PTCB exam pharmacy conversions

Every conversion the PTCB exam relies on, the four measurement systems and where each still appears, roman numerals and ss on prescriptions, military time, and the fraction, decimal and ratio work the calculation questions sit on.

Systems of Measurement

Metric / SI

Pharmacy calculations run on the metric (SI) system. It is decimal-based, so every step on the ladder is a factor of 10.

• Mass: mcg → mg → g → kg
• Volume: mL → L
• Length: mm → cm → m → km

Critical shortcut: 1 cm³ = 1 mL, and 1 mL of water weighs approximately 1 g.

Exam Tip: For the pharmacy units you will actually use, think in thousand-fold jumps: kg → g → mg → mcg, and L → mL. Three decimal places per hop.

Mnemonic: "King Henry Died (By) Drinking Chocolate Milk" — Kilo / Hecto / Deka / Base / Deci / Centi / Milli (left = larger, right = smaller; the pharmacy ladder continues one more triad past milli to micro/mcg — the mg → mcg hop is 1,000×, the single most-tested conversion in this chapter). Pair with "Fish-eye (5/15/30)" — 5 mL = tsp, 15 mL = tbsp, 30 mL = fl oz; "2.2 Pound Pup" (1 kg = 2.2 lb); "65 mg = 1 grain." See the Mnemonic Library cheat sheet Section 7.

Common Trap: Mixing mg and mcg. A 0.25 mg dose is 250 mcg. A prescription handwritten as 0.25 mg that looks like 25 mg on a copier is a 100× error. Always convert before cross-multiplying.

Safety Rule — Micro Symbol: The Greek µ is on the ISMP error-prone list because it can be read as m. Use mc (as in mcg).

Converting within the metric system

• To a smaller unit: shift the decimal right. Number grows; unit shrinks.
• To a larger unit: shift the decimal left. Number shrinks; unit grows.
• Each step between adjacent prefixes moves the decimal one place; the standard pharmacy pairs (g/mg, mg/mcg, L/mL) sit three places apart.

Worked: 0.004 kg = 4 g = 4,000 mg. A 650 mg tablet = 0.65 g = 650,000 mcg.

Using a conversion factor

• 1 g = 1,000 mg, so the factor is 1 g / 1,000 mg.

• Convert 65 mg to g: 65 mg × (1 g / 1,000 mg) = 0.065 g.

• Solid oral doses usually come in mg or g.

• Liquid doses usually come in mL or L.

Apothecary

An older system still occasionally seen on thyroid, phenobarbital, and aspirin orders.

• Grain (gr): 1 grain ≈ 65 mg. Aspirin 5 grains = 325 mg; 10 grains = 650 mg. The exact apothecary/USP value is 64.8 mg (64.79891 mg); 60 mg is a legacy dose-equivalence rounding. The PTCE® may use either 60 or 65 mg per grain — use whichever value the question specifies.
• Dram: On a Sig the dram is read as 1 teaspoonful = 5 mL (the PTCE convention). (A true apothecary fluid dram is ≈ 3.7 mL, but in dosing it is treated as a 5 mL teaspoonful.) Rare on modern scripts; still used to describe prescription-vial capacity.

Avoirdupois

• The U.S. system for ounces and pounds.
• 1 lb = 16 oz.
• Unless the question says otherwise, use this relationship whenever you see "ounces" applied to weight.

Household

Teaspoons, tablespoons, cups. Prescribers sometimes write household units, but the safer practice is to dispense oral liquids in metric volumes using a pharmacy-calibrated device.

Exam Tip: Household spoons are not reliable measuring devices. If the Sig says "1 tsp," dispense a calibrated oral syringe or dosing cup labeled in mL.

Conversion Reference

Core conversions — memorize these cold

• Length: 1 in = 2.54 cm
• Mass: 1 kg = 2.2 lb; 1 lb = 454 g; 1 oz ≈ 28.35 g (rounded to 30 g)
• Volume: 1 tsp = 5 mL; 1 tbsp = 15 mL = 3 tsp; 1 fl oz = 30 mL (29.6 mL exact); 1 pint ≈ 473 mL (rounded to 480 mL)
• Household volume ladder: 1 cup = 8 fl oz; 2 cups = 1 pint; 2 pints = 1 quart; 4 quarts = 1 gallon.
• Temperature anchor: 20 °C = 68 °F.

