Presentation on theme: "Clinical Calculation 5th Edition"— Presentation transcript:
1 Clinical Calculation 5th Edition Appendix B from the book – PagesAppendix E from the book – PagesScientific Notation and DilutionsSignificant DigitsGraphs
2 Appendix B – Conversion between Celsius and Fahrenheit Temperatures Although digital thermometers are replacing the old fashion thermometers these days, but as health care provider you should be able to convert between the Celsius and Fahrenheit and vise versa.
3 Comparing different thermometers The ones we are concern are Celsius ( C ) and Fahrenheit ( F )
4 Converting Fahrenheit to Celsius 32F = _________________C
5 Converting Fahrenheit to Celsius 212F = _________________C
6 Converting Fahrenheit to Celsius 100F= _________________C
7 Converting Fahrenheit to Celsius 28F = ________________C
8 Converting Celsius to Fahrenheit 50 C = _________________ F
9 Converting Celsius to Fahrenheit 500 C = _________________ F
10 Converting Celsius to Fahrenheit 250 C = _________________ F
11 Appendix E – Twenty-four hour clock Twenty-four hour clock is for documenting medication administration, specially with use of computerized MARs.Rules:To convert from traditional to 24-hours:1:00am and 12:00noon – delete the colon and proceed single digit number with a zeroBetween 12noon and 12 midnight – add 12hours to the traditional time.To convert from 24-fours clock to traditional:Between 0100and 1200-replace colon and drop zero proceeding single digit numbersBetween 1300 and 2400-subtract 1200 (12 hours) and replace the colon.
12 1:00 am 2:00 am 3:00 am 4:00 am 5:00 am 6:00 am 7:00 am 8:00 am 9:00 am :00 am :00 am noon 1:00 pm 2:00 pm 3:00 pm 4:00 pm 5:00 pm 6:00 pm 7:00 pm 8:00 pm 9:00 pm :00 pm :00 pm midnight
13 24-Hour Clock Conversion Table 12hr Time 24hr Time Example: on the hourExample: 10 minutes past24 Hour ClockAM / PM01001:00 AM001012:10 AM02002:00 AM01101:10 AM03003:00 AM02102:10 AM04004:00 AM03103:10 AM05005:00 AM04104:10 AM06006:00 AM05105:10 AM07007:00 AM06106:10 AM08008:00 AM07107:10 AM09009:00 AM08108:10 AM100010:00 AM09109:10 AM110011:00 AM101010:10 AM120012 Noon111011:10 AM13001:00 PM121012:10 PM14002:00 PM13101:10 PM15003:00 PM14102:10 PM16004:00 PM15103:10 PM17005:00 PM16104:10 PM18006:00 PM17105:10 PM19007:00 PM18106:10 PM20008:00 PM19107:10 PM21009:00 PM20108:10 PM220010:00 PM21109:10 PM230011:00 PM221010:10 PM240012:00 PM231011:10 PM24-Hour Clock Conversion Table 12hr Time 24hr Time12 am (midnight) 0000hrs 1 am 0100hrs 2 am 0200hrs 3 am 0300hrs 4 am 0400hrs 5 am 0500hrs 6 am 0600hrs 7 am 0700hrs 8 am 0800hrs 9 am 0900hrs 10 am 1000hrs 11 am 1100hrs 12 pm (noon) 1200hrs 1 pm 1300hrs 2 pm 1400hrs 3 pm 1500hrs 4 pm 1600hrs 5 pm 1700hrs 6 pm 1800hrs 7 pm 1900hrs 8 pm 2000hrs 9 pm 2100hrs 10 pm 2200hrs 11 pm 2300hrs
14 Converting traditional clock to 24-hour clock Examples:12 Midnight = 12:00 AM = 0000 = 240012:35 AM = 003511:20 AM = 112012:00PM = 12:00 Noon = 120012:30 PM = 12304:45 PM = 164511:50 PM = 2350Midnight and Noon"12 AM" and "12 PM" can cause confusion, so we prefer "12 Midnight" and "12 Noon".
17 Scientific NotationScientists have developed a shorter method to express very large numbers.This method is called scientific notation.Scientific Notation is based on powers of the base number 10.The number 123,000,000,000 in scientific notation is written as :The first number 1.23 is called the coefficient.It must be greater than or equal to 1 and less than 10.The second number is called the base .It must always be 10 in scientific notation.The base number 10 is always written in exponent form.In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.
