Clinical Calculation 5th 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.

Known factors (learned) Obtained from Table 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 2 How 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 3 How 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 OR 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

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)

Clinical Calculation 5th 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)

Factors of 10 Metric Prefixes mega (M) micro (mc) kilo (k) hecto (h) deca (da) deci (d) milli (m) centi ( c ) Base unit deka = 10 hecto = 100 kilo = 1,000 Mega = 1,000,000 deci = 0.1 centi = 0.01 milli = 0.001 micro = 0.000001

Metric Prefixes - gram microgram (mcg) Mega gram (Mg) (ton) hectogram (hg) microgram (mcg) Mega gram (Mg) (ton) dekagram (dag) centigram ( cg ) kilogram (kg) decigram (dg) milligram (mg) gram (g) 1 dekagram = 10 g 1 hectogram = 100 g 1 kilogram = 1,000 g 1 Mega gram = 1,000,000 g 1 decigram = 0.1 g 1 centigram = 0.01 g 1 milligram = 0.001 g 1 microgram = 0.000001 g

Convert 375 mg to g (page 24, #3) Starting factor: 375 mg Ending unit: g Conversion factor: 1000mg = 1 g

Metric Prefixes - meter millimeter (mm) micrometer (mcm) megameter (Mm) hectometer (Hm) decameter (Dm) decimeter (dm) centimeter ( cm ) kilometer (Km) Meter (m) 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

Convert 25 mm to cm (page 24, #9) Starting factor: 25 mm Ending unit: cm Conversion factor: 10 mm = 1 cm

Metric Prefixes - Liter megaliter (ML) kiloliter (kL) hectoliter (hL) decaliter (daL) deciliter (dL) milliliter (mL) microliter (mcL) centiliter ( cL ) Liter (L) 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

Clinical Calculation 5th 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 system 2 pts to dr (page 29, #8) Starting factor: 2 pts Ending unit: dr Conversion factors: 16 oz = 1pt; 8 dr = 1 oz Please note that I had to use more than one conversion factors in order to reach my ending units

Clinical Calculation 5th 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 system 1 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 Please note that I had to use more than one conversion factors in order to reach my ending units

Convert within the household system ½ 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 Please note that I had to use more than one conversion factors in order to reach my ending units

Clinical Calculation 5th 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 = dram or fluid dram = ounce or fluid ounce

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

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

Convert and round to nearest tenth oz iv to tbs (page 38, #8) Starting factor: oz iv = 4 oz Ending unit: tbs Conversion factors: 1 oz = 8 tbs 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 tenth minims XX to mL (page 38, #7) Starting factor: minims XX = 20 minims Ending unit: mL Conversion factors: 75 minims = 5 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 tenth 157lb to kg (page 39, #20) Starting factor: 157lb Ending unit: kg Conversion factors: 2.2 lbs = 1 kg 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 tenth 5.5 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 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 tenth 6 tsp to dr (page 39, #18) Starting factor: 6 tsp Ending unit: dr Conversion factors: 4 dr = 3 tsp 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.