Clinical calculations

Dimensional analysis = label factor method = unit-conversion method Computation method whereby one particular unit of measurement is converted to another unit of measurement by use of a conversion factor or factors

Starting factor Answer unit Conversion factors

Steps in Dimensional Analysis 1.Determining the starting factor and answer unit 2.Formulating a conversion equation 3.Solving the convertion equation

Step I: Determining the Starting Factor and Answer Unit Example: How many inches are there in 29 feet? 29 feet – known quantity, which have to be converted – starting factor The desired unit – answer unit (in)

Step II: Formulating the Conversion Equation Conversion factors – bridges leading from starting factor to the desired unit The numerator and denominator must be of equivalent value The fraction always is equal to 1

Step II: Formulating the Conversion Equation 1 hr = 60 min – equivalents 1 hr/60 min = 60 min/1 hr - conversion factors

Step II: Formulating the Conversion Equation Example: Find the number of minutes in 90 seconds Equivalents: 1 min=60 sec Conversion Equation: Starting Convertion Answer factor factor unit 90 sec × 1 min/60 sec = ___ min

Solving the conversion equation Example: Find the number of yards in 1.5 miles Equivalents: 1 mi = 5280 ft; 3 ft = 1 yd Equation: 1.5 mi × 5280ft/1 mi × 1yd/3ft The identical units must be placed diagonally (in the numerator of one factor and in the denominator of the factor immediately following)

Solving the conversion equation 1.5 mi × 5280ft/1 mi × 1yd/3ft 1.5 × 5280/1 × 1 yd/3 (1.5 × 5280)/3=2640 yd

Systems of Measurement The metric system The apothecaries’ system The household system

Metric System of Measurement Based on the decimal system Basic units: –Gram – for weight –Liter – for volume –Meter – for length

Metric Units and Abbreviations Weight Gram g Miligram mg Microgram mcg (μg) Kilogram kg Volume Liter L Milliliter mL (cc) Length Meter m Centimeter cm Millimeter mm

Apothecaries’ System of Measurement The measures are approximations Roman numerals are often used Fractions are used (ss = ½) Symbol for a unit of measure is written before the quantity – gr viiss = gr VIIss A combination of Arabic numerals and fractions can be used - gr 7 ½

Apothecaries’ System of Measurement Weight –The basic unit is grain (gr) gr 15 = 1 g 60 mg = gr 1 –Dram (medication cup) dr –Ounce – oz –Pound (lb) = 16 oz

Apothecaries’ System of Measurement Volume –The smallest unit is the minim (m) –Dram (dr) dr 1= 4 mL –Ounce (oz) = 30 mL –Pint (pt) pt 1 =oz 16 = 500 mL –Quart (qt) qt 1 = pt 2= 1,000 mL

Household System Some of the units for liquid measures are the same as those in the apothecaries’ (pint and quart) There are no standart rules for expressing household measures Standart cookbook abbreviations, Arabic numerals and fractions are used

Household Units Drop (gtt) Teaspoon (t, tsp) Tablespoon (T, tbs) 1 tbs = 3 tsp Cup (C) 1 C = 16 tbs Pint (pt) 1 pt = 2 C Quart (qt) 1 qt = 2 pt 1 glassful = 8 ounces

Apothecaries’/Household/ Metric Equivalents 1 ounce (oz) = 30 mL 1 dram (dr) = 4 mL 1 tablespoon (T or tbs) = 15 mL 1 teaspoon (t or tsp) = 5 mL 1 cup = 240 mL (8 ounces) 1 pint (pt) = 500 mL (16 ounces) 1 quart (qt) = 1,000 mL (32 ounces) 15 or 16 minims (m) = 1 mL 1 kg = 2.2 lb