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Lesson 1: Math Foundations for Pharmacy
Master the unit conversions every pharmacy technician uses daily — weight, volume, and rounding rules that underpin every calculation in the course.
The unit chain — memorize this one line
mcg ↔ ×1,000 ↔ mg ↔ ×1,000 ↔ g ↔ ×1,000 ↔ kg
Going to a smaller unit (right to left): multiply. Going to a larger unit (left to right): divide. One rule, infinite applications.
Weight conversions — g/mg/mcg
g → mg: × 1,000 | mg → g: ÷ 1,000
mg → mcg: × 1,000 | mcg → mg: ÷ 1,000
g → mcg: × 1,000,000
Examples: 0.5 g = 500 mg | 75 mcg = 0.075 mg
Levothyroxine: always mcg on label
Vancomycin: ordered in g, dispensed in mg
mg → mcg: × 1,000 | mcg → mg: ÷ 1,000
g → mcg: × 1,000,000
Examples: 0.5 g = 500 mg | 75 mcg = 0.075 mg
Levothyroxine: always mcg on label
Vancomycin: ordered in g, dispensed in mg
Weight conversions — lb & kg
lb → kg: divide by 2.2
kg → lb: multiply by 2.2
44 lb = 20 kg | 154 lb = 70 kg
All weight-based doses start with lb → kg
Every pediatric problem: Step 1 = convert weight
kg → lb: multiply by 2.2
44 lb = 20 kg | 154 lb = 70 kg
All weight-based doses start with lb → kg
Every pediatric problem: Step 1 = convert weight
Volume conversions
1 tsp = 5 mL | 1 tbsp = 15 mL
1 fl oz = 30 mL | 1 cup = 240 mL
Parents often use a kitchen teaspoon — counsel them to use an oral syringe
tbsp = tablespoon = 3 tsp = 15 mL
1 fl oz = 30 mL | 1 cup = 240 mL
Parents often use a kitchen teaspoon — counsel them to use an oral syringe
tbsp = tablespoon = 3 tsp = 15 mL
Rounding rules for pharmacy
Liquids: round to nearest 0.1 mL
Tablets: round to whole number (round up if unscorable)
Weight (kg): round to 1 decimal place
Day supply: always round DOWN
Hospital doses: follow protocol (e.g., nearest 250 mg)
Tablets: round to whole number (round up if unscorable)
Weight (kg): round to 1 decimal place
Day supply: always round DOWN
Hospital doses: follow protocol (e.g., nearest 250 mg)
★ PTCB exam tip: Unit conversions appear across all 4 PTCB domains. Every dosage calculation question on the exam starts with a conversion. If your conversion is wrong, the entire answer is wrong — even if your math is perfect. Prioritize: g↔mg, mg↔mcg, and lb↔kg.
Most common mistakes: (1) Multiplying when you should divide — going from mcg to mg is divide, not multiply. (2) Forgetting the lb→kg step before a weight-based dose. (3) Using mcg as if it were mg — fentanyl 100 mcg is only 0.1 mg, not 100 mg. (4) Rounding day supply UP instead of DOWN.
Six worked examples progressing from basic conversions to real pharmacy scenarios. Work through each step before reading the solution.
EasyRetail
Levothyroxine Rx: 0.075 mg. Patient asks what this means in mcg (as seen on previous bottle).
Convert 0.075 mg to mcg.
Rule: mg → mcg = multiply by 1,0000.075 mg × 1,000 = 75 mcg
✓ 0.075 mg = 75 mcg — same dose, different unit
EasyRetail
Vancomycin order: 1.5 g IV q12h. Pharmacy system requires entry in mg.
Convert 1.5 g to mg.
Rule: g → mg = multiply by 1,0001.5 g × 1,000 = 1,500 mg
✓ Enter 1,500 mg in the pharmacy system
MediumPatient scenario
Child weighs 33 lb. Amoxicillin dose: 40 mg/kg/day. What is the daily dose in mg?
Step 1: convert lb to kg. Step 2: calculate dose.
Step 1 — Convert weight:33 lb ÷ 2.2 = 15 kg
Step 2 — Calculate dose:15 kg × 40 mg/kg = 600 mg/day
✓ 600 mg/day (usually divided TID = 200 mg per dose)
MediumRetail
Rx: take 2 tsp of amoxicillin suspension three times daily. How many mL per day?