Temperature

• Celsius → Fahrenheit: °F = (°C × 9/5) + 32
• Fahrenheit → Celsius: °C = (°F − 32) × 5/9

Worked: 35.4 °C → F. (35.4 × 9/5) + 32 = 63.72 + 32 = 95.72 °F.

Pharmacy Storage Ranges (USP)

Exam Tip: The PTCE® loves refrigerator range. 2 °C to 8 °C — 36 °F to 46 °F. Commit it. Insulin, vaccines, many biologics, and most reconstituted suspensions live in this range.

Worked Conversions

How many milliliters are in 2.5 teaspoons?

• 2.5 tsp × (5 mL / 1 tsp) = 12.5 mL

Convert a 176-lb body weight to kilograms.

• 1 kg / 2.2 lb = x kg / 176 lb
• x = (1 × 176) / 2.2 = 80 kg

Convert 5'10" to centimeters, then meters.

• 5 ft × 12 in/ft = 60 in
• 60 in + 10 in = 70 in
• 70 in × 2.54 cm/in = 177.8 cm
• 177.8 cm ÷ 100 = 1.778 m

Numerals, Roman Numerals, and ss

A numeral is the written symbol for a number. Pharmacy uses two sets: Arabic (0, 1, 2 . . .) and Roman (I, V, X . . .). The symbol ss is an older abbreviation meaning one-half — it is not a Roman numeral, and ISMP flags it as error-prone because it is easy to misread as "55."

Roman numerals still appear on handwritten prescriptions when the prescriber states a count — capsules, tablets, or grains.

Core Roman numeral values

• ss = 1/2 (older abbreviation, error-prone)
• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1,000

Mnemonic anchor: the seven numerals stack as I-V-X-L-C-D-M; remember "I Value Xylophones, Lucy Can't Dance Much." For calc setups: "Cross-Multiply, Then Solve" (a/b = c/d → a×d = b×c) and "Days' Supply = Total Quantity / Daily Use." See the Mnemonic Library cheat sheet Section 7.

The eight rules that control Roman-numeral interpretation

1. Repetition repeats the value. II = 2, XXX = 30.
2. A letter cannot be repeated more than three times. XXXX is not 40.
3. V, L, and D are never repeated. VV is not 10.
4. A smaller numeral before a larger one subtracts. IV = 4, IX = 9, XL = 40, CD = 400, CM = 900.
5. A smaller numeral after a larger one adds. VI = 6, XI = 11, LX = 60.
6. V, L, and D are never subtracted from a larger numeral. VL is not 45.
7. Only one numeral at a time is subtracted. IIX is not 8.
8. Use I only before V and X, X only before L and C, C only before D and M.

Worked translations

• gr. vii ss — 7 and one-half grains.
• caps. iv — 4 capsules.
• MCMXCIX — 1,999.

Exam Tip: The PTCE® will often drop the large numerals D (500) and M (1,000) into a fill-in-the-blank item. They are easy to miss because most prescriptions stop at double digits.

Fractions

A fraction expresses a portion of a whole. It has a numerator on top (parts present) and a denominator on the bottom (total parts). A mixed number is a whole number paired with a fraction, such as 1 1/4.

Pharmacy sees fractions in IV fluid names — 1/2 NS (half normal saline), 1/4 NS (quarter normal saline) — and occasionally in pediatric oral-liquid doses.

Common Trap: A handwritten fraction slash can look like the digit 1, which turns 1/2 into 12. When you transcribe by hand, write the slash large and clear, or use the decimal equivalent.

Adding fractions

1. Find the least common denominator (LCD).
2. Convert each fraction so both share the LCD.
3. Add the numerators. Keep the denominator.
4. Simplify.

Worked: 3/4 + 2/3. LCD = 12. 9/12 + 8/12 = 17/12 = 1 5/12.

Subtracting fractions

1. Force a common denominator. Convert mixed numbers to improper fractions first.
2. Subtract numerators. Keep the denominator.
3. Simplify.

Worked: 1 7/8 − 1/2. Convert 1 7/8 to 15/8; convert 1/2 to 4/8; 15/8 − 4/8 = 11/8 = 1 3/8.

Multiplying fractions

1. Multiply the numerators.
2. Multiply the denominators.
3. Simplify.

Worked: 9/10 × 4/5 = 36/50 = 18/25.

