1. Chapter 23 Mathematics Review and Medication Administration
Jeanelle F. Jimenez RN, BSN, CCRN
Mosby items and derived items © 2011, 2006, 2003, 1999, 1995, 1991 by Mosby, Inc., an affiliate of Elsevier Inc.

2. Decimal Fractions Names of Decimal Places .0001 Ten thousandths
One hundred thousandths
Ten thousandths
Thousandths
Hundredths
Tenths
Unit (whole number)
Tens
Hundreds
Thousands
10, Ten thousands
100, One hundred thousands

3. Decimal Fractions Names of Decimal Places (continued)
A decimal point found left of a whole number means that the number is a fraction of a whole number.
A decimal point found after a number means that it is a whole number.
A number without a decimal point is understood to have an “invisible” decimal point behind it.

4. Dosage Calculations 2 methods to use Ratio Proportion Method
Formula Method

5. Ratios
Ratios show the relationship of one number or quantity to another number or quantity.
Numbers of a ratio are separated by a colon.
A ratio is also a fraction.
The value of a ratio is not changed if both terms are multiplied or divided by the same number.
When numbers are written in ratio, they must all be expressed in the same units.
A fraction may be written as a ratio.

6. Proportions
Proportion shows that the relationship between two ratios has equal value.
Definitions
Means: inner terms of the proportion
Extremes: outer terms of the proportion
Set up the left side of the proportion as the “known” side using information that is known or given.

7. Proportions Set up the known side.
Set up the unknown side. Use x for what you are trying to find.
Set up the units in the same position on each side of the problem.
Multiply the means.
Multiply the extremes
Solve for x (divide the number with the x into the number on the opposite side of the problem).
Label the answer with the unit of measurement that accompanies the x in the problem.

8. Proportions Review of Proportion Method
Set up problems in the same order on both sides.
Multiply the means; multiply the extremes.
The number multiplied with the x is always that number with the x to the right of it.
Divide the number with the x into the number on the other side of the problem.
Label the problem by looking to see what unit of measurement the x is with the proportion.

9. Dosage Calculations: Example #1
The prescription is 1 mg Haldol IM (intramuscularly), and the medication is available in an ampule with a strength of 5 mg/1 mL. How many mL should be given?
SOLUTION: Set up a ratio
Known factors:
Medication available = 5 mg (strength): Factor 1
Volume = 1 mL: Factor 2
Prescribed dosage = 1 mg: Factor 3
Volume (mL) needed to give = X mL: Unknown

10. Dosage Calculations: Example #1 contd.
SOLUTION, cont.
Remember: Units of measure must cancel properly during calculations (see equation below).
Set up units in the same position on each side of the double colon:
5 mg is to 1 mL as 1 mg is to X mL

11. Dosage Calculations Example #2
The prescription of Penicillin G (oral tablets) is for 375 mg. Tablets are supplied in 250 mg scored (able to be divided in half) tablets. How many tablets should be given?
SOLUTION: Set up a ratio
250 mg is to 1 tablet as 375 mg is to X tablets
250 mg: 1 tablet::375 mg: X tablets

12. Dosage Calculations #2 contd.
SOLUTION: cont.
Multiply means:
375 mg × 1 tablet = 375 mg tablet
375 mg tablet ÷ 250 = X tablets
Therefore, X = 1.5 tablets
Answer: The nurse would give 1.5 tablets.
One scored tablet would need to be split in half

13. Dosage Calculations Example #3
The prescription is 75 mg Trazodone. The medication is provided in 150 mg scored tablets. How many tablet(s) are needed?
SOLUTION: Set up a ratio
150 mg is to 1 tablet as 75 mg is to X tablets
150 mg: 1 tablet::75 mg: X tablet

14. Dosage Calculations Example #3 contd.
SOLUTION, cont.
Multiply means:
75 mg × 1 tablet = 75 mg tablets
75 mg tablet ÷ 150 = X tablets
Therefore, 0.5 = X tablets
Answer: The nurse would give 0.5 tablet (½ tablet).
Note: If the dosage for tablets does not come out exactly, the prescribed dosage cannot be given.