Convert tsp to mL, then multiply by frequency.
Step 1 — mL per dose:2 tsp × 5 mL/tsp = 10 mL per dose
Step 2 — mL per day:10 mL × 3 (TID) = 30 mL/day
✓ 30 mL per day total
HardHospital
Fentanyl 100 mcg. Anesthesia asks: how many mg is this? (Important for documentation.)
Convert 100 mcg to mg.
Rule: mcg → mg = divide by 1,000100 mcg ÷ 1,000 = 0.1 mg
✓ 100 mcg = 0.1 mg — fentanyl is potent; the mg amount is tiny
Why this matters: Confusing mcg and mg for fentanyl could be fatal. 100 mg fentanyl (if that were a dose) = 100,000 mcg — a massive overdose. Always check units on high-alert medications.
HardHospital
Vancomycin calculated at 1,237.5 mg. Hospital rounds to nearest 250 mg. What dose should be prepared?
Apply hospital rounding protocol.
Options near 1,237.5:1,000 mg (237.5 away) vs 1,250 mg (12.5 away)
Choose nearest:1,250 mg is only 12.5 mg away = 1,250 mg
✓ Round to 1,250 mg — always follow your facility's rounding protocol
Difficulty
Context
Easy
Retail
Weight (g/mg/mcg)
A pharmacist labels metronidazole as 0.5 g.
Convert 0.5 g to mg.
Answer: 500 mg
Move decimal 3 places right: 0.5 g × 1,000 = 500 mg. Larger unit → smaller unit = multiply.
Move decimal 3 places right: 0.5 g × 1,000 = 500 mg. Larger unit → smaller unit = multiply.
Easy
Retail
Weight (g/mg/mcg)
Prescription reads: levothyroxine 0.075 mg. Patient asks what this is in mcg.
Convert 0.075 mg to mcg.
Answer: 75 mcg
Move decimal 3 places right: 0.075 mg × 1,000 = 75 mcg. Levothyroxine labels always list mcg.
Move decimal 3 places right: 0.075 mg × 1,000 = 75 mcg. Levothyroxine labels always list mcg.
Easy
Retail
Weight (g/mg/mcg)
Hospital vial label reads: amoxicillin 1 g.
Convert 1 g to mg.
Answer: 1,000 mg
1 g × 1,000 = 1,000 mg. Standard conversion: 1 g = 1,000 mg.
1 g × 1,000 = 1,000 mg. Standard conversion: 1 g = 1,000 mg.
Easy
Patient scenario
Weight (g/mg/mcg)
Patient asks: "Is my 250 mcg digoxin tablet the same as 0.25 mg?"
Convert 250 mcg to mg to answer the patient.
Answer: 0.25 mg
250 mcg ÷ 1,000 = 0.25 mg. Yes — they are identical. This is a common patient counseling scenario.
250 mcg ÷ 1,000 = 0.25 mg. Yes — they are identical. This is a common patient counseling scenario.
Easy
Retail
Weight (g/mg/mcg)
Folic acid 1,000 mcg tablet — is this the same as 1 mg?
Convert 1,000 mcg to mg.
Answer: 1 mg
1,000 mcg ÷ 1,000 = 1 mg. Folic acid 1 mg = 1,000 mcg. Correct — same dose.
1,000 mcg ÷ 1,000 = 1 mg. Folic acid 1 mg = 1,000 mcg. Correct — same dose.
Easy
Retail
Weight (g/mg/mcg)
Hospital pharmacy compound: prednisone 0.5 g bulk powder.
Convert 0.5 g to mcg.
Answer: 500,000 mcg
0.5 g → mg: 0.5 × 1,000 = 500 mg. 500 mg → mcg: 500 × 1,000 = 500,000 mcg. Two-step: g → mg → mcg.
0.5 g → mg: 0.5 × 1,000 = 500 mg. 500 mg → mcg: 500 × 1,000 = 500,000 mcg. Two-step: g → mg → mcg.
Med
Patient scenario
Weight (g/mg/mcg)
A Rx is written for lisinopril 0.02 g. The label must read in mg.
Convert 0.02 g to mg.
Answer: 20 mg
0.02 g × 1,000 = 20 mg. Lisinopril 20 mg is a standard dose. The Rx was written in an unusual unit.
0.02 g × 1,000 = 20 mg. Lisinopril 20 mg is a standard dose. The Rx was written in an unusual unit.