Dividing fractions

1. Flip the second fraction (take the reciprocal).
2. Multiply.
3. Simplify.

Worked: 2/3 ÷ 1/3. Reciprocal of 1/3 is 3/1. 2/3 × 3/1 = 6/3 = 2.

Decimals

Decimals and fractions express the same idea in a different notation. Digits to the left of the decimal are whole-number places (ones, tens, hundreds). Digits to the right are fractional places (tenths, hundredths, thousandths).

Safety Rule — Decimal Notation:

• Always use a leading zero. Write 0.5 mg, not .5 mg. A bare decimal point disappears on a fax, a photocopy, or a fast read and turns into 5 mg.
• Never use a trailing zero. Write 5 mg, not 5.0 mg. The trailing zero can look like 50 mg.
• Only include zeros that serve as placeholders after the decimal (write 7.05, not 7.050).

Converting a fraction to a decimal: divide the numerator by the denominator. A whole number sits to the left of the decimal point.

Worked: 1 2/3. Whole number is 1. 2 ÷ 3 = 0.6667. Final = 1.6667.

Converting a decimal to a fraction: read the decimal the way you would say it, then simplify. 0.5 = "five-tenths" = 5/10 = 1/2.

Significant figures are the digits in a measurement that convey precision — leading zeros do not count, trailing zeros after the decimal do.

Percentages

Percent means "per 100." To convert:

• Percent to fraction: place the number over 100. 78% = 78/100.
• Percent to decimal: drop the sign and shift the decimal two places left. 78% = 0.78.
• Percent with a decimal: 78.05% = 7,805/10,000 = 1,561/2,000 = 0.7805.

Ratios and Proportions

A ratio compares two quantities (mg/kg, mL/hr, units/mL). A proportion sets two ratios equal (a/b = c/d). A proportion solves for an unknown when the other three values are known, through cross-multiplication: a × d = b × c.

Calc Setup — Proportion Rule: Write units with every number. Confirm matching units stack in matching positions on both sides. If the units do not line up, convert first, then cross-multiply.

Worked example — weight-based proportion

A medication is ordered at 4 mg/kg for a patient weighing 70 kg. Calculate the dose.

• Proportion: x mg / 70 kg = 4 mg / 1 kg
• Cross-multiply: 4 mg × 70 kg = 1 kg × x mg
• Divide both sides by 1 kg: x = (4 × 70) / 1
• Answer: x = 280 mg

Worked example — concentration proportion

Diphenhydramine syrup is 12.5 mg/5 mL. How many milligrams are in 10 mL?

• Proportion: 12.5 mg / 5 mL = x mg / 10 mL
• Cross-multiply: 12.5 × 10 = 5 × x
• Solve: x = 125 / 5 = 25 mg

Military (24-Hour) Time

Hospital MARs and most pharmacy order-entry systems run on the 24-hour clock to eliminate AM/PM ambiguity. Pharmacy notation drops the colon.

• Midnight = 0000
• 1 AM through 9 AM = leading zero: 0100–0900
• 10 AM and 11 AM stay 1000 and 1100
• Noon = 1200
• 1 PM through 11 PM = add 12 to the hour: 1 PM = 1300, 4 PM = 1600, 8 PM = 2000, 11 PM = 2300

Worked: 4:15 PM = 12 + 4 = 16 hours, so 1615.

Common Traps

These are the calculation pitfalls the PTCE returns to most often. Each one is a setup error, not an arithmetic error — which is exactly why they slip past a fast reader.