15. Formula Method  D/H x Q = amount to give D = Desired dose (MD order)
H = What is available on hand
Q = Quantity (pill, tablet, ml, etc)

16. Significant Figures
Numbers that have practical meaning or dosages that can be measured
For example
Dosage prescribed is mL
When measured with a syringe that has markings of 1.3 mL, 1.4 mL, and 1.5 mL, last two numbers (the “25”) cannot be measured
Amount given is 1.3 mL, because this amount is closer to the prescribed dosage than 1.4 mL
The dosage that can be measured, 1.3 mL, is the significant figure.

17. Significant Figures contd.
When rounding
Dosage is rounded to the closest amount
Using the example
Values ranging from to are rounded down to 1.3
Values from to are rounded up to 1.4

18. The Metric System The metric system is based on the decimal system.
The decimal system uses the divisions and multiples of a unit, which is always in ratios of tens.
The metric system uses the following units:
liter (L) = volume (amount) of fluids
gram (g) = weight of solids
meter (m) = measure of length

19. The Metric System
Smaller units of the system are designated by the following prefixes:
deci = 0.1 of the unit (liter, gram, meter); tenths
centi = 0.01 of the unit; hundredths
milli = of the unit; thousandths
Larger units of the system are designated by the following prefixes:
deka = 10 times the unit (liter, gram, meter)
hecto = 100 times the unit
kilo = 1000 times the unit

20. The Metric System Units of Weight Units of Volume
1 gram (g) = milligrams (mg)
0.001 gram (g) = 1 milligram (mg)
1 kilogram (kg) = grams (g)
0.001 kilogram (kg) = 1 gram (g)
Units of Volume
1 liter (L) = milliliters (mL)
0.001 liter (L) = 1 milliliter (mL)
1 milliliter (mL) = 1 cubic centimeter (cc)

21. The Metric System
Approximate Equivalents of the Metric System and the Apothecary System
Volume
1 milliliter (mL) = 15 or 16 minims
4 or 5 milliliters (mL) = 1 fluid dram
30 milliliters (mL) = 1 fluid ounce
500 milliliters (mL) = 1 pint
1000 milliliters (mL) = 1 quart

22. The Metric System
Approximate Equivalents of the Metric System and the Apothecary System (continued)
Weight
60 milligrams (mg) = 1 grain (gr)
1000 milligrams (mg) = 15 grains
4 grams (g or gm) = 1 dram
30 grams (g) = 1 ounce
0.45 kilogram (kg) = 1 pound (lb.)
1 kilogram (kg) = 2.2 pounds (lbs.)
Give an example of a typical over-the-counter medication in which the label could provide grains. Aspirin.
Give an example of how to figure how many grains equals x mg.

23. The Metric System Metric Measurements of Length
The basic unit of length is the meter.
The meter is equal to inches.
0.001 meter = 1 millimeter (mm)
0.01 meter = 1 centimeter (cm)
0.1 meter = 1 decimeter (dm)
10 meters = 1 decameter (dam)
100 meters = 1 hectometer (hm)
1000 meters = 1 kilometer (km)

24. The Metric System Metric Measurements of Length
Most frequently used equivalents
1 meter (m) = 1000 millimeters (mm)
0.001 meter (m) = 1 millimeter (mm)
1 meter (m) = 100 centimeters (cm)
1 centimeter (cm) = 10 millimeters (mm)
1 millimeter (mm) = 0.1 centimeter (cm)

25. Pediatric Considerations
Young’s Rule
A method for the calculation of the appropriate dose of a drug for a child 2 years of age or older; applies to children up to the age of 12
Age of child _
(Age of child + 12)
 Average adult dose = Child’s dose

