Clinical Calculation5th Edition

Chapter 1

Dimensional Analysis

Pages 1-18

Introduction

Clinical calculations: refers to the solving of computational problems associated with administration of medications.

Determining correct dosage needed There are different approach to clinical calculations

Ratio and Proportion ( this methods may becomes cumbersome and confusing if 2 or more conversion may be required)

DIMENSIONAL ANALYSIS

Dimensional Analysis

Is a computation method whereby one particular unit of measure is converted to another unit of measure by use of a conversion factor or factors

It focus on quantity of unit in a problem that needs to be converted in the same or in the another system of measurement.

continued

Starting factor: the known quantity and unit.

Answer: Desired Unit. Conversion factors: Utilized to convert one

system of measurement to another. Known factors (learned) Obtained from Table

Steps in Dimensional Analysis

Determining the starting factor and answer UNIT. Formulating a conversion equations

LABEL FACTORS Conversion factors

Solving the conversion equation by use of cancellation and simple arithmetic.

Example 1: How many feet are there in 5 yards?

We are converting from yard to feet Starting factor in this problem is:

5 yards Final or ending unit in this problem is

Feet (ft) Conversion factor in this problem is

3 feet = 1 yard

Example 2How many minutes are in 480 seconds

We are converting from seconds to minutes Starting factor in this problem is:

480 seconds Final or ending unit in this problem is

minutes Conversion factor in this problem is

60 seconds = 1 minutes

Example 3How many ounces are there in 4 cups?

We are converting from cups to ounces Starting factor in this problem is:

4 cups Final or ending unit in this problem is

ounces Conversion factor in this problem is

8 ounce = 1 cup

Step II – Formulating the conversion equation

The second step in dimensional analysis is to setup a sequential series of equivalent values called conversion factors

For example: 60 sec = 1 min

The conversion factor

1min 1

sec 60 OR 1

sec 60

min 1

Note that all the conversions are 1:1 relationships and when written as conversion factors, the denominator and numerators can be interchangeable.

More on conversion factors

Approximate Equivalents You must know Table

There are some approximate equivalent sometimes fall within a range for example 60-65 mg = 1 grain (gr) or 4-5 ml = dram (dr) 1 For our purpose here we will use table 5-1 in chapter 5

(page 35 in the book) or the handout in class. During the test, we will use the handout.

Identifying the Equivalents

How many quarters are there in $25.00? Page 8, #3 Equivalent value: 4 quarters = $1.00

How many milliliters would be administered if the order was for 2 teaspoons? Page 8, #10 Equivalent value: 30 mL = 6 tsp (t)

How many quarters are there in $25.00? Page 8, #3

Starting factor: $25.00 Ending unit: quarters Equivalent value: 4 quarters = $1.00

quarterquarter

1001$

425$

How many milliliters would be administered if the order was for 2 teaspoons? Page 8, #10

Starting factor: 2 teaspoon (t) Ending unit: mL Equivalent value: 30 mL = 6 teaspoon (table 1-1)

mLt

mLt 10

6

302

Clinical Calculation5th Edition

Chapter 2

The metric System of Measurement

Pages 19-24

Basic Unit of Measurement in Metric System

Weight gram (g)

Volume Liter (L)

Length Meter (m)

Metric Prefixes

hect

o (h

)

Bas

e un

it

deca

(da

)

cent

i ( c

)

kilo

(k)

meg

a (M

)

deci

(d)

mill

i (m

)

mic

ro (

mc)

deka = 10

hecto = 100

kilo = 1,000

Mega = 1,000,000

deci = 0.1

centi = 0.01

milli = 0.001

micro = 0.000001

Factors of 10

Metric Prefixes - gram

hect

ogra

m (

hg)

gram

(g)de

kagr

am (

dag)

cent

igra

m (

cg

)

kilo

gram

(kg

)

Meg

a gr

am (

Mg)

(to

n)

deci

gram

(dg

)

mill

igra

m (

mg)

mic

rogr

am (

mcg

)

1 decigram = 0.1 g

1 centigram = 0.01 g

1 milligram = 0.001 g

1 microgram = 0.000001 g

1 dekagram = 10 g

1 hectogram = 100 g

1 kilogram = 1,000 g

1 Mega gram = 1,000,000 g

Convert 375 mg to g (page 24, #3)

