Why it matters
Pharmacy uses a single system of units that step up and down in factors of 1000. Each step is exactly three decimal places, so converting really is just moving the decimal point. Getting this wrong is not only an exam problem: confusing milligrams and micrograms is a recognised cause of serious, sometimes fatal, medication errors, which is why it is tested so heavily.
🧠 The theory: why factors of 1000
The metric system is decimal, and the common pharmacy prefixes (kilo, milli, micro, nano) each differ by a factor of 1000. Because 1000 is ten cubed, moving one prefix step shifts the decimal point exactly three places. That is why a conversion never changes the real quantity, only how it is written. Once you see it as sliding a decimal point rather than doing arithmetic, mistakes fall away.
The metric ladder
- •1 kilogram (kg) = 1000 grams (g)
- •1 gram (g) = 1000 milligrams (mg)
- •1 milligram (mg) = 1000 micrograms
- •1 microgram = 1000 nanograms
- •1 litre (L) = 1000 millilitres (mL)
The one rule
To change to a smaller unit, multiply by 1000 (the number gets bigger). To change to a larger unit, divide by 1000 (the number gets smaller). If you ever feel unsure which way to go, ask yourself whether the answer should be a bigger or smaller number, then check your working matches.
smaller unit: multiply by 1000 | larger unit: divide by 1000
Single-step conversions
Worked example
Convert 0.25 g to milligrams.
- Step 1 — Decide the direction. Grams to milligrams moves one rung down to a smaller unit, so you multiply by 1000.
- Step 2 — Do the multiplication: 0.25 x 1000 = 250.
Answer: 250 mg
Worked example
Convert 500 micrograms to milligrams.
- Step 1 — Decide the direction. Micrograms to milligrams moves one rung up to a larger unit, so you divide by 1000.
- Step 2 — Do the division: 500 / 1000 = 0.5.
Answer: 0.5 mg
Worked example
Convert 1.2 g to milligrams.
- Step 1 — Grams to milligrams is one step to a smaller unit, so multiply by 1000.
- Step 2 — Multiply: 1.2 x 1000 = 1200.
Answer: 1200 mg
Worked example
Convert 40 mg to grams.
- Step 1 — Milligrams to grams is one step to a larger unit, so divide by 1000.
- Step 2 — Divide: 40 / 1000 = 0.04.
Answer: 0.04 g
Tip: Always write the leading zero (0.04, not .04) so the decimal point cannot be missed.
Worked example
Convert 0.05 mg to micrograms.
- Step 1 — Milligrams to micrograms is one step to a smaller unit, so multiply by 1000.
- Step 2 — Multiply: 0.05 x 1000 = 50.
Answer: 50 micrograms
Worked example
Convert 3.5 litres to millilitres.
- Step 1 — Litres to millilitres is one step to a smaller unit, so multiply by 1000.
- Step 2 — Multiply: 3.5 x 1000 = 3500.
Answer: 3500 mL
Harder, multi-step conversions
Some conversions cross two rungs of the ladder. Take them one rung at a time rather than trying to jump.
Worked example
Convert 2,500,000 nanograms to milligrams.
- Step 1 — This is two rungs up (nanograms to micrograms, then micrograms to milligrams), so you will divide by 1000 twice.
- Step 2 — First rung, nanograms to micrograms: 2,500,000 / 1000 = 2500 micrograms.
- Step 3 — Second rung, micrograms to milligrams: 2500 / 1000 = 2.5.
Answer: 2.5 mg
Worked example
Convert 0.004 g to micrograms.
- Step 1 — Grams to micrograms is two rungs down, so you multiply by 1000 twice.
- Step 2 — First rung, grams to milligrams: 0.004 x 1000 = 4 mg.
- Step 3 — Second rung, milligrams to micrograms: 4 x 1000 = 4000.
Answer: 4000 micrograms
⚠️ Common mistakes
Mixing up micrograms and milligrams is the single most dangerous error, because they differ by a factor of 1000. Write micrograms and nanograms in full and never abbreviate them. Always put a zero before a decimal point, and never put an unnecessary zero after one (write 5 mg, not 5.0 mg), because a misread decimal can mean a tenfold dosing error.
Test yourself
Convert 0.125 mg to micrograms.
Answer: Smaller unit, so multiply by 1000: 0.125 x 1000 = 125 micrograms
Convert 2.4 g to milligrams.
Answer: Smaller unit, so multiply by 1000: 2.4 x 1000 = 2400 mg
Convert 750 mL to litres.
Answer: Larger unit, so divide by 1000: 750 / 1000 = 0.75 litres
Convert 3,000,000 nanograms to milligrams.
Answer: Two rungs up: 3,000,000 / 1000 = 3000 micrograms; 3000 / 1000 = 3 mg