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
How this quiz works: Pick your question count and difficulty, then start. After answering, click Reveal explanation to see the full step-by-step solution — answers never show automatically. Score and type breakdown appear at the end.
ⓘ This lesson has 34 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
ⓘ This lesson has 34 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
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Lesson 1 · Math Foundations for Pharmacy · AlabamaPharmTech.com
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