Transcript olsen_ch01_lecture

Medical Dosage Calculation
A Dimensional Analysis Approach
Tenth Edition
CHAPTER
1
Review of Arithmetic
for Medical Dosage
Calculations
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Directory
• Classroom Response System Questions
• Lecture Note Presentation
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Classroom Response
System Questions
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #1
Convert 5/8 to a decimal number.
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #1 Choices
1.
2.
3.
4.
0.624
0.615
0.525
0.625
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #1 Response
1.
2.
3.
4.
0.624
0.615
0.525
0.625
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #2
Convert 4500/1000 to a decimal number.
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Question #2 Choices
1.
2.
3.
4.
450.0
45.0
4.5
0.45
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #2 Response
1.
2.
3.
4.
450.0
45.0
4.5
0.45
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Question #3
Simplify: 7.2/0.06
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Question #3 Choices
1.
2.
3.
4.
120
1200
12,000
12
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #3 Response
1.
2.
3.
4.
120
1200
12,000
12
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #4
Simplify: 4/15 x 30 x 1/2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #4 Choices
1.
2.
3.
4.
1/4
4/1
2/1
1/2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #4 Response
1.
2.
3.
4.
1/4
4/1
2/1
1/2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #5
Write 38 2/5% as a decimal number
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #5 Choices
1.
2.
3.
4.
38.40
3.840
0.384
384.0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Question #5 Response
1.
2.
3.
4.
38.40
3.840
0.384
384.0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Lecture Note Presentation
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Decimal Numbers
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Adding and Subtracting
Decimal Numbers
Keep the decimal points aligned
0.115
+ 12.34
12.455
78.952
− 2.12
76.832
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Multiplying and Dividing
Decimal Numbers
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
304.2 × 0.16 = ?
304.2
× 0.16
18 252
30 42 .
48.672
1 decimal place
2 decimal places
}
Total of 3
decimal places
There are 3 decimal places in the answer.
Place the decimal point here.
So, 304.2 × 0.16 = 48.672
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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23.597 × 1,000 = ?
There are three zeros in 1,000 so move the
decimal point in 23.597 three places to the right.
23.597 × 1,000 = 23 5 9 7
23.597 × 1,000 = 23,597
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
4
8
?
0
.0
0
2
Because there are three decimal places in 0.002,
move the decimal points three places to the right in
both the numerator and denominator.
48
means 0.002 48. or 0 . 0 0 2 4 8 . 0 0 0
0.002
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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2 4 000
.
2 48000.
4
8
8
0
4
8
2
4
,
0
0
0
Therefore:
0
.
0
0
2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Rounding Decimal
Numbers
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Rounding Decimal Numbers
Rounding off may either increase or decrease
the number. For example, round off 1.267 to the
nearest tenth (one decimal place)
Answer: 1.3
Rounding down a number will not increase the
number. In particular, to round 1.267 down to the
tenths place (one decimal place)
Answer: 1.2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
(a) Round off 3.726 to the nearest hundredth,
tenth, and whole number.
3.726 Rounded off to the nearest:
hundredth = 3.73
tenth = 3.7
whole number = 4
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
(b) Round down 3.726 to the hundredth, tenth, and
whole number place.
3.726 Rounded down to the:
hundredth = 3.72
tenth = 3.7
whole number = 3
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Rounding Decimal Numbers
For small liquid volumes:
amounts less than 1 mL will be rounded to
hundredths,
while
amounts greater than 1 mL will be rounded to
tenths.
For example, 0.345 mL ≈
And 1.345 mL ≈
0.35 mL
1.3 mL
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Because the danger of an overdose must always be
guarded against (particularly with pediatric meds and
high-alert drugs), the amount of medication to be
administered is sometimes
rounded down instead of rounded off
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
• A decimal number represents a fraction with
a denominator of 10, 100, 1000, and so on.
• Each decimal number has three parts: the
whole number part, the decimal point, and
the fraction part.
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Changing Decimal Numbers to
Fractions
• Reading a decimal number will help you to write it as a
fraction:
Decimal Number
Read
4.1
four and one tenth
0.3
three tenths
3
10
0.07
seven hundredths
7
100
0.231
two hundred thirty-one thousandths
231
1000
0.0025
twenty-five ten thousandths
25
10,000
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Fraction
4
1
10
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A number can be written in many different forms.
For example, the decimal number 0.5 is read as
five tenths. In fraction form, it is:
5
10
or
1
2
½ is referred to as a proper fraction,
where the numerator (the number on top) of the
fraction is smaller than its denominator (the
number on bottom).
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
A decimal number greater than 1, such as 3.5 is read as
three and five tenths, and can also be written as a mixed
number which combines a whole number and a proper
fraction,
1
3
2
This mixed number, can also be changed to an improper
fraction where the numerator (top number) is larger than or
equal to its denominator (bottom number).
1 3  21 7
3 