26. Pediatric Considerations
Clark’s Rule
A method of calculating the approximate pediatric dosage of a drug for a child
Weight of child (lbs.)
150
 Average adult dose
= Child’s dose

27. Pediatric Considerations
Fried’s Rule
This rule is used for infants younger than 2 years of age.
Age in months
150
 Average adult dose = Child’s dose

28. Pediatric Considerations
Estimating Body Surface Area in Children
Body surface area is defined as the total area exposed to the outside environment.
Use body surface area scale to find the correct surface area (SA).
SA (m2)
1.73 m2
 Adult dose = Child’s dose

29. Pharmacology
This is the study of drugs and their action on the living body.
Substances derived from plants and animals, from vitamins and minerals, and from synthetic sources can be used as drugs in the treatment and prevention of disease.
The action of any drug on the body is a complicated process.

30. Pharmacology Drug Dosage
The dosage is the amount of a drug prescribed for the patient by the physician.
A dose of medicine refers to a single prescribed amount of drug given at one time.
Nurses must become familiar with therapeutic dosages of frequently used drugs to confidently administer dosages of medication to each patient.

31. Pharmacology Drug Actions and Interactions Two general types
Local: Affect only the area where the drug is placed
Systemic: Affect the entire body
Drug interaction: One drug alters another drug
Potentiation: One drug increases the action or effect of another drug
Incompatibility: Drugs that do not combine chemically with other drugs
Antagonist: Drug that will block the action of another drug

32. Pharmacology
An idiosyncratic response to a drug is an individual’s unique hypersensitivity to a particular drug.
A reduced response to a drug is called tolerance.
An adverse drug reaction is a harmful, unintended reaction to a drug administered at a normal dosage.
Contraindications are conditions under which the drug should not be given.
Interactions are modifications of the effect of a drug when administered with another drug.
Give an example of an idiosyncratic response. Dopamine and tachycardia
Give an example of an adverse drug reaction.

33. Pharmacology
Factors that may affect how patients respond to medication:
Age
Weight
Physical health
Psychological status
Environmental temperature
Gender
Amount of food in the stomach
Dosage forms

34. Medication Orders
The nurse is ethically and legally responsible for ensuring that the patient receives the correct medication ordered by the physician.
Medication orders should include the following:
Patient's name
Date and time of the order
Name of the drug
Dosage of the drug
Route of administration
Time or frequency drug is given
Signature of the physician
Any special instructions

35. Medication Orders Controlled Substances
Opioids, barbiturates, and other controlled drugs that have a high possibility for abuse or addiction are double-locked.
“Narcotic keys” are kept by designated nurses per shift.
Each controlled drug used is logged into the narcotic log book.
At the end of each shift, controlled drugs are carefully counted by a nurse from the outgoing shift and a nurse from the incoming shift.
Always have a witness to the “wasting” of a controlled substance.

36. Medication Orders Types of Orders Standing orders Verbal orders
Already written by a physician for all patients on a particular unit or area
Carried out without having to call the physician
Verbal orders
May be given in the presence of an LPN/LVN or an RN directly or over the telephone
Should be written on the chart and signed by the physician as soon as possible

37. Medication Administration
Six Rights
Right medication
Right dose
Right time
Right route
Right patient
Right documentation

38. Medication Orders
Important Considerations of Medication Administration
If you did not pour it, do not give it.
If you gave it, chart it.
Do not chart for someone else or have someone else chart for you.
Do not transport or accept a container that is not labeled.
Do not put down an unlabeled syringe.
If given a verbal order, repeat it to the physician.
If you make an error, report it immediately.

39. Medication Orders
Important Considerations of Medication Administration (continued)
Never leave a medication with a patient or family member. Watch the patient take it and swallow it.
Always return to assess the patient’s response.
Chart as soon as possible after giving medication.
If a patient refuses medication, do not force it; chart “Refused medication because of ”
If you elect to omit a dose based on your nursing judgment, let another nurse help make the decision. If medication is not given, document “Dose omitted because ” Report to the physician.