Med
Retail
Weight (g/mg/mcg)
New Rx: atorvastatin 0.04 g. Computer system requires entry in mg.
Convert 0.04 g to mg.
Answer: 40 mg
0.04 g × 1,000 = 40 mg. Atorvastatin 40 mg is a common maintenance dose.
0.04 g × 1,000 = 40 mg. Atorvastatin 40 mg is a common maintenance dose.
Med
Hospital
Weight (g/mg/mcg)
Physician orders vancomycin 1.5 g IV q12h. The pharmacy tracks doses in mg.
How many mg is 1.5 g?
Answer: 1,500 mg
1.5 g × 1,000 = 1,500 mg. Vancomycin IV doses are commonly ordered in grams by physicians but entered in mg in pharmacy systems.
1.5 g × 1,000 = 1,500 mg. Vancomycin IV doses are commonly ordered in grams by physicians but entered in mg in pharmacy systems.
Med
Hospital
Weight (g/mg/mcg)
Handwritten order: morphine sulfate 0.01 g IV PRN. Confirm in mg.
Convert 0.01 g to mg.
Answer: 10 mg
0.01 g × 1,000 = 10 mg. Morphine 10 mg IV is a high dose — always verify unit conversions on opioids before dispensing.
0.01 g × 1,000 = 10 mg. Morphine 10 mg IV is a high dose — always verify unit conversions on opioids before dispensing.
Hard
Hospital
Weight (g/mg/mcg)
Fentanyl vial labeled 100 mcg/2 mL. Anesthesia asks the mg equivalent for documentation.
Convert 100 mcg to mg.
Answer: 0.1 mg
100 mcg ÷ 1,000 = 0.1 mg. Fentanyl is measured in mcg due to its extreme potency — the mg equivalent is tiny.
100 mcg ÷ 1,000 = 0.1 mg. Fentanyl is measured in mcg due to its extreme potency — the mg equivalent is tiny.
Hard
Patient scenario
Weight (g/mg/mcg)
Synthroid tablet labeled 0.088 mg. Patient's prior pharmacy labeled it in mcg. Convert for the patient.
Convert 0.088 mg to mcg.
Answer: 88 mcg
0.088 mg × 1,000 = 88 mcg. Levothyroxine is always dispensed in mcg on retail labels — Synthroid 88 mcg is the same as 0.088 mg.
0.088 mg × 1,000 = 88 mcg. Levothyroxine is always dispensed in mcg on retail labels — Synthroid 88 mcg is the same as 0.088 mg.
Easy
Retail
Weight (lb/kg)
Child's weight recorded as 44 lb for weight-based dosing.
Convert 44 lb to kg. (Divide by 2.2)
Answer: 20 kg
44 lb ÷ 2.2 = 20 kg. Always divide lb by 2.2 to convert to kg. This is Step 1 for every pediatric weight-based dose.
44 lb ÷ 2.2 = 20 kg. Always divide lb by 2.2 to convert to kg. This is Step 1 for every pediatric weight-based dose.
Easy
Hospital
Weight (lb/kg)
ICU chart shows patient weight as 176 lb. Needed in kg for dosing.
Convert 176 lb to kg.
Answer: 80 kg
176 ÷ 2.2 = 80 kg. Standard adult weight used for many hospital weight-based protocols.
176 ÷ 2.2 = 80 kg. Standard adult weight used for many hospital weight-based protocols.
Easy
Retail
Weight (lb/kg)
Toddler weighed at 22 lb at the pediatrician office.
Convert 22 lb to kg.
Answer: 10 kg
22 ÷ 2.2 = 10 kg. 10 kg is a commonly used pediatric weight benchmark (about 22 months old).
22 ÷ 2.2 = 10 kg. 10 kg is a commonly used pediatric weight benchmark (about 22 months old).
Med
Hospital
Weight (lb/kg)
Patient weighs 154 lb. Gentamicin loading dose: 5 mg/kg.
What is the total loading dose in mg?
Answer: 350 mg
Step 1: 154 ÷ 2.2 = 70 kg. Step 2: 70 kg × 5 mg/kg = 350 mg. Always convert lb to kg first, then multiply by the dose.
Step 1: 154 ÷ 2.2 = 70 kg. Step 2: 70 kg × 5 mg/kg = 350 mg. Always convert lb to kg first, then multiply by the dose.
