--- title: "Lesson 1 — Math Foundations for Pharmacy | AlabamaPharmTech.com" description: "Master pharmacy weight, volume, and rounding conversions in Lesson 1. Worked examples, 34+ practice problems, and quizzes for PTCB prep." lang: en json-ld: | { "@context": "https://schema.org", "@type": "LearningResource", "name": "Math Foundations for Pharmacy", "description": "Master pharmacy weight, volume, and rounding conversions in Lesson 1. Worked examples, 34+ practice problems, and quizzes for PTCB prep.", "url": "https://www.alabamapharmtech.com/lessons/lesson1-math-foundations.html", "inLanguage": "en", "learningResourceType": "Interactive lesson", "educationalLevel": "Beginner", "isPartOf": { "@type": "Course", "name": "Pharmacy Math Mastery", "url": "https://www.alabamapharmtech.com/pharmacy-math-practice" }, "provider": { "@type": "Organization", "name": "AlabamaPharmTech", "url": "https://www.alabamapharmtech.com" } } --- AlabamaPharmTech .com An Allied Health Academy company Pharmacy Math Mastery ALBOP-Approved · PTCB & NHA Prep Overall progress 14% Lessons 1 Math Foundations 25 min · In progress 2 Dimensional Analysis 30 min 3 Day Supply Calculations 40 min 4 Dosage Conversions 35 min 5 Ratio, Proportion & Percent 35 min 6 Sig Interpretation 30 min Final exam ★ Bringing It All Together Cumulative · All 6 lessons AlabamaPharmTech.com › Pharmacy Math Mastery › Lesson 1 of 6 Core # 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. [Back to Course](/pharmacy-math-practice) [Back to Dashboard](/modules) Overview Examples Practice 34 Quiz 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 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_ 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 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) **★ 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. Easy Retail 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 1,000 0.075 mg × 1,000 = 75 mcg ✓ 0.075 mg = 75 mcg — same dose, different unit Easy Retail Vancomycin order: 1.5 g IV q12h. Pharmacy system requires entry in mg. Convert 1.5 g to mg. Rule: g → mg = multiply by 1,000 1.5 g × 1,000 = 1,500 mg ✓ Enter 1,500 mg in the pharmacy system Medium Patient 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) Medium Retail 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 Hard Hospital Fentanyl 100 mcg. Anesthesia asks: how many mg is this? (Important for documentation.) Convert 100 mcg to mg. Rule: mcg → mg = divide by 1,000 100 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. Hard Hospital 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 Easy Medium Hard Context Retail Hospital Patient Easy Retail Weight (g/mg/mcg) A pharmacist labels metronidazole as 0.5 g. Convert 0.5 g to mg. Check Show solution **Answer: 500 mg** 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. Check Show solution **Answer: 75 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. Check Show solution **Answer: 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. Check Show solution **Answer: 0.25 mg** 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. Check Show solution **Answer: 1 mg** 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. Check Show solution **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. 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. Check Show solution **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. Med Retail Weight (g/mg/mcg) New Rx: atorvastatin 0.04 g. Computer system requires entry in mg. Convert 0.04 g to mg. Check Show solution **Answer: 40 mg** 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? Check Show solution **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. Med Hospital Weight (g/mg/mcg) Handwritten order: morphine sulfate 0.01 g IV PRN. Confirm in mg. Convert 0.01 g to mg. Check Show solution **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. 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. Check Show solution **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. 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. Check Show solution **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. 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) Check Show solution **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. Easy Hospital Weight (lb/kg) ICU chart shows patient weight as 176 lb. Needed in kg for dosing. Convert 176 lb to kg. Check Show solution **Answer: 80 kg** 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. Check Show solution **Answer: 10 kg** 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? Check Show solution **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. 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? Check Show solution **Answer: 600 mg** 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? Check Show solution **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. Easy Retail Volume (tsp/mL/oz) Patient told to take 2 tsp of liquid medication. Convert 2 tsp to mL. Check Show solution **Answer: 10 mL** 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? Check Show solution **Answer: 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. Check Show solution **Answer: 15 mL** 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? Check Show solution **Answer: 2 tsp** 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) Check Show solution **Answer: 30 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. Check Show solution **Answer: 120 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? Check Show solution **Answer: 30 mL** 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? Check Show solution **Answer: 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? Check Show solution **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. Easy Retail Rounding Rules Calculated tablet dose: 2.7 tablets. The tablet cannot be split. What quantity do you dispense? A. 2 tabletsB. 3 tabletsC. 2.5 tabletsD. 2.7 tablets Show solution **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. 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. Check Show solution **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**. Med Retail Rounding Rules Pediatric dose calculation yields 7.33 mL. What is the correct rounded volume to dispense? Check Show solution **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. 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? Check Show solution **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. 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? A. 1 tabletB. 1.5 tabletsC. 2 tabletsD. 0.5 tablets Show solution **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. 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? Check Show solution **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). 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? Check Show solution **Answer: 5.3 mL** 266.67 mg ÷ (250 mg/5 mL) = 266.67/50 = 5.333 mL. Rounded to one decimal: **5.3 mL**. **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. How many questions? 102030 Question difficulty Random mixEasy onlyMedium onlyHard only Options Randomize question order Shuffle every time you start Timed mode 45-second countdown per question Number of sets Each set draws a fresh pool − 1 + 10 Questions 1 Sets 10 Total ~10 min Est. time ▶  Start quiz — Math Foundations for Pharmacy Question 1 of 10 0 correct · 0 skipped \--% Score Quiz complete! Lesson 1 · Math Foundations for Pharmacy · AlabamaPharmTech.com \-- Correct \-- Wrong \-- Skipped \-- Time Performance by question type \--% Overall accuracy \-- Weakest area Miss rate by question type Retry missed + skipped Next set New quiz Answer review — every question this session [Home](/) [Back to Dashboard](/modules) Previous [Back to Course](/pharmacy-math-practice) Lesson 1 of 6 Next lesson