Clinical Calculation 5 th Edition Appendix B from the book – Pages 314 - 315 Appendix E from the...

Clinical Calculation5th Edition

Appendix B from the book – Pages 314 - 315

Appendix E from the book – Pages 319 - 321

Scientific Notation and Dilutions

Significant Digits

Graphs

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.

Comparing different thermometers The ones we are concern are Celsius ( C ) and Fahrenheit ( F )

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http://weather.msn.com/

Converting Fahrenheit to Celsius

CC

08.1

0

8.1

3232

32F = _________________C

8.1

32F

C


CC

1008.1

180

8.1

32212

212F = _________________C

8.1

32F

C


CC

8.378.1

68

8.1

32100

100F= _________________C

8.1

32F

C


CC

2.28.1

4

8.1

3228

28F = ________________C

8.1

32F

C

Converting Celsius to Fahrenheit

328.1 CF

50 C = _________________ F

FF 413258.1


328.1 CF

500 C = _________________ F

FF 12232508.1


328.1 CF

250 C = _________________ F

FF 7732258.1

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 zero

Between 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 numbers Between 1300 and 2400-subtract 1200 (12 hours) and

replace the colon.

01 00 - 1:00 am02 00 - 2:00 am03 00 - 3:00 am04 00 - 4:00 am05 00 - 5:00 am06 00 - 6:00 am07 00 - 7:00 am08 00 - 8:00 am09 00 - 9:00 am10 00 - 10:00 am11 00 - 11:00 am12 00 - 12 noon

13 00 - 1:00 pm14 00 - 2:00 pm15 00 - 3:00 pm16 00 - 4:00 pm17 00 - 5:00 pm18 00 - 6:00 pm19 00 - 7:00 pm20 00 - 8:00 pm21 00 - 9:00 pm22 00 - 10:00 pm23 00 - 11:00 pm24 00 - midnight

Example: on the hour Example: 10 minutes past

24 Hour Clock AM / PM 24 Hour Clock AM / PM

0100 1:00 AM 0010 12:10 AM

0200 2:00 AM 0110 1:10 AM

0300 3:00 AM 0210 2:10 AM

0400 4:00 AM 0310 3:10 AM

0500 5:00 AM 0410 4:10 AM

0600 6:00 AM 0510 5:10 AM

0700 7:00 AM 0610 6:10 AM

0800 8:00 AM 0710 7:10 AM

0900 9:00 AM 0810 8:10 AM

1000 10:00 AM 0910 9:10 AM

1100 11:00 AM 1010 10:10 AM

1200 12 Noon 1110 11:10 AM

1300 1:00 PM 1210 12:10 PM

1400 2:00 PM 1310 1:10 PM

1500 3:00 PM 1410 2:10 PM

1600 4:00 PM 1510 3:10 PM

1700 5:00 PM 1610 4:10 PM

1800 6:00 PM 1710 5:10 PM

1900 7:00 PM 1810 6:10 PM

2000 8:00 PM 1910 7:10 PM

2100 9:00 PM 2010 8:10 PM

2200 10:00 PM 2110 9:10 PM

2300 11:00 PM 2210 10:10 PM

2400 12:00 PM 2310 11:10 PM

24-Hour Clock Conversion Table

12hr Time 24hr Time 12 am (midnight) 0000hrs 1 am 0100hrs 2 am 0200hrs3 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

Converting traditional clock to 24-hour clock

Examples: 12 Midnight = 12:00 AM = 0000 = 2400 12:35 AM = 0035 11:20 AM = 1120 12:00PM = 12:00 Noon = 1200 12:30 PM = 1230 4:45 PM = 1645 11:50 PM = 2350

Midnight and Noon"12 AM" and "12 PM" can cause confusion, so we prefer "12 Midnight" and "12 Noon".

Converting 24 Hour Clock to AM/PM traditional

Examples: 0010 = 12:10 AM 0040 = 12:40 AM 0115 = 1:15 AM 1125 = 11:25 AM 1210 = 12:10 PM 1255 = 12:55 PM 1455 = 2:55 PM 2330 = 11:30 PM

Scientific Notation

Scientists 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.

