Research-use only. This guide explains general laboratory calculation principles. It is not medical advice and does not provide dosing or administration instructions.
Why precision is not the same as accuracy
A calculator can display many decimal places, but those digits are not automatically meaningful. Accuracy describes how close a result is to the accepted value. Precision describes how consistently measurements agree with one another. A result may be precise but inaccurate when equipment is miscalibrated, and it may be accurate on average while individual readings vary.
What significant figures communicate
Significant figures are a practical way to show the resolution supported by the source data. Leading zeros are placeholders, while zeros between non-zero digits are significant. Trailing zeros are significant when the notation makes that intention clear. Scientific notation is often the clearest format: 1.20 × 10² shows three significant figures, whereas 1.2 × 10² shows two.
Do not report a calculated concentration to six decimal places when the mass and volume were measured only to two or three significant figures. Extra digits create an impression of certainty that the inputs cannot support.
Keep guard digits until the end
Rounding at every stage can accumulate error. Retain the calculator’s unrounded value during intermediate steps, then round the final reported result to a precision justified by the least precise input. Store both the raw and reported values when traceability matters.
Measurement uncertainty
Every measurement has uncertainty. Sources include instrument resolution, calibration status, operator technique, temperature, evaporation and sample handling. Uncertainty is not a mistake; it is information about the range within which a result is reasonably expected to fall.
For routine records, note the instrument and its stated tolerance. For formal work, follow the validated method used by the laboratory. The research calculator performs arithmetic but cannot assess equipment condition or uncertainty.
A simple propagation idea
When a result depends on several measurements, uncertainty in each input contributes to uncertainty in the result. A concentration calculated from mass divided by volume inherits limitations from both measurements. The exact propagation method depends on the procedure and should be documented rather than guessed.
Worked reporting example
Suppose a calculation produces 3.333333 mg/mL from inputs recorded as 10.0 mg and 3.00 mL. Reporting 3.33 mg/mL is more consistent with the precision of the inputs than displaying every calculator digit. The unrounded number may still be retained in the worksheet.
Use unit checks before rounding
Rounding cannot repair a unit error. Confirm that mass and volume units are compatible first. One milligram equals 1,000 micrograms, and one millilitre equals 1,000 microlitres. See the unit-conversion guide for a dimensional-analysis workflow.
Good documentation practice
- Record the original values and units.
- Identify the measuring equipment.
- Record calibration or verification status where relevant.
- Keep intermediate values unrounded.
- State the rounding rule used.
- Have critical calculations independently reviewed.
Common reporting problems
Frequent problems include copying only the rounded number, omitting units, changing units without recording the conversion factor, and using a precision that varies across the same dataset. A consistent worksheet template reduces these risks.
A short verification checklist
- Are all inputs labelled with units?
- Do the displayed digits reflect instrument resolution?
- Were intermediate results kept unrounded?
- Does the final rounding rule match the least precise input?
- Can another reviewer reproduce the result?
For the underlying arithmetic, read How It Works. More educational material is listed in Research Guides.