Rounding replaces a number with a nearby value at a chosen accuracy. Decimal places count digits after the decimal point; significant figures start with the first non-zero digit. Look at the next digit to decide whether the last kept digit stays or increases. Estimation uses rounded values to check whether an answer is sensible. A rounded measurement represents a whole interval of possible original values. Half the rounding step lies on each side of the stated value. Under the usual round-half-up convention for positive measurements, include the lower boundary and exclude the upper one.
Learning objectives
- Round to a stated accuracy and estimate calculations.
- Find the error interval for a rounded positive measurement.
Key ideas
Decimal places count from the decimal point; significant figures start at the first non-zero digit.
Inspect the next digit: five or more rounds up; otherwise keep the selected digit.
Estimate by rounding inputs to convenient numbers; keep full accuracy in exact working.
For usual rounding of positive measurements, use half the rounding step on each side.
The lower boundary is included; the upper boundary is excluded.
Worked examples
Example 1
Find the interval for a length stated to the nearest tenth of a centimetre.
Answer
Example 2
Round the decimal to two significant figures.
The next digit is eight, so round up.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Round a value, estimate a calculation or state an error interval.
AO2 · Reasoning
Explain whether a rounded answer is sensible and whether an endpoint is included.
AO3 · Problem solving
Use rounded measurements to decide what values are possible.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Leading zeros are not significant figures. Do not round intermediate steps unless the question requests an estimate.
Try it yourself
Attempt each question before opening its answer.
Check 1: Round 0.04786 to 2 significant figures.
Answer: 0.048
The first two significant digits are 4 and 7. The next digit is 8, so increase 7 to 8.
Check 2: A mass is 120 g to the nearest 10 g. Give its error interval.
Answer: 115 ≤ mass < 125 g
Half of 10 g is 5 g. 115 g rounds to 120 g, while 125 g rounds to 130 g.
Explain it in your own words
- Mark the first significant digit in 0.00382 and round to 2 significant figures.
- Explain why rounding to 2 decimal places is different from 2 significant figures.
- Draw an interval for a positive measurement rounded to the nearest whole unit.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Number specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.