111023.1

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. 1.23

In the number 123,000,000,000 The coefficient will be 1.23 To find the exponent count the number of places from the

decimal to the end of the number. 1011

In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as: 1.23 X 1011

Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as: 1.23 E+11 or as 1.23 X 10^11

Scientific Notation

For small numbers we use a similar approach. Numbers less smaller than 1 will have a negative exponent. A millionth of a second (0.000001 sec) is:

Put the decimal after the first non-zero digit and drop the zeroes 1.0 (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 number 0.000001 has 6 places 0.000001 in scientific notation is written as:

Exponents are often expressed using other notations. The number 0.000001 can also be written as: 1.0 E-6 or as 1.0^-6

Fun

Do you know this number, 300,000,000 m/sec.? It's the Speed of light !

Do you recognize this number, 0.000 000 000 753 kg. ? This is the mass of a dust particle!

8100.3

101053.7

Now it is your turn. Express the following numbers in their equivalent scientific notational form:

1. 123,876.3

2. 1,236,840.

3. 4.22

4. 0.000000000000211

5. 0.000238

6. 9.10

5101.238763 .1 6101.236840 .2

0104.22 .3 -13102.11 .4

-4102.38 .5 0109.1 .6

Now it is your turn. Express the following numbers in their equivalent standard notational form:

1. 566.3

2. 123,000.

3. 70,020,000

4. 0.918

5. 7.18

6. 80,000

2105.663 .1 5101.23 .2

7107.002 .3 -1109.18 .4 0107.18 .5

4108.0 .6

Dilutions

Understanding 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

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).