Starting factor: 375 mg Ending unit: g Conversion factor: 1000mg = 1 g

gmg

gmg 375.0

1000

1375

Metric Prefixes - meter

hect

omet

er (

Hm

)

Met

er (

m)

deca

met

er (

Dm

)

cent

imet

er (

cm

)

kilo

met

er (

Km

)

meg

amet

er (

Mm

)

deci

met

er (

dm)

mill

imet

er (

mm

)

mic

rom

eter

(m

cm)

1 dekameter = 10 m

1 hectometer = 100 m

1 kilometer = 1,000 m

1 Mega meter = 1,000,000 m

1 decimeter = 0.1 m

1 centimeter = 0.01 m

1 millimeter = 0.001 m

1 micrometer = 0.000001 m

Convert 29 cm to m (page 24, #5)

Starting factor: 29 cm Ending unit: m Conversion factor: 100 cm = 1 m

mcm

mcm 29.0

100

129

Convert 25 mm to cm (page 24, #9)

Starting factor: 25 mm Ending unit: cm Conversion factor: 10 mm = 1 cm

cmmm

cmmm 5.2

10

125

Metric Prefixes - Liter

hect

olite

r (h

L)

Lite

r (L

)deca

liter

(da

L)

cent

ilite

r (

cL )

kilo

liter

(kL

)

meg

alite

r (M

L)

deci

liter

(dL

)

mill

ilite

r (m

L)

mic

rolit

er (

mcL

)

1 dekaliter = 10 L

1 hectoliter = 100 L

1 kiloliter = 1,000 L

1 Megaliter = 1,000,000 L

1 deciliter = 0.1 L

1 centiliter = 0.01 L

1 milliliter = 0.001 L

A microliter = 0.000001 L

Convert 0.75 L to mL (page 24, #6)

Starting factor: 0.75 mL Ending unit: L Conversion factor: 1000mL = 1 L

LmL

LmL 00075.0

1000

175.0

Clinical Calculation5th Edition

Chapter 3

The Apothecaries System of Measurement

Pages 25 - 29

Apothecaries Basic units and Abbreviations

Weight grain (gr)

Volume Minim Fluid dram = drams Fluid ounce = ounces

For dry weight they also use drams and ounces, but it is rarely used.

In traditional apothecaries system one pound consists of 12 (dry weight) ounces.

What is conversion that is used today 1 pound = ?? ounces?

Table 3-2 – Apothecaries Notations

1/10 grain = gr 1/10 1 grain = gr I 1 ½ grain = gr 1 ½ 7 grain = gr vii 10 grain = gr x 15 minims = minims 15 150 minims = minims 150 2 ½ ounces = oz 2 ½

Table 3-3 Apothecaries Fluid units

60 minims = 1 dr 8 dr = 1 oz 16 oz = 1 pt 2pt = 1 qt

pt = pint

qt = quarts

Convert within the apothecaries system2 pts to dr (page 29, #8)

Starting factor: 2 pts Ending unit: dr Conversion factors: 16 oz = 1pt; 8 dr = 1 oz

CCLVI 2561

8

1

162 drdr

oz

dr

pt

ozpts

Please note that I had to use more than one conversion factors in order to reach my ending units

Clinical Calculation5th Edition

Chapter 4

The Household System of Measurement

Pages 30 - 33

Basic Unit of Measurement in Household System

Weight Pounds (lbs) Ounces (oz)

Length Inch (in) Feet (ft) Yard (yard) Mile (mile)

Volume Gallon (gal) Ounce (oz) Teacup (teacup) Cup/Glass (c/gl) Quart (qt) Pint (pt) Teaspoon (tsp) (t) Tablespoon (tbs) (T) Drop (gtt)

Table 4-2 Household Equivalents and more

60 gtt = 1 tsp 3 tsp = 1 tbs 2 tbs = 1 oz 6 oz = 1 teacup 8 oz = 1 cup/glass 16 oz = 1 pt 2 pt = 1 qt 4 qt = 1 gal