Med
Patient scenario
Weight (lb/kg)
Child weighs 33 lb. Amoxicillin prescribed at 40 mg/kg/day.
What is the total daily dose in mg?
Answer: 600 mg
33 ÷ 2.2 = 15 kg. 15 × 40 = 600 mg/day. Commonly divided TID (200 mg per dose).
33 ÷ 2.2 = 15 kg. 15 × 40 = 600 mg/day. Commonly divided TID (200 mg per dose).
Hard
Hospital
Weight (lb/kg)
Patient weighs 220 lb. Vancomycin 15 mg/kg IV every 12 hours.
What is each individual dose in mg?
Answer: 1,500 mg
220 ÷ 2.2 = 100 kg. 100 × 15 = 1,500 mg per dose. For a 100 kg patient, vancomycin 1.5 g q12h is typical for serious infections.
220 ÷ 2.2 = 100 kg. 100 × 15 = 1,500 mg per dose. For a 100 kg patient, vancomycin 1.5 g q12h is typical for serious infections.
Easy
Retail
Volume (tsp/mL/oz)
Patient told to take 2 tsp of liquid medication.
Convert 2 tsp to mL.
Answer: 10 mL
1 tsp = 5 mL. 2 tsp × 5 = 10 mL. Always check: does the patient have a proper dosing syringe?
1 tsp = 5 mL. 2 tsp × 5 = 10 mL. Always check: does the patient have a proper dosing syringe?
Easy
Retail
Volume (tsp/mL/oz)
Robitussin label says: take 1 tablespoon every 4 hours.
How many mL is 1 tablespoon?
Answer: 15 mL
1 tbsp = 15 mL. 15 mL per dose. 1 tablespoon = 3 teaspoons = 15 mL.
1 tbsp = 15 mL. 15 mL per dose. 1 tablespoon = 3 teaspoons = 15 mL.
Easy
Retail
Volume (tsp/mL/oz)
Rx reads: take 3 tsp by mouth twice daily.
Convert 3 tsp to mL.
Answer: 15 mL
3 tsp × 5 mL/tsp = 15 mL per dose. 15 mL BID = 30 mL per day.
3 tsp × 5 mL/tsp = 15 mL per dose. 15 mL BID = 30 mL per day.
Easy
Patient scenario
Volume (tsp/mL/oz)
Prescription says 10 mL per dose. Parent only has a teaspoon at home.
How many teaspoons is 10 mL?
Answer: 2 tsp
10 mL ÷ 5 mL/tsp = 2 tsp. Counsel parents: a kitchen teaspoon is not accurate. Recommend an oral dosing syringe.
10 mL ÷ 5 mL/tsp = 2 tsp. Counsel parents: a kitchen teaspoon is not accurate. Recommend an oral dosing syringe.
Med
Retail
Volume (tsp/mL/oz)
Antacid dose: 1 fluid ounce per dose.
Convert 1 fl oz to mL. (1 fl oz = 30 mL)
Answer: 30 mL
1 fl oz = 30 mL. Memorize: 1 oz = 30 mL. A 16 oz bottle = 480 mL.
1 fl oz = 30 mL. Memorize: 1 oz = 30 mL. A 16 oz bottle = 480 mL.
Med
Retail
Volume (tsp/mL/oz)
Customer asks how many mL are in a 4 fl oz bottle.
Convert 4 fl oz to mL.
Answer: 120 mL
4 fl oz × 30 mL/oz = 120 mL. Standard small antibiotic bottles are often 100 or 150 mL.
4 fl oz × 30 mL/oz = 120 mL. Standard small antibiotic bottles are often 100 or 150 mL.
Hard
Retail
Volume (tsp/mL/oz)
Sig: take 2 tsp by mouth three times daily.
How many mL per day total?
Answer: 30 mL
2 tsp × 5 = 10 mL per dose. 10 mL × 3 (TID) = 30 mL per day. Used for day supply calculation.
2 tsp × 5 = 10 mL per dose. 10 mL × 3 (TID) = 30 mL per day. Used for day supply calculation.
Hard
Patient scenario
Volume (tsp/mL/oz)
Child needs 200 mg ibuprofen. Available: 100 mg/5 mL suspension.
How many teaspoons should the parent give?
Answer: 2 tsp
Volume needed: 200 mg ÷ (100 mg/5 mL) = 10 mL. Convert: 10 mL ÷ 5 = 2 tsp.
