Pharmacy Calculations & Sig Codes

1. A patient is prescribed metformin 500 mg, Sig: 1 tablet by mouth twice daily, dispense #180. How many days will this supply last?

The patient takes 2 tablets per day (1 tablet BID = 2x/day). 180 tablets divided by 2 tablets/day = 90 days. 60 days would result from taking 3 tablets/day, 45 days from taking 4 tablets/day, and 180 days would only be correct if the patient took just 1 tablet daily, not BID.

2. A prescription reads: Amoxicillin 500 mg PO TID x 7 days. The pharmacy stocks amoxicillin oral suspension 250 mg/5 mL. How many mL should be dispensed to cover the full course?

Each 500 mg dose requires 10 mL (250 mg/5 mL means 500 mg needs twice the volume, or 10 mL). Three doses per day = 30 mL/day; over 7 days that is 30 x 7 = 210 mL. 150 mL and 175 mL underestimate the daily volume or day count, and 300 mL would represent 10 days of therapy, not 7.

3. A physician orders 750 mg of a medication available as an oral solution labeled 250 mg/5 mL. How many mL should be measured for one dose?

750 mg is 3 times the 250 mg in the labeled concentration, so 3 x 5 mL = 15 mL. 10 mL would only deliver 500 mg, 12.5 mL would deliver 625 mg, and 20 mL would deliver 1000 mg, none of which match the ordered 750 mg dose.

4. How many milliliters are in 2 teaspoons?

One household teaspoon is standardized as 5 mL in pharmacy practice, so 2 teaspoons = 10 mL. 5 mL is only 1 teaspoon, 15 mL equals 1 tablespoon (3 teaspoons), and 20 mL would be 4 teaspoons.

5. Sig: ii tab PO qid. If #120 tablets are dispensed, what is the days supply?

qid means 4 times daily, and 'ii' means 2 tablets per dose, so the patient takes 2 x 4 = 8 tablets per day. 120 tablets divided by 8 tablets/day = 15 days. 30 days would assume only 4 tablets/day, 8 days confuses the daily tablet count with the days supply, and 60 days would assume 2 tablets/day.

6. A patient is dispensed one 10 mL vial of U-100 insulin (1000 units total) and is instructed to inject 24 units subcutaneously once daily at bedtime. What is the approximate days supply?

U-100 insulin contains 100 units/mL, so a 10 mL vial holds 1000 units. Dividing 1000 units by 24 units/day gives 41.67, which is rounded down to 41 full days since a partial day's dose isn't a complete day of therapy. 42 or 45 days overstate the supply, and 40 days underestimates it.

7. A powder for oral suspension is reconstituted to a final volume of 150 mL and contains 250 mg of drug per 5 mL dose. What is the concentration of the reconstituted suspension in mg/mL?

Concentration is found by dividing the mg amount by the mL it's dissolved in: 250 mg / 5 mL = 50 mg/mL. This ratio holds regardless of the total 150 mL volume, since concentration is uniform throughout. 25 mg/mL and 12.5 mg/mL are half and a quarter of the correct value, and 45 mg/mL does not match the given ratio.

8. How many mL of 50% dextrose injection (D50W) are needed to prepare 500 mL of a 10% dextrose solution, using the dilution formula C1V1 = C2V2?

Using C1V1 = C2V2: (50%)(V1) = (10%)(500 mL), so V1 = (10 x 500)/50 = 100 mL of D50W, with sterile water or another diluent added to bring the total to 500 mL. 50 mL and 250 mL don't satisfy the equation, and 500 mL would mean no dilution occurred at all.

9. An IV order calls for 1000 mL of normal saline to infuse over 8 hours using tubing with a drop factor of 20 gtt/mL. What is the correct flow rate in gtt/min?

First find the hourly rate: 1000 mL / 8 hr = 125 mL/hr. Convert to mL/min: 125/60 = 2.08 mL/min. Multiply by the drop factor: 2.08 x 20 = about 41.7, rounded to 42 gtt/min. 125 gtt/min mistakenly uses the hourly mL rate directly, 21 gtt/min is half the correct rate, and 63 gtt/min does not correspond to this calculation.

10. A pediatric patient weighs 22 lb. The physician orders a medication dosed at 15 mg/kg/day, divided into two equal doses. What is the total daily dose in mg?

First convert weight to kg: 22 lb / 2.2 = 10 kg. Total daily dose = 15 mg/kg x 10 kg = 150 mg/day (split into 75 mg per dose twice daily). 75 mg is only the per-dose amount, not the total daily dose; 220 mg and 100 mg do not result from this calculation.

1. A physician's order specifies 750 mcg. How many mg is this equivalent to?

Since 1 mg = 1000 mcg, 750 mcg / 1000 = 0.75 mg. 7.5 mg and 75 mg are off by factors of 10 and 100 respectively, and 0.075 mg is 10 times too small.

2. A dose is ordered as 2.5 grains. Using the standard pharmacy conversion of 1 grain = 65 mg, how many mg is this dose?

2.5 grains x 65 mg/grain = 162.5 mg. 65 mg is the value for only 1 grain, 130 mg would be 2 grains, and 150 mg does not correspond to this conversion factor.

3. A prescription is written as: 1 tablet PO every morning and 1 tablet PO every evening, for 90 days. How many tablets should be dispensed?

Taking 1 tablet in the morning and 1 in the evening equals 2 tablets per day, the same as BID dosing. 2 tablets/day x 90 days = 180 tablets. 90 tablets would only supply 45 days at this rate, 360 tablets would be double what's needed, and 45 tablets is far too few.

