Pharmacology Math Chapter 34

proper fraction
numerator is smaller than the denominator

improper fraction
numerator is equal or larger than the denominator

Amount or volume of a liquid medication is expressed in
milliliters (mL)

Weight or strength of a solid medication is expressed in
grams (g)

Length is expressed in
meters (m)

One inch is equal to
2 1/2 centimeters (cm)

Units in the metric system are converted by moving the decimal point in multiples of
10

When going from larger to smaller units of measure, as in converting grams to milligrams, the answer will be a larger number, so move the decimal point
three places to the right
0.35 g = 350 mg
OR multiply 0.35 g × 1000 = 350 mg

The following equivalents can be used to make conversions in the metric system
1 kg = 1000 g
1 g = 1000 mg
1 mg = 0.001 g or 1/1000 g
1 kl = 1000 liters
1 liter = 1000 mL
1 mL = 0.0001 liter or 1/1000 liter

Apothecary System
In the apothecary system, the basic unit of weight for a solid medication is the grain (gr) and the basic unit of volume for a liquid medication is the minim (M)
As in the metric system, these two units are related; the grain is based on the weight of a single grain of wheat, and the minim is the volume of water that weighs 1 gr
Either symbols or abbreviations are used; for example, 1½ drams might be written Diss or dr 1½ (p. 664)

Household Measurements
Basic measure of weight is the pound (lb) and of volume is the drop (gtt)
1 gtt = 1 M
60 gtt = 1 tsp (5 ml)
3 tsp = 1 Tbsp (tablespoon) (15 ml)
2 Tbsp = 1 oz (30 ml)
8 oz = 1 cup (240 ml)

Formula Conversion Method

You must convert the ordered unit of measurement (grains) to match the unit of measurement on the drug label (grams)

Drug have × Wanted/Have = Unit wanted in new system
Drug have: unit of measurement that is on the label
Wanted: amount or strength ordered by physician
Have: conversion (15 gr = 1 g)

1 g (label) × 30 gr (physician order) / 15 gr (conversion factor) = 2 g = 2 tabs

Calculating Drug Dosages for Administration
Standard formula:
“Available strength” /”Ordered strength” = “Available amount” /”Amount to give”

Alternative Formula: D/H × Q
Regardless of which formula is used, the answer will be the same
D: desired dose (the physician’s order)
H: what is on hand (the dosage strength listed on the medication label)
Q: quantity in the unit (identified on the label as one tablet, 5 mL, etc.)
(D/H) × Q

Pediatric Dosages
Pediatric doses are much more accurate when based on weight; children can vary greatly in size and body weight
Factors used in calculating pediatric doses are either body surface area or weight

Clark’s Rule
Is a medical term referring to a mathematical formula used to calculate the proper dosage of medicine for children aged 2-17
This rule is based on the weight of the child
This system is much more accurate, because children of any age can vary greatly in size and body weight
Pediatric dose = (Child’s weight in pounds/150 lb) × Adult dose (Adult doses are based on average adult weight of 150 lb)

West’s Nomogram
West’s nomogram uses a calculation of the body surface area (BSA) of infants and young children to determine the pediatric dose
Pediatric dose = (BSA of child in m2 / 1.7 m2) × Adult dose

Dosages Based on Body Weight
Carefully weigh the child before beginning to calculate the dose to make sure you have an accurate weight
Convert the weight to kilograms by dividing number of pounds by 2.2 kg
Calculate the total daily dose of the medication
Calculate a single dose of drug based on how frequently the medication is ordered throughout the day
After calculating amount of a single dose, compare the ordered amount to drug label

Reconstituting Powdered Injectable Medications
Crystals or powder mixed with isotonic saline/sterilized water
This forms a solution
Must be made before injection
Read label directions carefully

Legal and Ethical Issues
Must master dosage calculations
Responsible for his/her own actions
Know state laws before administering medications

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