Calculations- NAPLEX Exam Questions
With Worked-out Solutions Graded A+
Measuring Drugs - CORRECT ANSWER-Drugs can be measured in different ways:
- As weights, using grams (g), milligrams (mg), micrograms (mcg), and nanograms (ng).
- A liquid volumes, using liters (L), or milliliters (mL)
- As percentage strengths (grams in 100mL, grams in 100g, or mL in 100mL)
- As concentrations of a given amount of a drug in a given volume of liquid (mcg/mL,
mg/L). Very small amounts of measured in ng/mL. BUN and SCr are measured in
mg/dL (1 liter is 10 dL, so 1 dL is 100mL or 0.1 Liters).
- As concentrations using milliequivalents (mEq) per Liter (mEq/L).
Common Liquid Volume Conversions - CORRECT ANSWER-- tsp (t) = 5 mL
- tbsp (T) = 15 mL
- 1 fl oz = ~30 mL, 29.57 mL (actual)
- 1 cup = 8 fl oz, ~240 mL, 236.56 mL (actual)
- 1 pint = 16 fl oz, ~480 mL, 473 mL (actual)
- 1 quart = 2 pints, 32 fl oz, ~960 mL, 946 mL (actual)
- 1 gallon = 4 quarts, 8 pints, 128 fl oz, ~3,840 mL, 3,785 mL (actual)
Common Solid Weight, Height, and Other Conversions - CORRECT ANSWER-Weight
- 1 kg = 2.2 pounds
- 1 oz = 28.4 grams
- 1 pound = 454 grams
- 1 grain (gr) = ~65 mg, 64.8 mg (actual)
Height
- 1 inch (in) = 2.54 centimeters (cm)
,- 1 meter (m) = 100 cm
Other: Milliequivalents and Millimoles
- K, Na, and other MONOvalent ions: 1 mEq = 1 mmol
- Ca, Mg, and other DIvalent ions: 1 mEq = 0.5 mmol
If mEq are provided for potassium, and the answer requires mmols, use the same
numbers. When mEq is provided for calcium, and the answer requires mmols, use half
the mEq number.
Percentage Strength - CORRECT ANSWER-Drug concentrations can be expressed in
many ways, but there are a ratio of the amount of an ingredient to the total amount of
product.
A percent is the number of parts in *100*. Percents are often written as decimals or
fractions, such as 0.25 or 25/100. The type of percentage concentrations are as follows:
1. Percent weight-in-volume (% w/v), which is expressed in *g/100mL*. This is a solid
mixed into a liquid. This % concentration also applies to common IV fluids.
2. Percent volume-in-volume (% v/v), which is expressed as *mL/100mL*. This is a
liquid mixed in a liquid.
3. Percent weight-in-weight (% w/w), which is expressed as *g/100g*. This is a solid
mixed into a solid.
Ratio Strength - CORRECT ANSWER-The concentration of a weak solution can be
expressed as a ratio strength. It is denoted as *one unit of solute* contained *in the total
amount* of the solution or mixture (e.g. 1:500). Ratio strength is another way of
presenting a percentage strength. This makes sense because percentages are ratios of
parts per 100.
However, in clinical practice, ratio strengths have been associated with medication
errors. The FDA now requires removal of ratio strengths from the labeling of injectable
,drug products with only 1 active ingredient (e.g. epinephrine, isoproterenol). Ratio
strength is still commonly used in compounding.
Shortcut for Ratio Strength Calculations - CORRECT ANSWER-Most multi-step
calculations will require converting ratio strength to percentage strength. If a ratio
strength is presented in a problem, convert it to a percentage strength and convert it
back if needed.
1. Ratio strength to percentage strength: 100/ratio strength = % strength
2. Percentage strength to ratio strength: 100/% strength = ratio strength
Parts Per Million/Billion and Shortcuts - CORRECT ANSWER-PPM and PPB are used
to express the strength of very dilute solutions. They are defined as the number of
*parts of the drug per 1 million (or 1 billion) parts of the whole*. The same designations
are used as for percentage strength (% w/w, %w/v, % v/v).
The shortcuts for PPM and PPB and converting to percentage strength and back are as
follows:
- If PPM to % strength: Move the decimal *to the left 4 places*
- If % strength to PPM: Move the decimal *to the right 4 places*
If the question asks to express something in PPB, divide by 1,000,000,000 (9 zeros).
Specific Gravity - CORRECT ANSWER-Specific Gravity is the ratio of the density of a
substance to the density of water. SG can be important for calculating doses of IV
medications, in compounding, and interpreting a urinalysis. *Water has a SG of 1, 1g
water = 1mL water*. Substances with a SG <1 are *lighter* than water and those with a
SG >1 are *heavier* than water.
Essentially, specific gravity is mass of the substance over the volume it takes up, in mL.
So SG is:
- SG = grams of substance/mL of substance
, *SG is essentially equivalent to density in g/mL*. If asked for the density in the problem,
the specific gravity is what they are looking for.
Q1C1 Calculations - CORRECT ANSWER-This formula can be used to change the
strength of the quantity. Q1C1 is used specifically when the problem deals with *two
concentrations*. Be careful, as *the units on each side must match*, and one or more
may need to be changed, such as mg to grams, or vice-versa.
Q1 x C1 = Q2 x C2, where Q1 is the old quantity, C1 is the old concentration, and C2 is
the new concentration and Q2 is the new quantity.
0% and 100% Purity - CORRECT ANSWER-If the prescription calls for an ingredient
that is *pure*, the concentration is 100%.
A diluent, such as petrolatum, lanolin, alcohol, ointment base, inert base, lactose, or
Aquafor, does not contain any drug, so the concentration of the diluent is 0%.
Osmolarity - CORRECT ANSWER-The total number of particles in a given solution is
directly proportional to its osmotic pressure. The particles are usually measured in
milliosmoles. Osmolarity is the measure of total number of particles, or solutes, per liter
of solution, defined as osmoles/liter (Osmol/L), or more commonly milliosmoles/liter
(mOsmol/L).
Solutions can either be *ionic*, such as NaCl, which dissociates into two solutions in
solution Na and Cl, or *non-ionic*, which does NOT dissociate (such as glucose or
urea).
Since the volume of water changes according to temperature, the term osmolality is
used in clinical practice (mOsmol/kg). It is independent of temperature. When solute
concentrations are very low, osmolarity and osmolality are similar.
Milliosmole calculation problems differ from osmolarity calculations in that *osmolarity
will always need to be normalized to a volume of 1 liter*. When doing these calculations,
the dissociation particles need to be known for the exam.
