Imagine measuring a microscopic chemical reaction with a wooden ruler meant for building houses. The tool you use limits how precisely you can report your final answer. In chemistry, we use significant figures to communicate the precision of a measurement, ensuring we do not claim a result is more accurate than the equipment used to measure it.
To identify the number of significant figures in a given value, follow these rules:
When calculations produce a long string of decimals on your calculator, you must use rounding to shorten the number to the correct precision.
In chemistry, you will frequently perform multi-step calculations. The most critical rule is the "least precise" rule: for multiplication and division, your final answer must be rounded to match the least significant measurement in the provided data.
However, you must never round intermediate values during the steps of your calculation. You should carry the full calculator display (or at least two extra "guard digits") through every step. Rounding too early causes a rounding error, which will shift your final answer away from the true value. Note that exact values, such as the large numbers used for balancing equations or unit conversions (like dividing by to turn into ), have infinite precision and do not affect your final significant figures.
A student performs a titration. They find that of sodium hydroxide (NaOH) neutralises of sulfuric acid (). Calculate the concentration of the sulfuric acid. Give your answer to an appropriate number of significant figures.
Step 1: Identify the significant figures in the provided data.
has 3 s.f.
has 3 s.f.
has 4 s.f.
The lowest number of significant figures is 3. The final answer must be given to 3 s.f.
Step 2: Calculate the moles of NaOH.
Step 3: Use the molar ratio to find the moles of .
The balanced equation is .
The ratio is , so divide the moles of NaOH by 2.
(Note: We do not round this intermediate value).
Step 4: Calculate the concentration of the sulfuric acid.
Step 5: Round the final answer to the appropriate number of significant figures (3 s.f.).
The number of significant figures you can record in an experiment depends directly on the precision of the equipment you are using.
Burettes: Readings must always be recorded to two decimal places, ending in either or (e.g., ). This typically gives 4 significant figures.
Pipettes: A standard laboratory pipette measures exactly , providing 3 significant figures.
Measuring cylinders: A standard reading of from a basic cylinder only provides 2 significant figures.
When calculating an average titre in OCR practicals, you must only use concordant results (results within of each other). If you make a mathematical error early in a multi-step question, examiners apply the Error Carried Forward principle, but you will still lose marks if your final answer has the wrong number of significant figures.
Students often forget to include placeholder zeros (e.g., writing 5 instead of 5.0). If a calculation requires 2 s.f., leaving off the .0 will lose you the accuracy mark.
Premature rounding is a frequent cause of mark loss. Always carry the full calculator display through your intermediate steps and ONLY round at the very end.
If an OCR chemistry question does not specify a required degree of accuracy, the default expectation is to provide your final answer to 3 significant figures.
When reading a burette in an exam diagram, ensure your answer always has two decimal places and ends in a 0 or a 5 (e.g., 23.40 or 23.45).
Significant figures
The digits in a measured quantity that carry meaningful information about its precision, including all certain digits plus one estimated digit.
Rounding
The process of simplifying a number while keeping its value close to the original, usually to match a required level of precision.
Least significant measurement
The piece of data in a calculation set with the lowest count of significant figures, which dictates the precision of the final result in multiplication or division.
Rounding error
An inaccuracy in a final calculation result caused by rounding numbers prematurely during intermediate calculation steps.
Standard form
A way of writing numbers as a coefficient between 1 and 10 multiplied by a power of 10, used to clearly show significant figures for very large or small numbers.
Resolution
The smallest change in the quantity being measured that gives a perceptible change in the reading on a piece of apparatus.
Precision
A measure of how close a series of measurements are to one another.
Error Carried Forward
A marking principle where a student is not penalised repeatedly for the same initial calculation error in subsequent steps.
Put your knowledge into practice — try past paper questions for Chemistry A
Significant figures
The digits in a measured quantity that carry meaningful information about its precision, including all certain digits plus one estimated digit.
Rounding
The process of simplifying a number while keeping its value close to the original, usually to match a required level of precision.
Least significant measurement
The piece of data in a calculation set with the lowest count of significant figures, which dictates the precision of the final result in multiplication or division.
Rounding error
An inaccuracy in a final calculation result caused by rounding numbers prematurely during intermediate calculation steps.
Standard form
A way of writing numbers as a coefficient between 1 and 10 multiplied by a power of 10, used to clearly show significant figures for very large or small numbers.
Resolution
The smallest change in the quantity being measured that gives a perceptible change in the reading on a piece of apparatus.
Precision
A measure of how close a series of measurements are to one another.
Error Carried Forward
A marking principle where a student is not penalised repeatedly for the same initial calculation error in subsequent steps.