.08 3.1.16 x 0.05 More problems like this on page 13 of your text book!

14. Division of Decimal Fractions 0.25 = ____? _______(top #) 0.125 = ____?______(bottom #)

15. Division of Decimal Fractions 0.25 = numerator (top #) 0.125 = ____?___ (bottom #)

16. Division of Decimal Fractions 0.25 = numerator (top #) 0.125 = denominator (bottom #)

17. Division of Decimal Fractions 3 step process 1.Eliminate the decimal point 2.Reduction of numbers ending in zero 3.Reduction of numbers using common denominator

18. Division of Decimal Fractions

19. Division of Decimal Fractions

20. Look for which number has the must numbers to the right of the decimal – start there. Count how many places you have to move the decimal to the right before it is “gone” Move the decimal the same number of places to the other number. What ever you do the numerator you must do to the denominator

21. Division of Decimal Fractions

22. Division of Decimal Fractions

23. Division of Decimal Fractions

24. Division of Decimal Fractions

25. Division of Decimal Fractions

26. Division of Decimal Fractions

27. Division of Decimal Fractions

28. Division of Decimal Fractions

29. Eliminate the decimal point from the decimal fraction

30. Eliminate the decimal point from the decimal fraction

31. Eliminate the decimal point from the decimal fraction 3.45 / 0.6 A.345 / 6 B.345 / 60 C.345 / 600 D.345 / 6000

32. Division of Decimal Fractions 3 step process 1.Eliminate the decimal point 2.Reduction of numbers ending in zero 3.Reduction of numbers using common denominator

33. Reduction of numbers ending in zero Numbers that end in zero or zero’s may initially be reduced by crossing off the same number of zeros in both the numerator and denominator – Example 500 = 20

34. Reduction of numbers ending in zero Numbers that end in zero or zero’s may initially be reduced by crossing off the same number of zeros in both the numerator and denominator – Example 500 = 20

35. Reduction of numbers ending in zero Numbers that end in zero or zero’s may initially be reduced by crossing off the same number of zeros in both the numerator and denominator – Example 500 = 500 = 50 20 20 2

36. Reduction of numbers ending in zero

37. Reduction of numbers ending in zero Example 4200 = 4200 = 42 4000

38. Reduction of numbers ending in zero Example 4200 = 4200 = 42 4000 400040

39. Reduction of numbers ending in zero

40. Reduction of numbers ending in zero

41. Division of Decimal Fractions 3 step process 1.Eliminate the decimal point 2.Reduction of numbers ending in zero  3.Reduction of numbers using common denominator

42. Reducing fractions To reduce fractions, divide the numerator and the denominator by the highest common denominator (the highest number that will divide into both) – Usually 2, 3, 4, 5

43. Reducing fractions

44. Reducing fractions

45. Reducing fractions

46. Reducing fractions

47. Reducing fractions

48. Reducing fractions

49. Reducing fractions

50. Reducing fractions

51. Reducing fractions

52. Reducing fractions

53. Reducing fractions

54. Reducing fractions

55. Putting it all together!

56. Putting it all together!

57. Putting it all together!

58. Putting it all together!

59. Putting it all together!

60. Putting it all together!

61. Putting it all together!

62. Putting it all together!

63. Reduction of numbers ending in zero Example 4200 = 4000

64. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 21 4000 4000 40 20

65. Reduction of numbers ending in zero Example 4200 = 4000

66. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (?) 4000 4000 40

67. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 4000 4000 40

68. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 42/2 4000 4000 40 ?

69. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 42/2 = 4000 4000 40 40/2

70. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 21 4000 4000 40 20

71. Reduction of numbers ending in zero Example 4200 = 4200 = 42 (2) = 21 = 1.05 4000 4000 40 20

72. Reduce the fractions as much as possible in preparation for final division

73. Reduce the fractions as much as possible in preparation for final division

74. Reduce the fractions as much as possible in preparation for final division

75. Your Turn Reduce the fractions as much as possible in preparation for final division 1.40 / 16 (2)  20 / 8 (2)  10 / 4 (2)  5/2 2.22 / 8 (2)  11 / 4 3.66 / 8 (3)  22 / 9 4.1450 / 1000 (5)  29 / 20 More problems like this on page 15 of your text book

76. Division of Decimal Fractions 3 step process 1.Eliminate the decimal point 2.Reduction of numbers using common denominator 3.Reduction of numbers ending in zero

77. Reduce the fraction to their lowest terms in preparation for final division. 500 / 2500 A.5 / 25 B.1 / 5 C.2 / 1 D.5 / 1 E.None of the above

78. Reduce the fraction to their lowest terms in preparation for final division. 400 / 150 A.80 / 30 B.4 / 15 C.40 / 15 D.4 / 5 E.None of the above

79. Reduce the fraction to their lowest terms in preparation for final division. 210,000 / 600,000 A.21 / 60 B.2 / 6 C.7 / 20 D.6 / 21 E.None of the above