Volume needed: 200 mg ÷ (100 mg/5 mL) = 10 mL. Convert: 10 mL ÷ 5 = 2 tsp.
Easy
Retail
Rounding Rules
Calculated suspension dose: 4.666 mL.
How should you round 4.666 mL for dispensing?
Answer: 4.6 mL
Liquids round to one decimal place. 4.666 → 4.6 mL. Look at the second decimal (6) — but standard practice rounds liquid doses to nearest 0.1 mL, so 4.6 mL.
Liquids round to one decimal place. 4.666 → 4.6 mL. Look at the second decimal (6) — but standard practice rounds liquid doses to nearest 0.1 mL, so 4.6 mL.
Easy
Retail
Rounding Rules
Calculated tablet dose: 2.7 tablets. The tablet cannot be split.
What quantity do you dispense?
Answer: 3 tablets
Unscorable tablets must be whole numbers. Round up to 3 tablets — rounding down would under-dose. This requires physician clarification in practice.
Unscorable tablets must be whole numbers. Round up to 3 tablets — rounding down would under-dose. This requires physician clarification in practice.
Easy
Hospital
Rounding Rules
Digital scale reads 68.18 kg. Hospital protocol uses one decimal place for weight-based dosing.
Round 68.18 kg to one decimal place.
Answer: 68.2 kg
68.18 rounded to one decimal: the second decimal digit is 8 (≥5), so round the first decimal up. 68.18 → 68.2 kg.
68.18 rounded to one decimal: the second decimal digit is 8 (≥5), so round the first decimal up. 68.18 → 68.2 kg.
Med
Retail
Rounding Rules
Pediatric dose calculation yields 7.33 mL.
What is the correct rounded volume to dispense?
Answer: 7.3 mL
7.33 mL rounded to one decimal: look at second decimal (3 < 5) → keep first decimal. 7.3 mL. Standard liquid dispensing rounds to nearest 0.1 mL.
7.33 mL rounded to one decimal: look at second decimal (3 < 5) → keep first decimal. 7.3 mL. Standard liquid dispensing rounds to nearest 0.1 mL.
Med
Hospital
Rounding Rules
Vancomycin dose calculated at 1,237.5 mg. Hospital protocol rounds to the nearest 250 mg.
What is the rounded vancomycin dose?
Answer: 1,250 mg
1,237.5 is between 1,000 and 1,250. Distance to 1,250 = 12.5 mg. Distance to 1,000 = 237.5 mg. 1,250 mg is nearest.
1,237.5 is between 1,000 and 1,250. Distance to 1,250 = 12.5 mg. Distance to 1,000 = 237.5 mg. 1,250 mg is nearest.
Med
Retail
Rounding Rules
Calculated clonidine dose: 1.5 of the 0.1 mg tablets (tablet is scored). Round down for safety.
What is the safe rounded dose in tablets?
Answer: 1 tablet
Scored tablets can be split, but rounding down is safer for clonidine (BP medication). 1 tablet (0.1 mg). Physician clarification should be sought to adjust dose.
Scored tablets can be split, but rounding down is safer for clonidine (BP medication). 1 tablet (0.1 mg). Physician clarification should be sought to adjust dose.
Hard
Hospital
Rounding Rules
Heparin infusion rate calculated at 1,185 units/hr. Protocol: round to nearest 100 units.
What is the rounded heparin rate?
Answer: 1,200 units/hr
1,185 is between 1,100 and 1,200. 1,185 − 1,100 = 85. 1,200 − 1,185 = 15. 1,200 units/hr is nearest (15 away vs. 85 away).
1,185 is between 1,100 and 1,200. 1,185 − 1,100 = 85. 1,200 − 1,185 = 15. 1,200 units/hr is nearest (15 away vs. 85 away).
Hard
Patient scenario
Rounding Rules
Child needs 266.67 mg. Available: 250 mg/5 mL suspension.
What volume (mL) should be dispensed, rounded to one decimal?
Answer: 5.3 mL
266.67 mg ÷ (250 mg/5 mL) = 266.67/50 = 5.333 mL. Rounded to one decimal: 5.3 mL.
266.67 mg ÷ (250 mg/5 mL) = 266.67/50 = 5.333 mL. Rounded to one decimal: 5.3 mL.
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Lesson 1 · Math Foundations for Pharmacy · AlabamaPharmTech.com
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