40. Routes of Administration
Enteral
Via the GI tract
Powders
Pills
Tablets
Liquids or suspensions
Suppositories
Give an example of when the enteral route might be chosen for medications.

41. Routes of Administration
Percutaneous
Through the skin or mucous membranes
Topical
Instillation
Inhalation

42. Routes of Administration
Parenteral
Methods other than the GI tract; needle route
Ampules
Vials
Intramuscular
Subcutaneous
Intradermal
Intravenous

43. Enteral Administration
Preparation of Tablets, Pills, and Capsules
These preparations enter the GI tract and are absorbed more slowly into the blood stream than via any other route.
The slow absorption rate makes the PO (by mouth) route relatively safe.
Some PO medications are irritating to the patient’s GI tract, and larger tablets may be difficult for some patients to swallow.

44. Administering tablets, pills, and capsules.
Skill 23-1: Step 5
(From Potter, P.A., Perry, A.G. [2005]. Fundamentals of nursing. [6th ed.]. St. Louis: Mosby.)
Administering tablets, pills, and capsules.

45. Enteral Administration
Preparation of Liquid Medications
Liquid medications are often given to children; to patients who cannot swallow tablets, pills, or capsules; and to geriatric patients.
Medications may be given PO or via a nasogastric, gastrostomy, or jejunostomy tube.
Liquids must not be given to unconscious patients because of the possibility of aspirating.
Some liquid medications are not to be followed by water, and some may stain the teeth.
Give examples in which liquid medications should not be administered.
What types of medications should not be followed by water?

46. Administering liquid medications.
Skill 23-2: Step 13
(From Potter, P.A., Perry, A.G. [2005]. Fundamentals of nursing. [6th ed.]. St. Louis: Mosby.)
Administering liquid medications.

47. Enteral Administration
Tubal Medications
Nasogastric (NG) tubes are used to administer liquid medications to unconscious patients, dysphagic patients, and those who are too ill to eat.
Many medications come in liquid form; if they do not, solid tablets may be pulverized in a mortar and pestle, and capsules can be opened.
Not all tablets are safe to use when crushed, and not all capsules are safe to use when opened.

48. Administering tubal medications.
Skill 23-3: Step 13a
Administering tubal medications.

49. Administering tubal medications.
Skill 23-3: Step 16
Administering tubal medications.

50. Enteral Administration
Suppositories
Cone-shaped, egg-shaped, or spindle-shaped medication made for insertion into the rectum or vagina
Dissolves at body temperature and absorbed directly into the bloodstream
Useful for infants, patients who cannot take oral preparations, and patients with nausea and vomiting
Stored in cool place so they do not melt

51. Percutaneous Administration
With these routes, medications are absorbed through the skin or the mucous membranes.
Most produce a local action, but some produce a systemic action.
Drugs include topical applications, instillations, and inhalations and ointments, creams, powders, lotions, and transdermal patches.
Absorption is rapid but of short duration.

52. Percutaneous Administration
Ointments
An oil-based semisolid medication; may be applied to the skin or a mucous membrane
Creams
Semisolid, nongreasy emulsions that contain medication for external application
Lotions
Aqueous preparations that are used as soothing agents that relieve pruritus, protect the skin, cleanse the skin, or act as astringents

53. Percutaneous Administration
Transdermal Patches (Topical Disk)
Adhesive-backed medicated patches applied to the skin provide sustained, continuous release of medication over several hours or days.
Eyedrops and Eye Ointments
Care should be taken to keep all ophthalmic preparations sterile by not touching the dropper or the tube to the eye.
Eardrops
Containers of solutions to be used as eardrops will be labeled “otic.” They must be at room temperature when applied.

54. A variety of medications are available as transdermal patches.
Figure 23-4
(From Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
A variety of medications are available as transdermal patches.