Serial dilutions

http://www.wellesley.edu/Biology/Concepts/Animations/dilution.mov

Serial dilutions -

410

1Original solution

9mL 9mL 9mL 9mL

1 mL 1 mL 1 mL 1 mL

10

1

10

1

10

110

1

Serial dilutions -

510

1

Original solution

9.9 mL 9mL 9mL 9mL

0.1 mL 1 mL 1 mL 1 mL

210

1

100

1

10

1.0

10

1

10

110

1

310

1410

1

Serial dilutions -

81

1

3

14

Original solution

2 mL 2mL 2mL 2mL

1 mL 1 mL 1 mL 1 mL

3

13

1

3

13

1

9

1

3

12

27

1

3

13

Build Dilution ratio of 1:16 using 4 water blanks provided

16

1

2

14

Original solution

3 mL 3 mL 3 mL 3 mL

3 mL 3 mL 3 mL 3 mL

2

12

1

2

12

1

4

1

2

12

8

1

2

13

Build Dilution ratio of 1:104 using 4 water blanks

410

1

Original solution

9 mL 9 mL 9 mL 9 mL

1 mL 1 mL 1 mL 1 mL

10

1

10

110

110

1

210

1310

1

Build Dilution ratio of 1:104 using 3 water blanks

Original solution

9.9 mL 9 mL 9 mL

0.1 mL 1 mL 1 mL

100

1

10

1.0

10

110

1

1000

1

10

13

10000

1

10

14

Build Dilution ratio of 1:104 using 2 water blanks provided

Original solution

9.9 mL 9.9 mL

0.1 mL 0.1 mL

100

1

10

1.0

410

1100

1

10

1.0

Build Dilution ratio of 1:27 using water blanks provided

Original solution

10 mL 10 mL 10 mL

5 mL 5 mL 5 mL

3

13

1

3

1

9

1

3

12

27

1

3

13

Serial dilutions -

mLN

1

1025.3

10

1

10

1

10

1

10

1 3

743 1025.3101025.3 N

Original solution

9mL 9mL 9mL 9mL

1 mL 1 mL 1 mL 1 mL1 mL

N

31025.3

10

1

10

1

10

1

10

1

EXPECTED NUMBER OF BACTERIA IN ORIGINAL SOLUTION

# of bacteria found

mLN

1

1025.3

10

1 3

4

Serial dilutions -

mLN

5

1015.1

10

1

10

1

10

1

100

1 4

8954

103.21023.05

101015.1

mlN

Original solution

9mL 9mL 9mL 9mL

0.1 mL 1 mL 1 mL 1 mL5 mL

N

41015.1

100

1

10

1

10

1

10

1

EXPECTED NUMBER OF BACTERIA IN ORIGINAL SOLUTION

# of bacteria found

mLN

5

1015.1

10

1 4

5

Serial dilutions -

mLN

2

1012.5

100

1

100

1

100

1

100

1 1

Original solution

9.9mL 9.9mL 9.9mL 9.9mL

0.1 mL 0.1 mL 0.1 mL 0.1 mL2 mL

N

11012.5

100

1

100

1

100

1

100

1

981

1056.22

101012.5

mlN EXPECTED NUMBER OF BACTERIA

IN ORIGINAL SOLUTION

# of bacteria found

Significant DigitsThe number of significant digits in an answer to a calculation will depend on the

number of significant digits in the given data

When are Digits Significant? Non-zero digits are always significant. Thus,

22 has two significant digits, and 22.3 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 digits 8300. has four significant digits 8300 has three significant digits

Example: Identify number of significant digits

27.4 18.045 7600 7600. 7600 0.4003 4003 0.40030 40030 400.30 0.00403 40300

3 significant digits 5 significant digits 2 significant digits 4 significant digits 3 significant digits 4 significant digits 4 significant digits 5 significant digits 4 significant digits 5 significant digits 3 significant digits 3 significant digits

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 problem5.67 (two decimal places) 1.1 (one decimal place) 0.9378 (four decimal place) 7.7078

7.7 (one decimal place)

Example - How precise can the answers to the following be expressed to?

17.142 + 2.0013 + 24.11 17.142 has 3 numbers after the decimal points 2.0013 has 4 numbers after the decimal points 24.11 has 2 numbers after the decimal points

The 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.

Example: Add / Subtract

Subtract:

17.034

– 4.57

12.464

Add:

10.003

173.1

4

+ 8.00003

195.00303

Subtract:

76

– 5.839

70.161

Add:

18.123

3.1

4.76

+ 1.00

26.983

Final answer is 12.46Final solution is 195.

Final answer is 70.

Final solution is 27.0

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: 0.000170 X 100.40 The product could be expressed with no more than three

significant digits since 0.000170 has only three significant digits, and 100.40 has five. So according to the rule the product answer could only be expressed with three significant digits.

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 digits

Final answer will have 2 significant digits

Sample problems on significant figures

1. 37.76 + 3.907 + 226.4 =

2. 319.15 - 32.614 =

3. 104.630 + 27.08362 + 0.61 =

4. 125 - 0.23 + 4.109 =

5. 2.02 × 2.5 =

6. 600.0 / 5.2302 =

7. 0.0032 × 273 =

8. (5.5)3 =

9. 0.556 × (40 - 32.5) =

10. 45 × 3.00 =

1. 268.1 (4 significant)



4. 129 (3 significant)




8. 1.7 x 102=170 (2 significant)

9. 4 (1 significant)

10. 1.4 x 102 (2 significant)

Rounding or Precision significant digits

Rules for rounding off numbers If 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.

For example, 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. For example,

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,

12.5 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.

Graphs – Plotting Points on the Graph – how?

1

3

4

6

0

-1

-2

-4

x y

2

7

3

6

-2

-3

5

-6

x

y

Decide the scale and follow within that scale setting (1=1)

Graphs – Plotting Points on the Graph

1

3

4

6

0

-1

-2

-4

x y

2

1

3

4

-2

-3

5

-1

x

y

Decide the scale and follow within that scale setting (2=1)

Graphs – Plotting Points on the Graph

1

3

4

0

-1

x y

1

7

10

-2

-5

x

y

1=1

Drawing Straight Line

1

3

4

0

-1

x y

1

7

10

-2

-5

x

y

1=1

Points written as ordered pair: (1, 1), (3, 7), (4, 10), (0, -2), (-1, -5)

Drawing Straight Line y = 2x - 3

0

1

2

-1

x y

-3

-1

1

-5

1=1

(2, 1)

(1, -1)

(-1, -5)

(0, -3)

