Drug Math For Nurses

Dimensional Analysis for Meds Junior Level I Summer 2011

Objectives

• At the conclusion of this presentation, students will: • • • Have a general understanding of basic dimensional analysis calculations for nursing drug math Verbalize basic medical terms for drug math calculations Identify key points to review and understand before taking 1 st Drug Math Exam at UAMS College of Nursing

Resources

• LRC [5 th floor of library—Ed II) – Computer Assisted Instruction (CAI) programs available in the LRC during LRC hours • www.atitesting.com

Made Easy - My E Learning - Tutorials - Meds

UAMS College of Nursing Drug Math Examination Policy

• • • • Basics Students are required to take the drug math exam prior to each course with a clinical component Students must score a minimum of 90% to pass the exam 3 opportunities to pass – 1 st two (2) attempts are computerized and proctored in the LRC (5 th floor of Library) during normal business hours – If you do not score 90% or above on Exam 2, you must remediate with the Drug Math Coordinator prior to taking exam 3 (Notify the Drug Math Coordinator immediately after failing exam 2 to arrange remediation; [email protected]) – 3 rd attempt, if necessary, is arranged with the appropriate Drug Math Coordinator Practice Exams may be taken at home or in the LRC during normal hours

Metric Conversions

• You must be able to read the problem – Know the terminology and abbreviations used

• • • • • • • • • • •

Metric & International System (SI) Terms

L = liter mL = milliliter cc = cubic centimeter tsp = teaspoon kg = kilogram g = gram mg = milligram mcg = microgram cm = centimeter mEq = milliequivalent gtt = drop • PO = by mouth

Basic Conversions

• • • • • • 1 mL = 1 cc 1 ounce = 30 mL or 30 cc 1 tablespoon = 15 mL or 15 cc 1 teaspoon (tsp) = 5 mL or 5 cc 3 teaspoons (tsp) = 1 tablespoon 1 liter (L) = 1000 mL or 1000 cc

Basic Conversions

• 1 kilogram (kg) = 2.2 pounds

• • • • • • •

Medical Terms for Medication Administration Times

Q D = Every day (once per day) BID = Twice daily TID = Three times per day QID = Four times per day Q HS = At bedtime (once per day) ac = before meals pc = after meals

Relative Value of Decimals

• Values on the left side of the decimal are increasing in value 100 is larger than 10.00

• Values on the right side of the decimal are decreasing in value 0.1 is larger than 0.01

Relative Value of Decimals

1 2 3 4 . 5 6 7 8

Thousands Hundreds Tens Ten Thousandths Hundredths Thousandths Tenths Ones

UAMS Rounding Rules

ml or cc: If the answer is < 1cc (or ml) then round to the nearest 100th.

Ex: 0.376 = 0.38 cc (or ml) If the answer is > 1cc (or ml) then round to the nearest 10th.

Ex: 1.57 = 1.6 cc (or ml) Tablets: Tablets, as a rule, can only be given whole or broken in half. Round to the nearest half (0.5) Ex: 1.45 = 1.5 tablets 1.2 = 1 tablet

Round at the end of the problem, when you get to the answer (exception is when you’re converting pounds to kilograms (kg)) then you should round to the nearest tenth as soon as you convert, then complete the problem (2.345 = 2.4)

UAMS Rounding Rules

Rounding Rules Basic Rounding: If the number is



5 then round up. Ex: 1.57 = 1.6 1.45 = 1.5 0.686 = 0.69

If the number is < 5 then round down. Ex: 0.543 = 0.54

Remember: Round at the end of the problem.

The exception to this rule is when you are converting pounds to Kgs. Always convert and round to the nearest 10th and then complete the problem.

Converting pounds and kilograms: Round to the nearest 10th.

Ex: 120 pounds = 54.54 or 54.5 Kg

UAMS Rounding Rules

• Basically it means, when you’re working a problem, don’t forget to round your answer at the end (when you get your answer)

The computer is very specific and will count you wrong if you round wrong!!

• • • • 0.345 mL = 0.35 mL (answer is < 1 mL) 1.345 mL = 1.4 mL (answer is > 1 mL) 0.99 mL = 0.99 mL (answer is < 1 mL) 0.995 mL = 1 mL (answer is 1 mL or greater)

• Fractions

Basic Math Review

1 --- 4 (numerator) (denominator)

Convert Fraction to Decimal

1 ____ --- = 4 ) 1 4 0.25

= 4 ) 1.00

8 20 20 0

Convert Fraction to Decimal

1 --- = 3 0.3333

3 ) 1.0000

9 10 9 10 9 10 9 10 infinite

Convert Pounds to Kilograms (kg)

• You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______

Convert Pounds to Kilograms (kg)

• You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______ • We know 1 kg = 2.2 pounds

Convert Pounds to Kilograms (kg)

• You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? __

33.2

__ • We know 1 kg = 2.2 pounds • 73 divided by 2.2 = 33.181818 = 33.2 kg round to nearest tenth

Convert Pounds to Kilograms (kg)

Hints • When you convert pounds (larger number) to kilograms (smaller number) your answer will always be smaller – 100 pounds (divided by) 2.2 kg/pound = 45.5 kg • When you convert kilograms (smaller number) to pounds you need to multiply; your answer will always be larger – 10 kg X 2.2 pounds/kg = 22 pounds

Reading Drug Labels

• • • • • • Drug name will be available – Generic – Trade Container size Concentration (unit of measure) Lot number Expiration date Additional Information – Manufacturer – Safety Precautions (but not always)

Reading Drug Labels

• Find the concentration (unit of measure) of the drug – How many mg is in each tablet?