16 oz = 1 lb

12 in = 1 ft 3 ft = 1 yard 5280 ft = 1 mile

Convert within the household system1 glass to tsp (page 33, #1)

Starting factor: 1 glass Ending unit: teaspoon Conversion factors: 8oz = 1 cup; 2 tbs = 1 oz; 3 tsp = 1 tbs

tsptbs

tsp

oz

tbs

glass

ozglass 48

1

3

1

2

1

81

Please note that I had to use more than one conversion factors in order to reach my ending units

Convert within the household system½ gal to oz

Starting factor: ½ gallon (gal) Ending unit: ounces (oz) Conversion factors: 16 oz = 1 pt; 2 pt = 1 qt; 4 qt = 1 gal

ozpt

oz

qt

pt

gal

qtgal 64

1

16

1

2

1

4

2

1

Please note that I had to use more than one conversion factors in order to reach my ending units

Clinical Calculation5th Edition

Chapter 5

Conversion of Metric, Apothecaries, and Household Units

Pages 34 - 39

Table 5-1 Approximate Equivalent among Metric, Apothecaries and Household Units – Dry Weight

DRY WeightMetric Apothecaries Household60 mg = 1 gr =1 g = 15 gr =15 g = 4 dr = 1 tbs (3 tsp)30 g = 1 oz (8 dr)

16 oz= 1 lb

1 kg = 2.2 lb

= dram or fluid dram

= ounce or fluid ounce

Table 5-1 Approximate Equivalent among Metric, Apothecaries and Household Units - Liquid

LIQUIDMetric Apothecaries Household1 mL = 15 - 16 minims = 15 gtt4 mL = 1 dr =5 mL = 75 minims = 1 tsp15 mL = 4 dr = 1 tbs (3 tsp)30 mL = 1 oz (8 dr) = 1 oz (2 tbs)500 mL = 16 oz (1pt) = 16 oz (1pt or 2 cups)1000 mL = 32 oz (1 qt) = 32 oz (1 qt)

Table 5-1 Approximate Equivalent among Metric, Apothecaries and Household Units - Length

LENGTHMetric Apothecaries Household2.54 cm = = 1 in1 m = = 39.4 in

Convert and round to nearest tenthoz iv to tbs (page 38, #8)

Starting factor: oz iv = 4 oz Ending unit: tbs Conversion factors: 1 oz = 8 tbs

tbsoz

tbsoz 0.32

1

84

If problem asks to round to nearest tenth, then the final answer has to be written that way and with correct unit, 32.0tbs otherwise it is counted incorrect.

Convert and round to nearest tenthminims XX to mL (page 38, #7)

Starting factor: minims XX = 20 minims Ending unit: mL Conversion factors: 75 minims = 5 mL

mL3.1mL33.1mL3

4

minims75

5minims20

mL

If problem asks to round to nearest tenth, then the final answer has to be written that way and with correct unit, 1.3mL otherwise it is counted incorrect.

Convert and round to nearest tenth157lb to kg (page 39, #20)

Starting factor: 157lb Ending unit: kg Conversion factors: 2.2 lbs = 1 kg

kgkglbs

kglb 4.7136.71

2.2

1157

If problem asks to round to nearest tenth, then the final answer has to be written that way and with correct unit, 71.4kg otherwise it is counted incorrect.

Convert and round to nearest tenth5.5 g to gr (page 39, #28)

Starting factor: 5.5g Ending unit: gr Conversion factors: 60mg=15gr; 1000mg= 1g OR 1 g = 15 gr You

may use either of the two equivalent, they both consider correct, one is more direct conversion

LXXXIIss 5.821

155.5 grgr

g

grg

ss = ½ your test book may not use this, but your handout may refer to it.

If problem asks to round to nearest tenth, then the final answer has to be written that way and with correct unit, 82.5gr otherwise it is counted incorrect.

Convert and round to nearest tenth6 tsp to dr (page 39, #18)

Starting factor: 6 tsp Ending unit: dr Conversion factors: 4 dr = 3 tsp

drtsp

drtsp 0.8

3

46

If problem asks to round to nearest tenth, then the final answer has to be written that way and with correct unit, 8.0dr otherwise it is counted incorrect.