2
2
2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Write 2.25 as an improper fraction.
The number 2.25 is read as
two and twenty-five hundredths
and written
25
2
100
1
25
1
2 4 1 9
2
= 2
=
=
100
4
4
4
4
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Changing Fractions to
Decimal Numbers
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
2
To change a fraction to a decimal number, think of
the fraction as a division problem.
For example:
2
5
means
2 ÷ 5 or 5 2
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Here are the steps for this division:
Step One: Replace 2 with 2.0 and then place a
decimal point directly above the decimal point in
2.0
.
5 2 .0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Step Two: Perform the division.
.4
5 2.0
Therefore,
2 0
0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
2
 0.4
5
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Write
193
10
193
10
Step 1:
as a decimal number.
means
10 193
.
10 193.0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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1 9. 3
Step 2:
10 193.0
10
93
90
30
30
0
1
9
3
Therefore,
1
9
.3
1
0
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
An easier way to do
the problem 193 /10
There is 1 zero in 10 so move the decimal
point in 193. 1 place to the left.
1 9 3
193/10 = 19.3
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Multiplying and
Dividing Fractions
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
4 3 2
0
  
?
5 1
0 7
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
It is often convenient to cancel before you
multiply.
2
4 3 2
0 24
 

5 1
0 7 35
1
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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2
7
1 
?
5
9
2
7
 7 7
Write 1
as the fraction . Division   
 5 9
5
5
 7 9
Becomes the multiplication   
 5 7
1
4
9
7
9
 1


5
5
5
7
1
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
1
1

6
0


?
3
0
0
0
.
4
1
1
1
1
6
0 1


 
.4 2
3
0
0 1 0
.
4 50
5
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
1
0
.
3
5
?
6
0
0.35 1
0.35


60
1
60
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
The numerator of this fraction is 0.35, a
decimal number.
You can write an equivalent form of the
fraction by multiplying the numerator and
denominator by 100.
0.35 100
35
0. 3 5
7




60 100 60. 0 0
6000 1200
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Complex Fractions
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Complex Fractions
Complex fractions have
fractions in their
numerators and/or fractions
in their denominators.
A longer fraction line
separates the main
numerator from the main
denominator, and indicates
division.
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
1
 500
25
1
4
Copyright ©2012, ©2008 by Pearson Education, Inc.
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1
 500
25
?
1
4
 1
 1
 25  500  4
 1
 4
 25  500  1
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
20
1 500 4


25
1
1
1
1
 500
25
= 80
1
4
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Adding and Subtracting Fractions
Add (or subtract) the numerators when the
denominators are the same:
3 4

11 11
34
11
=
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
7
11
Copyright ©2012, ©2008 by Pearson Education, Inc.
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9
4

13 13
Subtract the numerators
94
13
=
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
5
13
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When the denominators are Different
use a Common Denominator
3 1

8 2
3 14

8 24
3 4 7
 
8 8 8
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
When the denominators are Different
use a Common Denominator
3 1

4 2
3 1 2

4 2 2
3 2 1
 
4 4 4
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Percentages
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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Percent means per hundred
70
70% 
100
= 0.7
25
1

25% 
= 0.25
100
4
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
Write 0.5% as a fraction.
0.5%
1
5
0.5



200
1000
100
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.
There is another way to get the answer.
1
Write 0.5% as
2
1
%=
0.5% =
2
1
 100 
2
1
1
1


2 100
200
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
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What is 20% of 60?
20% of 60
20% × 60
0.20 × 60
=12
Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition
June L. Olsen • Anthony P. Giangrasso • Dolores Shrimpton
Copyright ©2012, ©2008 by Pearson Education, Inc.
All rights reserved.