– How many mg is in how many mL of the solution?

– Example • • • • The drug is supplied as 750 mg per 5 mL The available dosage strength is 1 gram in 3.5 mL Pharmacy sends 325 mg tablets The drug available is 500 mg per tablet

Reading Drug Labels

• Sometimes, you may be confused by a question that gives you “extra” information, like telling you how large the container is – Example • The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon • What does this mean???

Reading Drug Labels

• The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon • What does this mean?

– It means you have a bottle that contains 500 mL of Drug A – Each teaspoon (5 mL) contains 30 mg of Drug A – So, the entire bottle contains 3000 mg of Drug A • 500 mL (divide by) 5 mL = 100 X 30 mg = 3000 mg

Reading Drug Labels

• For dosage calculation, you need to be able to find the concentration (unit of measure) even when more information is given than needed – Take the same example • The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon • The concentration (unit of measure) is calculate how many mL to give

30 mg per teaspoon

; the 500 mL is “extra” information that you don’t need in order to – Remember, 1 tsp = 5 mL, so you have

30 mg/5 mL

Dimensional Analysis

Steps • Find the unit of measure being calculated and write it, then put an equal = sign – This guides you so you know where to put each piece of information; Very important step • Example mL = tab =

Dimensional Analysis

• 2 nd step Find what you have on hand [the concentration of drug (unit of measure)] – Example • • • • • 100 mg per 5 mL 0.125 mg per 3.5 mL 500 mg per tablet 1 gram / 10 mL 2 grams / 1 ounce

Dimensional Analysis

• • 2 nd step continued This is placed in the first spot right of the equal sign as a ratio (clinical ratio) The numerator must match the unit of measure being calculated – Example

numerator

5 mL mL = -------- 100 mg

denominator

Dimensional Analysis

3 rd step • The unit of measure in each denominator must be matched in the successive numerator entered – Example • If the doctor orders 50 mg of Drug A (previous slide). The concentration was 100 mg/5 mL

successive numerator numerator

5 mL 50 mg mL = --------- X ---------- 100 mg

denominator

Dimensional Analysis

• • Final Step Cancel out common denominator & numerator Cancel out common terms (mg, gram & so on) – Example 5 mL mL = ---------- X 100 mg 2 1 50 mg -----------

Dimensional Analysis

• Now, do the math to get your answer – Remember your rounding rules 5 mL 1 50 mg 5 mL = ---------- X --------- = ---- = 2.5 mL 100 mg 2 2

Dimensional Analysis

• Prepare a 500 mg dose of Vancomycin from an available solution of 1000 mg per 3 mL.

3 mL 500 mg mL = ------------ X ---------- = 1000 mg

Dimensional Analysis

1

3 mL 500 mg mL = ------------ X ---------- = 1000 mg

2

1 st reduce the common numerator & denominator

Dimensional Analysis

1

3 mL 500 mg mL = ------------ X ---------- = 1000 mg

2

next, cancel out “like terms”

Dimensional Analysis

1

3 mL 500 mg 3 mL = ------------ X ---------- = ---- = 1.5 mL 1000 mg 2

2

Last, do the math!

Dimensional Analysis

• If you need to do a metric conversion, it is added to the equation in the middle – Example 1 tab 500 mg tab = --------- X ---------- 1 gram As you can see, we can’t cancel out any “like terms”

Dimensional Analysis

• Metric Conversion 1 tab 500 mg tab = --------- X ---------- 1 gram

1 gram 1000 mg

• We know that 1 gram = 1000 mg, so we can put this into the equation (in the middle)

Dimensional Analysis

• Metric Conversion 1 tab 1 gram 500 mg tab = --------- X ----------- X ----------- = 1 gram 1000 mg

Dimensional Analysis

• Metric Conversion 1 tab

1

1 gram 500 mg tab = --------- X ----------- X ----------- = 1 gram 1000 mg

2

Now we can cancel out and reduce commons

Dimensional Analysis

• Metric Conversion 1 tab

1

1 gram 500 mg 1 tab = --------- X ----------- X ----------- = --- = 0.5 tab 1 gram 1000 mg 2

2

Last, do the math for your answer!!

Insulin Administration

– Insulin is always ordered in units – Do not abbreviate units as U, it must be spelled out to prevent medication errors – Insulin is supplied in U-100 doses • 1 unit = 0.01 mL • • 10 units = 0.1 mL or 0.10 mL 100 units = 1 mL – You must use specially marked syringes [they are usually orange color] to give insulin (they are called insulin syringes); do not draw up insulin in a standard syringe