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Medical Dosage Calculation Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach,

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Presentation on theme: "Medical Dosage Calculation Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach,"— Presentation transcript:

1 Medical Dosage Calculation Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton CHAPTER Tenth Edition A Dimensional Analysis Approach Review of Arithmetic for Medical Dosage Calculations 1

2 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Directory Classroom Response System Questions Lecture Note Presentation

3 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Classroom Response System Questions

4 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #1 Convert 5/8 to a decimal number.

5 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #1 Choices 1.0.624 2.0.615 3.0.525 4.0.625

6 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #1 Response 1.0.624 2.0.615 3.0.525 4.0.625

7 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #2 Convert 4500/1000 to a decimal number.

8 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #2 Choices 1.450.0 2.45.0 3.4.5 4.0.45

9 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #2 Response 1.450.0 2.45.0 3.4.5 4.0.45

10 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #3 Simplify: 7.2/0.06

11 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #3 Choices 1.120 2.1200 3.12,000 4.12

12 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #3 Response 1.120 2.1200 3.12,000 4.12

13 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #4 Simplify: 4/15 x 30 x 1/2

14 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #4 Choices 1.1/4 2.4/1 3.2/1 4.1/2

15 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #4 Response 1.1/4 2.4/1 3.2/1 4.1/2

16 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #5 Write 38 2/5% as a decimal number

17 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #5 Choices 1.38.40 2.3.840 3.0.384 4.384.0

18 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Question #5 Response 1.38.40 2.3.840 3.0.384 4.384.0

19 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Lecture Note Presentation

20 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Decimal Numbers

21 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton

22 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Keep the decimal points aligned Adding and Subtracting Decimal Numbers 0.115 + 12.34 12.455 78.952 − 2.12 76.832

23 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Multiplying and Dividing Decimal Numbers

24 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 304.2 × 0.16 = ? 304.2 × 0.16 18 252 30 42. 48.672 So, 304.2 × 0.16 = 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. }

25 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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 = 23,597 23.597 × 1,000 = 23 5 9 7

26 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Because there are three decimal places in 0.002, move the decimal points three places to the right in both the numerator and denominator. meansor

27 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Therefore :

28 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Rounding Decimal Numbers

29 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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 Rounding Decimal Numbers

30 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton (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

31 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton (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

32 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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. Rounding Decimal Numbers For example, 0.345 mL0.35 mL And 1.345 mL1.3 mL ≈ ≈

33 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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

34 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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.

35 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Changing Decimal Numbers to Fractions Reading a decimal number will help you to write it as a fraction: Decimal NumberReadFraction 4.1four and one tenth 0.3three tenths 0.07seven hundredths 0.231two hundred thirty-one thousandths 0.0025twenty-five ten thousandths

36 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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: where the numerator (the number on top) of the fraction is smaller than its denominator (the number on bottom). ½ is referred to as aproper fraction, or

37 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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, 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).

38 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Write 2.25 as an improper fraction. The number 2.25 is read as and written two and twenty-five hundredths === 1 4

39 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Changing Fractions to Decimal Numbers

40 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 2 To change a fraction to a decimal number, think of the fraction as a division problem. For example: means or 2 ÷ 5

41 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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

42 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Step Two: Perform the division. Therefore,

43 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Write as a decimal number. Step 1: means

44 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Step 2: Therefore,

45 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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. 193/10 = 19.3 1 9 3

46 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Multiplying and Dividing Fractions

47 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton

48 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton It is often convenient to cancel before you multiply. 1 2

49 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Writeas the fraction Division Becomes the multiplication

50 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton

51 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton

52 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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.

53 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Complex Fractions

54 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 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. Complex Fractions

55 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton

56 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton 1 20 = 80

57 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Adding and Subtracting Fractions Add (or subtract) the numerators when the denominators are the same: =

58 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Subtract the numerators =

59 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton When the denominators are Different use a Common Denominator

60 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton When the denominators are Different use a Common Denominator

61 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Percentages

62 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Percent means per hundred 70% = 0.7 25% = 0.25

63 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton Write 0.5% as a fraction. 0.5%

64 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton There is another way to get the answer. Write 0.5% as 0.5% = % =

65 Copyright ©2012, ©2008 by Pearson Education, Inc. All rights reserved. Medical Dosage Calculations: A Dimensional Analysis Approach, Tenth Edition June L. Olsen Anthony P. Giangrasso Dolores Shrimpton What is 20% of 60? =12 20% of 60 20% × 60 0.20 × 60


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