Unit-canceling is one of the safest ways to handle pharmacy technician math because it forces each step to make sense on paper. If the unit you do not want disappears, you are moving in the right direction. The three study examples below stay arithmetic-only: gram and milligram conversion, milliliter and liter conversion, and percent of inventory.
When you want more mixed review, use the relevant math and operations questions in these free PTCB practice questions and write out the units beside every number instead of doing the work in your head.
Study example 1: g to mg
Study example: Convert 2.5 g to mg.
Start with what you have: 2.5 g
Use the conversion factor so grams cancel:
2.5 g × 1000 mg / 1 g
Now cancel g with g. That leaves mg.
2.5 × 1000 = 2500
Answer: 2500 mg
Why this works: you began with grams and multiplied by a fraction equal to 1, because 1000 mg and 1 g represent the same amount. The setup changes the unit without changing the quantity.
Study example 2: mL to L
Study example: Convert 750 mL to L.
Start with 750 mL
Use a factor that cancels mL:
750 mL × 1 L / 1000 mL
Cancel mL. You now have liters.
750 ÷ 1000 = 0.75
Answer: 0.75 L
A common mistake is flipping the factor and multiplying by 1000. Unit canceling helps catch that error because the unwanted unit would not disappear.
Study example 3: percent of inventory
Study example: A shelf has 18 bottles of Item A out of 60 total bottles in that section. What percent of the section inventory is Item A?
Use the basic percent setup:
part / whole × 100%
18 / 60 × 100%
18 ÷ 60 = 0.3
0.3 × 100% = 30%
Answer: 30%
This type of problem is not a unit conversion, but the same habit helps: label the part and the whole before calculating so you do not reverse them.
For broader review of formulas, terminology, and common setup patterns, a publicly readable PTCB study guide can help you collect the conversions and percent rules you keep missing.
Quick check question
Which setup correctly converts 0.4 g to mg?
- A: 0.4 g × 1 mg / 1000 g
- B: 0.4 g × 1000 mg / 1 g
- C: 0.4 g × 1000 g / 1 mg
- D: 0.4 g ÷ 1000 mg
Correct answer: B.
Reasoning: the starting unit is g, so g must appear in the denominator of the conversion factor to cancel. After canceling grams, the remaining unit should be mg. Then 0.4 × 1000 = 400, so 0.4 g = 400 mg. Choice A gives 0.0004 mg, which is far too small. Choice C leaves the wrong unit relationship. Choice D does not use a valid conversion setup.
A useful paper habit is to circle the unit you want in the final answer, then check whether your work leaves that exact unit after canceling. That single check can prevent many arithmetic mistakes.
Official exam reference: PTCB PTCE content outline. These study examples are independently written.