Drawing Straight Line y = 5x + 7

0

1

2

-1

x y

7

12

17

2

1=1

1=2

(-1, 2)

(0, 7)

(1, 12)

(2, 17)

Drawing Straight Line y = -30x + 50

0

1

2

-1

x y

50

20

-10

+80

1=10

1=1

(-1, 80)

(0, 50)

(1, 20)

(2, -10)

Slope of the linePositive and negative slope

POSITIVE SLOPE

Slope of the linePositive and negative slope

NEGATIVE SLOPE

Finding slope from the known points

run

riseslope

Rise

Run

5

3

run

riseslope

RiseRun

Finding slope from the known points

run

riseslope

RiseRun

3

1

9

3

run

riseslope

RiseRun

Finding slope using the 2 ordered pair (x1, y1) and (x2, y2)

12

12

xx

yy

run

riseslope

Finding slope using the 2 ordered pair (-1, -1) and (3, 6)

4

7

4

16

)1(3

)1(6

run

riseslope

RISE = 7

RUN = 4

Finding slope using the 2 ordered pair (1, -1) and (3, 6)

2

7

2

16

13

)1(6

run

riseslope

Finding slope using the 2 ordered pair (-2, -3) and (-1, 5)

81

8

21

35

)2(1

)3(5

run

riseslope

Finding slope using the 2 ordered pair (-1, 0) and (1, 2)

12

2

11

2

)1(1

)0(2

run

riseslope

Finding slope using the 2 ordered pair (0, -3) and (1, -5)

21

2

1

35

)0(1

)3(5

run

riseslope

Equation of straight line y = mx + bIdentifying slope and y-intercepts

y = m x + bx and y represents points on the graph

m = Slope

b = y-intercepts (0, b) ordered pair

Drawing Straight Line y = 2x - 3

For this problem:

Slope = 2 and y-intercept = -3 [if written as ordered pair (0, -3)]

Drawing Straight Line y = 5x + 7

For this problem:

Slope = 5 and y-intercept = 7 [if written as ordered pair (0, 7)]

Drawing Straight Line y = -30x + 50For this problem:

Slope = -30 and y-intercept = 50 [if written as ordered pair (0, 50)]

Collecting data and plotting the pointsHeight (inches) of a child at different age (year)

0.5

1

2

3

4

5.5

x y

16

21

28

40

35

50

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 It is about 55 inches

Interpolation and Extrapolation

Definition Interpolation – When the value for dependent variable

is estimated from independent variable within the data set range

Extrapolation – When the value for dependent variable is estimated from independent variable out side the data set range

Collecting data and plotting the pointsHeight (inches) of a child at different age (year)

0.5

1

2

3

4

5.5

x y

16

21

28

40

35

50

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 - Interpolation It is about 55 inches - Extrapolation

X = 5 is within the data range (0.5 – 5.5)

X = 6 is outside the data range (0.5 – 5.5)

From last problem!

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+b Then write the equation of the line

EBay, 2007 - http://moneycentral.msn.com/investor/charts/chartdl.aspx?

EBay, 2007 - http://quotes.nasdaq.com/quote.dll?page=nasdaq100

Google, 2007 - http://quotes.nasdaq.com/quote.dll?page=nasdaq100

Microsoft, 2007 - - http://quotes.nasdaq.com/quote.dll?page=nasdaq100

Dell, 2007 - - http://quotes.nasdaq.com/quote.dll?page=nasdaq100

Yahoo, 2007 - http://quotes.nasdaq.com/quote.dll?page=nasdaq100

Bar graph - http://www.shodor.org/interactivate/activities/BarGraph/?version=1.6.0_02&browser=MSIE&vendor=Sun_Microsystems_Inc.

Pie graph http://www.shodor.org/interactivate/activities/BarGraph/?version=1.6.0_02&browser=MSIE&vendor=Sun_Microsystems_Inc.

Clinical Calculation 5 th Edition Appendix B from the book – Pages 314 - 315 Appendix E from the...

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Transcript of Clinical Calculation 5 th Edition Appendix B from the book – Pages 314 - 315 Appendix E from the...