18 To write a number in scientific notation: To write 123,000,000,000 in scientific notation:Put the decimal after the first non-zero digit and drop the zeroes.1.23In the number 123,000,000,000 The coefficient will be 1.23To find the exponent count the number of places from the decimal to the end of the number. 1011In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as: X 1011Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as:1.23 E+11 or as1.23 X 10^11
19 Scientific NotationFor small numbers we use a similar approach. Numbers less smaller than 1 will have a negative exponent. A millionth of a second ( sec) is:Put the decimal after the first non-zero digit and drop the zeroes1.0 (in this problem zero after decimal is place holder)To find the exponent count the number of places from the decimal to the end of the numberhas 6 placesin scientific notation is written as:Exponents are often expressed using other notations. The number can also be written as:1.0 E-6 or as1.0^-6
20 Fun Do you know this number, 300,000,000 m/sec.? It's the Speed of light !Do you recognize this number, kg. ?This is the mass of a dust particle!
21 Now it is your turn. Express the following numbers in their equivalent scientific notational form: 123,876.31,236,8126.96.36.199
22 Now it is your turn. Express the following numbers in their equivalent standard notational form: 566.3123,000.70,020,0000.9187.1880,000
23 DilutionsUnderstanding how to make dilutions is an essential skill for any scientist. This skill is used, for example, in making solutions, diluting bacteria, diluting antibodies, etc. It is important to understand the following: - how to do the calculations to set up the dilution - how to do the dilution optimally - how to calculate the final dilution
24 Volume to volume dilutions describes the ratio of the solute to the final volume of the diluted solution.To make a 1:10 dilution of a solution,you would mix one "part" of the solution with nine "parts" of solvent (probably water), for a total of ten "parts."Therefore, 1:10 dilution means 1 part + 9 parts of water (or other diluent).
26 Serial dilutions - 1 mL 1 mL 1 mL 1 mL Original solution 9mL 9mL 9mL
27 Serial dilutions - 0.1 mL 1 mL 1 mL 1 mL Original solution 9.9 mL 9mL
28 Serial dilutions - 1 mL 1 mL 1 mL 1 mL Original solution 2mL 2 mL 2mL
29 Build Dilution ratio of 1:16 using 4 water blanks provided 3 mL3 mL3 mL3 mL3 mL3 mL3 mL3 mLOriginal solution
30 Build Dilution ratio of 1:104 using 4 water blanks 1 mL1 mL1 mL1 mL9 mL9 mL9 mL9 mLOriginal solution
31 Build Dilution ratio of 1:104 using 3 water blanks 0.1 mL1 mL1 mL9.9 mL9 mL9 mLOriginal solution
32 Build Dilution ratio of 1:104 using 2 water blanks provided 0.1 mL0.1 mL9.9 mL9.9 mLOriginal solution
33 Build Dilution ratio of 1:27 using water blanks provided 5 mL5 mL5 mL10 mL10 mL10 mLOriginal solution
34 N Serial dilutions - 1 mL 1 mL 1 mL 1 mL 1 mL # of bacteria found Original solution9mL9mL9mL9mLNEXPECTED NUMBER OF BACTERIA IN ORIGINAL SOLUTION
35 N Serial dilutions - 0.1 mL 1 mL 1 mL 1 mL 5 mL # of bacteria found Original solution9mL9mL9mL9mLNEXPECTED NUMBER OF BACTERIA IN ORIGINAL SOLUTION
36 N Serial dilutions - 0.1 mL 0.1 mL 0.1 mL 0.1 mL 2 mL # of bacteria foundOriginal solution9.9mL9.9mL9.9mL9.9mLNEXPECTED NUMBER OF BACTERIA IN ORIGINAL SOLUTION
37 Significant DigitsThe number of significant digits in an answer to a calculation will depend on the number of significant digits in the given dataWhen are Digits Significant?Non-zero digits are always significant. Thus,22 has two significant digits, and22.3 has three significant digits.With zeroes, the situation is more complicated:Zeroes placed before other digits are not significant;0.046 has two significant digits.Zeroes placed between other digits are always significant;4009 kg has four significant digits.Zeroes placed after other digits but behind a decimal point are significant;7.90 has three significant digits.Zeroes at the end of a number are significant only if it is followed by a decimal point or underlined emphasized on the precision:8300 has two significant digits8300. has four significant digits8300 has three significant digits
38 Example: Identify number of significant digits 27.418.04576007600.0.4003400340030400.3040300
39 Operation using significant digits Adding and subtracting – add and subtract as you normally do.For the final solution the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted. .Add the following problem(two decimal places) (one decimal place) (four decimal place)7.7 (one decimal place)
40 17.142 has 3 numbers after the decimal points Example - How precise can the answers to the following be expressed to?has 3 numbers after the decimal pointshas 4 numbers after the decimal points24.11 has 2 numbers after the decimal pointsThe answer could have two positions to the right of the decimal since the least precise term, 24.11, has only two positions to the right.
41 Example: Add / Subtract 17.034– 4.5712.464Add:10.003173.14Final answer is 12.46Final solution is 195.Subtract:76–70.161Add:18.1233.14.7626.983Final answer is 70.Final solution is 27.0
42 Operation using significant digits Multiplying and dividing – do the operation as you normally do.For the final solution use the least significant digits between all the numbers involved.For example:XThe product could be expressed with no more than three significant digits since has only three significant digits, and has five. So according to the rule the product answer could only be expressed with three significant digits.