80. Your turn! Reduce the fraction to their lowest terms in preparation for final division. 1.500 = 500 = 5 (5) = 1 2500 2500 255 2. 400 = 400 = 40 (5) 8 150 150 15 3 3.210,000 = 210,000 = 21 (3) = 7 600,000 600,000 60 20 More problems on page 16 of your text

81. Expressing to the nearest tenth 1234.567 – 5 is in the tenth place – 6 is in the hundredth place – 7 is in the thousandth place –. Decimal point – 4 is in the ones place – 3 is in the tens place – 2 is in the hundreds place – 1 is in the thousands place

82. Expressing to the nearest tenth To express an answer to the nearest tenth, the division is carried to hundredths (2 places after the decimal). When the number representing hundredth is 5 or larger, the number representing tenths is increased by one. – Example 1.66  – 1.7

83. Expressing to the nearest tenth Example 1.1.16  – 1.2 2.6.22 – 6.3 3.1.98 – 2.0  2

84. Express your answer to the nearest tenths 7.598111 A.7.5 B.7.6 C.7.50 D.7.59 E.7

85. Express your answer to the nearest tenths 1.454545 A.1.4 B.1.5 C.1.45 D.1.6 E.1

86. Express your answer to the nearest tenths 1.838383 A.1.8 B.1.9 C.1.7 D.1.83 E.2

87. Express your answer to the nearest tenths 2.976543 A.2.9 B.2.97 C.2.8 D.3.0 E.3

88. Express your answer to the nearest tenths 5.038578 A.5.0 B.5.1 C.5.03 D.5.2 E.None of the above

89. Your turn You did a problem on the calculator and the answer came out as follows. Express your answer to the nearest tenths. 1.7.598111  7.6 2.1.454545  1.5 3.1.838383  1.9 4.2.976543  3.0  3 5.5.038578  5.0  5

90. Some harder questions? You did a problem on the calculator and the answer came out as follows. Express your answer to the nearest tenths. 1.1 2.2.01 3.3.00009 4.40 5.500

91. Some harder questions? You did a problem on the calculator and the answer came out as follows. Express your answer to the nearest tenths. 1.1  1 2.2.01  2 3.3.00009  3 4.40  40 5.500  500

92. Expressing to the nearest hundredth 1234.567 – 5 is in the tenth place – 6 is in the hundredth place – 7 is in the thousandth place –. Decimal point – 4 is in the ones place – 3 is in the tens place – 2 is in the hundreds place – 1 is in the thousands place

93. Expressing to the nearest hundredth To express an answer to the nearest hundredth, the division is carried to the thousandths (3 places after the decimal point). When the number representing the thousandth is 5 or larger, the number representing the hundredths is increased by one. – Example 0.893 –  0.89

94. Expressing to the nearest hundredth Example – 0.666  0.67 – 0.836  0.84 – 0.958  0.96 – 0.999  1.0  1

95. Express the numbers to the nearest hundredth. 1.854 A.1.8 B.1.9 C.1.85 D.1.86 E.None of the above

96. Express the numbers to the nearest hundredth. 2.165 A.2.1 B.2.2 C.2.26 D.2.27 E.None of the above

97. Express the numbers to the nearest hundredth. 0.507 A.0.5 B.0.50 C.0.51 D.0.57 E.None of the above

98. Express the numbers to the nearest hundredth. 3.496 A.3.5 B.3.49 C.3.46 D.3.4 E.None of the above

99. Your turn! Express the numbers to the nearest hundredth. 1.1.854 –  1.85 2.2.165 –  2.17 3.0.507 – 0.51 4.3.496 – 3.50  3.5 More problems on pg 19

100. Mrs. Keele, I want to be a nurse, not a mathematician! Why do I have to learn this? What does this have to do with nursing?

101. You are to administer 3 tablets with a dosage strength of 0.04 mg each. What total dosage are you giving? – 3 tablets x 0.04 mg = 3 (0 places to the left) x 0.04 mg (2 places to the left) 12 mg (2 to the left) .12 mg  0.12 mg – 3 tablets x 0.04 mg = 0.12 mg

102. Tablets are labeled 0.2 mg and you are to give 3 ½ (3.5) tablets. What total dosage is this? – 3.5 tablets x 0.2 mg = 3.5 (1 place) x 0.2 mg(1 place) 70 mg (2 places) .7 mg  0.7 mg – 3.5 tablets x 0.2 mg = 0.7 mg

103. You gave 2.5 tablets labeled 0.4 mg each, and the dosage ordered was 1.2 mg. Was this the correct dosage? 2.5 tablets x 0.4 mg = 2.5 (1 place) x 0.4 mg (1 place) 100 (2 places)  1.00 mg  1 mg 2.5 tablets x 0.4 mg = 1 mg Answer the question – – No this was too little of the medication!