4. How many grams of dextrose are contained in 500 mL of D5W (5% dextrose in water)?

A 5% w/v solution contains 5 g per 100 mL. For 500 mL: 5 g/100 mL x 500 mL = 25 g. 12.5 g would apply to 250 mL, 50 g would apply to 1000 mL, and 5 g is only the amount per 100 mL, not the full 500 mL.

5. A 1:200 ratio strength solution is equivalent to what percentage strength?

A 1:200 ratio means 1 g (or 1 part) per 200 mL (or parts). Converting to percentage: 1/200 = 0.005, and 0.005 x 100 = 0.5%. 5% and 2% are too concentrated for this ratio, and 0.05% is 10 times too dilute.

6. A patient is prescribed one eye drop in each eye twice daily. The dispensed bottle contains 5 mL, and standard ophthalmic droppers deliver approximately 20 drops/mL. What is the approximate days supply?

The 5 mL bottle contains about 5 x 20 = 100 total drops. The patient uses 1 drop per eye, twice daily: 1 x 2 eyes x 2 times/day = 4 drops/day. 100 drops / 4 drops per day = 25 days. 10 and 50 days miscalculate the daily drop usage, and 100 days ignores that both eyes are being treated.

7. Sig: 1 tablespoon PO TID x 10 days. How many total mL should be dispensed?

One tablespoon = 15 mL. TID means 3 times daily, so 15 mL x 3 = 45 mL/day. Over 10 days: 45 mL x 10 = 450 mL. 150 mL only covers about 3 days, 300 mL covers about 6.7 days, and 600 mL overestimates the amount needed.

8. An IV admixture is prepared by adding 400 mg of a drug to a 250 mL bag of D5W. What is the resulting concentration in mcg/mL?

First convert mg to mcg: 400 mg x 1000 = 400,000 mcg. Divide by the total volume: 400,000 mcg / 250 mL = 1600 mcg/mL. 400 mcg/mL and 160 mcg/mL are far too low, and 4000 mcg/mL overstates the concentration.

9. A patient weighs 176 lb. What is this weight in kilograms?

To convert pounds to kilograms, divide by 2.2: 176 / 2.2 = 80 kg. 176 kg fails to convert units at all, 88 kg divides by only 2, and 40 kg divides by 4.4, none of which use the correct conversion factor.

10. An IV bag containing 1000 mL is infusing at a rate of 50 mL/hr. How many hours will the bag last?

Total volume divided by hourly rate gives infusion time: 1000 mL / 50 mL/hr = 20 hours. 10 hours would require a rate of 100 mL/hr, 50 hours would require only 20 mL/hr, and 8 hours does not match this rate.

1. A tablet is labeled as containing 0.125 mg of a drug. How many mcg is this?

To convert mg to mcg, multiply by 1000: 0.125 mg x 1000 = 125 mcg. 12.5 mcg is 10 times too small, 1250 mcg is 10 times too large, and 0.0125 mcg moves the decimal in the wrong direction entirely.

2. A patient injects 10 units of rapid-acting insulin before each of 3 meals, plus 20 units of long-acting insulin at bedtime. A vial contains 1000 units (10 mL of U-100 insulin). What is the days supply?

Total daily units = (10 units x 3 meals) + 20 units = 30 + 20 = 50 units/day. 1000 units / 50 units/day = 20 days. 10 days would assume 100 units/day, 50 days would assume only 20 units/day, and 33 days does not match this calculation.

3. A compounding order requires 240 mL of a 2% w/v solution. How many grams of active ingredient are needed?

A 2% w/v solution means 2 g per 100 mL. For 240 mL: (2 g/100 mL) x 240 mL = 4.8 g. 2.4 g is half the correct amount, 24 g is 5 times too much, and 48 g is 10 times too much.

4. Equal parts (by weight) of a 10% hydrocortisone cream and a 2% hydrocortisone cream are mixed together. What is the approximate resulting percentage strength?

When equal parts of two strengths are combined, the resulting strength is approximately the simple average: (10% + 2%) / 2 = 6%. 2% and 10% are the strengths of the individual starting creams, not the mixture, and 12% would result from adding rather than averaging the strengths.

5. What does the Sig abbreviation 'q.h.s.' instruct the patient to do?

q.h.s. stands for 'quaque hora somni,' Latin for 'every night at bedtime.' 'Every hour' corresponds to q.h., 'before meals' corresponds to a.c., and 'as needed' corresponds to p.r.n., none of which are the same as q.h.s.

6. What number does the Roman numeral 'XL' represent on a prescription?

In Roman numerals, X = 10 and L = 50; when a smaller value precedes a larger one, it is subtracted, so XL = 50 - 10 = 40. Thirty would be written XXX, fifty is simply L, and sixty would be LX.

7. What does the abbreviation 'NPO' mean on a patient's chart or order?

NPO comes from the Latin 'nil per os,' meaning 'nothing by mouth,' commonly used to instruct that a patient should not eat or drink, such as before surgery. 'Take with food' and 'before meals' relate to oral administration timing, and 'apply topically' refers to a completely different route of administration.

8. In prescription Sig codes, what does the abbreviation 'gtt' stand for?

'gtt' is derived from the Latin 'gutta,' meaning drop, and is commonly used for liquid medications like eye or ear drops (e.g., 'gtt ii' means 2 drops). It is unrelated to weight (gram), volume containers (gallon), or feeding routes (gastric tube).