43 Example - Indicate the number of significant digits the answer to the following would have. (I don't want the actual answer but only the number of significant digits the answer should be expressed as having.)(20.04) ( 16.0) (4.0 X 102)(20.04) has 4 significant digits( 16.0) has 3 significant digits(4.0 X 102) has 2 significant digitsFinal answer will have 2 significant digits
45 Rounding or Precision significant digits Rules for rounding off numbersIf the digit to be dropped is greater than 5, the last retained digit is increased by one.For example,12.6 is rounded to 13.If the digit to be dropped is less than 5, the last remaining digit is left as it is.12.4 is rounded to 12.If the digit to be dropped is 5, and if any digit following it is not zero, the last remaining digit is increased by one.12.51 is rounded to 13.If the digit to be dropped is 5 and is followed only by zeroes, the last remaining digit is increased by one if it is odd, but left as it is if even. For example,11.5 is rounded to 12, is rounded to 12. This rule means that if the digit to be dropped is 5 followed only by zeroes, the result is always rounded to the even digit. The rationale is to avoid bias in rounding: half of the time we round up, half the time we round down.
46 Graphs – Plotting Points on the Graph – how? yxy1346-1-2-42736-2-35-6xDecide the scale and follow within that scale setting (1=1)
47 Graphs – Plotting Points on the Graph yxy1346-1-2-42134-2-35-1xDecide the scale and follow within that scale setting (2=1)
48 Graphs – Plotting Points on the Graph yxy134-11710-2-5x1=1
49 Drawing Straight Line y x y 1 3 4 -1 1 7 10 -2 -5 x 1=1 -11710-2-5x1=1Points written as ordered pair: (1, 1), (3, 7), (4, 10), (0, -2), (-1, -5)
50 Drawing Straight Line y = 2x - 3 12-1-3-11-5(2, 1)(1, -1)(0, -3)(-1, -5)1=1
51 Drawing Straight Line y = 5x + 7 (2, 17)12-1712172(1, 12)(0, 7)(-1, 2)1=11=2
52 Drawing Straight Line y = -30x + 50 12-15020-10+80(-1, 80)(0, 50)(1, 20)1=1(2, -10)1=10
53 Slope of the line Positive and negative slope POSITIVE SLOPE
55 Finding slope from the known points RiseRunRiseRun
56 Finding slope from the known points RiseRunRiseRun
57 Finding slope using the 2 ordered pair (x1, y1) and (x2, y2)
58 Finding slope using the 2 ordered pair (-1, -1) and (3, 6) RISE = 7RUN = 4
59 Finding slope using the 2 ordered pair (1, -1) and (3, 6)
60 Finding slope using the 2 ordered pair (-2, -3) and (-1, 5)
61 Finding slope using the 2 ordered pair (-1, 0) and (1, 2)
62 Finding slope using the 2 ordered pair (0, -3) and (1, -5)
63 Equation of straight line Equation of straight line y = mx + b Identifying slope and y-interceptsy = m x + bx and y represents points on the graphm = Slopeb = y-intercepts (0, b) ordered pair
64 Drawing Straight Line y = 2x - 3 For this problem:Slope = 2 and y-intercept = -3 [if written as ordered pair (0, -3)]
65 Drawing Straight Line y = 5x + 7 For this problem:Slope = 5 and y-intercept = 7 [if written as ordered pair (0, 7)]
66 Drawing Straight Line y = -30x + 50 For this problem:Slope = -30 and y-intercept = 50 [if written as ordered pair (0, 50)]
67 Collecting data and plotting the points Height (inches) of a child at different age (year) xy0.512345.5162128403550Year(2=1)Height(1=5)What is the child height at the age 5?What is the child height at the age 6?It is about 46 inchesIt is about 55 inches
68 Interpolation and Extrapolation DefinitionInterpolation – When the value for dependent variable is estimated from independent variable within the data set rangeExtrapolation – When the value for dependent variable is estimated from independent variable out side the data set range
69 Collecting data and plotting the points Height (inches) of a child at different age (year) From last problem!xy0.512345.5162128403550X = 5 is within the data range (0.5 – 5.5)X = 6 is outside the data range (0.5 – 5.5)Year(2=1)Height(1=5)What is the child height at the age 5?What is the child height at the age 6?It is about 46 inches - InterpolationIt is about 55 inches - Extrapolation
70 Find the equation of the line for this graph. What is the y-intercept?What is the slope of this line?Use the equation of the line y=mx+bThen write the equation of the line
71 Find the equation of the line for this graph. What is the y-intercept?What is the slope of this line?Use the equation of the line y=mx+bThen write the equation of the line