Common Registration Assessment, Part 1
Scientific notation and very small quantities
Practise powers of ten, nanograms and micrograms, with three original worked questions.
Published 9 October 2026. Independent revision material, not GPhC questions, not for patient care.
Very small quantities such as nanograms are often written in scientific notation. A number times 10 to a negative power is a small number. Moving the decimal point is all that changes.
The figures are fictional. Convert to one unit first, then multiply by volume if needed.
The method
- Write the number in scientific notation if it helps, such as 2.5 × 10^-3 g.
- Convert to the unit asked: 1 g = 1000 mg and 1 mg = 1000 micrograms.
- 1000 nanograms = 1 microgram.
- For a total, multiply the concentration by the volume.
- Check the decimal point has moved the right way.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
Convert 2.5 × 10^-3 g to mg.
Show the answer
Answer: 2.5 mg
Working: 2.5 × 10^-3 g × 1000 = 2.5 mg.
Question 2
Convert 150 nanograms to micrograms.
Show the answer
Answer: 0.15 micrograms
Working: 150 ÷ 1000 = 0.15 micrograms.
Question 3
A fictional solution is 4 × 10^-6 g/mL. How many mg are in 500 mL?
Show the answer
Answer: 2 mg
Working: 4 × 10^-6 g/mL = 4 micrograms/mL. 4 × 500 = 2000 micrograms = 2 mg.
Say it in words
Say "four micrograms per mL" aloud. Words often expose a slip that digits hide.
Where marks are lost
- Moving the decimal point in the wrong direction.
- Confusing nanograms with micrograms.
- Forgetting to multiply by volume.
Frequently asked questions
What does 10^-3 mean?
It means one thousandth, or 0.001.
Do I always use scientific notation?
No. It helps when numbers are very small but plain decimals work too.
Sources
- The Pharmaceutical Journal, medication maths: using provided formula
- The Pharmaceutical Journal, preparing for the GPhC pharmaceutical calculations assessment
- GPhC, 2026 assessment specification and permitted items
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Direct proportion and cross-multiplication
- Stock use and reorder quantities
See also the formula sheet, the eight sample questions and the approved calculator page.