• The mg/mcg 1,000× error. Mixing milligrams and micrograms is the most common dose miscalculation. A 0.25 mg dose is 250 mcg; a proportion that leaves mg on one side and mcg on the other is off by a factor of 1,000. Here's the rule: convert both quantities to the same unit before you cross-multiply.
• Per-dose versus per-day. A weight-based order written as mg/kg/day is not the dose you draw — it is the total for 24 hours. Divide the daily amount by the number of doses per day before you measure anything. Reading mg/kg/day as mg/kg/dose multiplies the patient's intended dose by the dosing frequency.
• Squaring BMI height in centimeters instead of meters. BMI is weight in kilograms divided by height in meters squared. Square the height in meters — not centimeters. A height squared in centimeters produces a BMI roughly 10,000 times too small; reporting that wrong figure as a plausible-looking number is the trap.
• D.T.D. versus M. ft. These two compounding abbreviations look similar and are interpreted in opposite directions. D.T.D. (dentur tales doses) means the listed amounts are per dose — prepare that number of each. M. ft. (misce fiat) means the listed amounts are the total recipe. Misreading either one is a dangerous dispensing error.
• Not rounding up on ophthalmic and inhaler dispensing. Eye-drop and inhaler days-supply problems expect you to round the number of bottles or units up to the next whole container, because device loss during administration is expected. Rounding down short-fills the patient.
• Forgetting the fixed drug mass in reconstitution. When the wrong volume of diluent is added, the milligrams of drug in the bottle do not change — only the final volume and therefore the concentration change. Calculate total mg in the bottle first, then redo the concentration.

Quick Review Checklist

Math fundamentals

• [ ] I can run the four basic fraction operations.
• [ ] I know the leading-zero / trailing-zero rule.
• [ ] I can set up and solve a proportion with the correct units.
• [ ] I can round to tenths, hundredths, and thousandths.

Systems of measurement

• [ ] I know the metric prefixes: kilo, centi, milli, micro.
• [ ] I know 1 mL water = 1 cm³ = 1 g.
• [ ] I know 1 grain ≈ 65 mg (or 60 mg; use the exam's value).
• [ ] I know 1 lb = 16 oz (avoirdupois).

Conversions

• [ ] 1 kg = 2.2 lb
• [ ] 1 tsp = 5 mL
• [ ] 1 tbsp = 15 mL = 3 tsp
• [ ] 1 fl oz = 30 mL (29.6 mL exact)
• [ ] 1 pint = 480 mL = 16 fl oz
• [ ] 1 oz weight ≈ 30 g
• [ ] 1 lb = 454 g
• [ ] 1 in = 2.54 cm
• [ ] 1 g = 1,000 mg; 1 mg = 1,000 mcg; 1 L = 1,000 mL

Formulas

• [ ] Desired / Have × Quantity (dose)
• [ ] C₁V₁ = C₂V₂ (dilution)
• [ ] BSA = √[ht(cm) × wt(kg) / 3,600] (Mosteller)
• [ ] IBW male = 50 + 2.3 × (inches over 5')
• [ ] IBW female = 45.5 + 2.3 × (inches over 5')
• [ ] BMI = wt(kg) / ht(m)² with NIH categories
• [ ] °F = (°C × 9/5) + 32
• [ ] °C = (°F − 32) × 5/9
• [ ] IV flow rate = volume / time
• [ ] DEA validation algorithm (odds + evens × 2 → check final digit)
• [ ] mg% = mg/dL; 1 mg/dL = 0.001% (w/v)
• [ ] ppm = g / 1,000,000 mL; 1 ppm = 1:1,000,000 = 0.0001%
• [ ] mEq = (mg × valence) / MW; mmol = mg / MW
• [ ] Weight = volume × SG; volume = weight / SG
• [ ] Powder volume = final volume − diluent
• [ ] Business: markup = SP − cost; turnover = purchases / avg inventory

Sig codes

• [ ] BID / TID / QID
• [ ] AC / PC / HS timing
• [ ] PRN / Stat / NPO
• [ ] PO / SL / SC-SQ
• [ ] OD / OS / OU; AD / AS / AU
• [ ] gtt = drop; q4h = every 4 hours

Compounding abbreviations

• [ ] D.T.D. = per dose
• [ ] M. ft. = total recipe
• [ ] q.s. / q.s. ad
• [ ] aa = of each
• [ ] ad = up to / to make

Error-prone abbreviations

• [ ] I know not to use: q.d., q.o.d., U, IU, µ, cc, MS/MSO4/MgSO4, TIW, HS, D/C, SS, @, >, <, &, /, trailing zeros, missing leading zeros.

Medical terminology

• [ ] Decompose any term into prefix + root + suffix.
• [ ] Brady- = slow; tachy- = fast; hyper- = excessive; hypo- = deficient.
• [ ] -itis = inflammation; -ectomy = removal; -oma = tumor; -pathy = disease.

Related

All Order Entry and Processing guides · What is on the PTCE and how it is weighted · The Federal Requirements domain