55. Percutaneous Administration
Nosedrops
Nosedrops are for individual use only.
Nasal Sprays
Sprays absorbed quickly; less medication is used and wasted when administered in this manner.
Inhalation
Drugs may be absorbed through the mucous membranes of the respiratory tract.
Inhalation produces a relatively limited effect or a systemic effect.
This method is actively used by respiratory therapy and anesthesiologists.

56. Percutaneous Administration
Sublingual Administration
Drug is administered by placing it beneath the tongue until it dissolves.
Drug may be a tablet or liquid squeezed out of a capsule.
It is rapidly absorbed into the bloodstream.
Buccal Administration
A tablet is placed between the cheek and teeth, or between the cheek and the gums.
Absorption into the capillaries of the mucous membranes of the cheek gives rapid onset of the drug’s active ingredient.

57. Parenteral Administration
Equipment
Syringes
Syringe consists of a barrel, a plunger, and a tip.
Outside of the barrel is calibrated in milliliters, minims, insulin units, and heparin units.
Types
Tuberculin syringe
Insulin syringe
Three-milliliter syringe
Safety-Lok syringes
Disposable injection units

58. Figure 23-5 Parts of a syringe.
(From Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
Parts of a syringe.

59. Tuberculin syringe calibration.
Figure 23-6
(From Clayton, B.D., Stock, Y.N. [2004]. Basic pharmacology for nurses. [13th ed.]. St. Louis: Mosby.)
Tuberculin syringe calibration.

60. Calibration of U100 insulin syringe.
Figure 23-7
(From Clayton, B.D., Stock, Y.N. [2004]. Basic pharmacology for nurses. [13th ed.]. St. Louis: Mosby.)
Calibration of U100 insulin syringe.

61. Reading the calibrations of a 3-mL syringe.
Figure 23-8
Reading the calibrations of a 3-mL syringe.

62. Figure 23-10
Safety-Glide syringe.

63. Figure 23-12 Parts of a needle.
(From Clayton, B.D., Stock, Y.N. [2004]. Basic pharmacology for nurses. [13th ed.]. St. Louis: Mosby.)
Parts of a needle.

64. Percutaneous Administration
Equipment (continued)
Needles
Parts are the hub, shaft, and beveled tip.
Opening at the needle’s beveled tip is the lumen.
Size of the diameter of the inside of the needle’s shaft determines the gauge of the needle; the smaller the gauge, the larger the diameter.
Needle gauge selection is based on the viscosity of the medication.

65. Percutaneous Administration
Equipment (continued)
Needle length
Selected based on the depth of the tissue into which the medication is to be injected
Intradermal: 3/8 to 5/8 inch
Subcutaneous: 5/8 to 1/2 inch
Intramuscular: 1 to 1 1/2 inch
Intravenous needles
Butterfly (scalp needle)
Over-the-needle catheter (Angiocath, Jelco)

66. Needle length and gauge.
Figure 23-13
(From Clayton, B.D., Stock, Y.N. [2004]. Basic pharmacology for nurses. [13th ed.]. St. Louis: Mosby.)
Needle length and gauge.

67. Percutaneous Administration
Equipment
Needleless devices
Devices are designed with a sheath or guard that covers the needle after it is withdrawn from the skin.
Intravenous catheters have been designed with blunt-edged cannulas, valves, or needle guards to minimize injuries.
IV tubing with recessed and shielded needle connectors has been designed, further reducing needlesticks.

68. Percutaneous Administration
Intramuscular Injections
Involves inserting a needle into the muscle tissue to administer medication
Site selection
Gluteal sites
Vastus lateralis muscle
Rectus femoris muscle
Deltoid muscle
Z-track method
Used to inject medications that are irritating to the tissues

69. Locating IM injection for ventrogluteal site.
Figure 23-15, C
(C, from Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
Locating IM injection for ventrogluteal site.

70. Giving IM injection in vastus lateralis site on adult.
Figure 23-16, C
(C, from Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
Giving IM injection in vastus lateralis site on adult.

71. Rectus femoris muscle. A, Child/infant. B, Adult.
Figure 23-17
(From Clayton, B.D., Stock, Y.N. [2004]. Basic pharmacology for nurses. [13th ed.]. St. Louis: Mosby.)
Rectus femoris muscle. A, Child/infant. B, Adult.

72. Giving IM injection in deltoid site.
Figure 23-18, C
(C, from Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
Giving IM injection in deltoid site.

73. Figure 23-19
(From Potter, P.A., Perry, A.G. [2005]. Fundamentals of nursing. [6th ed.]. St. Louis: Mosby.)
A, Z-track method. B, Using an air lock. C, Administering IM injection by airlock technique.

74. Percutaneous Administration
Intradermal Injections
Introduction of a hypodermic needle into the dermis for the purpose of instilling a substance such as a serum, vaccine, or skin test agent
Not aspirated
Small volumes (0.1 mL) injected to form a small bubblelike wheal just under the skin
Used for allergy sensitivity tests, TB screening, and local anesthetics
A tuberculin syringe used with a 25-gauge, 3/8- to 5/8-inch needle

75. Figure 23-20
(From Potter, P.A., Perry, A.G. [2005]. Fundamentals of nursing. [6th ed.]. St. Louis: Mosby.)
Angles of insertion for intramuscular (90°), subcutaneous (45°), and intradermal (15°).

76. Percutaneous Administration
Subcutaneous Injections
Injections made into the loose connective tissue between the dermis and the muscle layer
Drug absorption slower than with IM injections
Given at a 45-degree angle if the patient is thin or at a 90-degree angle if the patient has ample subcutaneous tissue
Usual needle length is 1/2 to 5/8 inch and 25 gauge
Used to administer insulin and heparin

77. Figure 23-21
(From Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and clinical skills. [3rd ed.]. St. Louis: Mosby.)
Subcutaneous injection. Angle and needle length depend on the thickness of skinfold.

78. Percutaneous Administration
Intravenous Therapy
Provide fluid and electrolyte maintenance, restoration, and replacement
Administer medication and nutritional feedings
Administer blood and blood products
Administer chemotherapy to cancer patients
Administer patient-controlled analgesics
Keep a vein open for quick access

79. Percutaneous Administration
Methods of Intravenous Administration
IV push
Intermittent venous access device
Intermittent infusion (or piggyback)
Continuous infusion
Electronic pumps and controllers
Patient-controlled analgesia
Volumetric chambers

80. Figure 23-23 PCA infusion pump.
(From Potter, P.A., Perry, A.G. [2005]. Fundamentals of nursing. [6th ed.]. St. Louis: Mosby.)
PCA infusion pump.

81. Figure 23-24
Volumetric chamber.

82. Percutaneous Administration
Nursing Responsibility
The nurse must ensure that fluid of the ordered type and amount is started and that the fluid is regulated to infuse over the period ordered.
To find the drops per minute (the drip rate), you must know which type of IV tubing will be used with the infusion and obtain the drip factor for the tubing to be used.

83. Percutaneous Administration
Nursing Responsibility (continued)
Monitor intravenous therapy
Check the infusion and the IV needle site at least every hour.
Flow of fluid
IV site: erythema, wetness, and edema
Phlebitis: inflamed vein
Infiltration: fluid passes into the tissues
Assess for chills, fever, headache, nausea, vomiting, anxiousness, and dyspnea.

84. Percutaneous Administration
Nursing Responsibility (continued)
Assess for anaphylactic shock
Respiratory distress
Skin reactions
Signs of circulatory collapse
GI signs and symptoms
Change in mental status
Requires immediate intervention.

85. Nursing Process Nursing Diagnoses Anxiety Health-seeking behaviors
Injury, risk for
Knowledge deficient
Mobility, impaired
Noncompliance: drug regimen
Sensory/perception, disturbed