A rounded measurement represents an interval of possible values, not a single exact value. Half the rounding unit gives the distance from the stated value to each boundary. For positive measurements, the largest quotient comes from the largest numerator and smallest denominator. The smallest quotient uses the opposite combination. Write the interval first so you can choose deliberately. An upper bound may be approached without being attained, so describe it as an upper bound rather than an actual maximum.
Learning objectives
- Write an error interval for a rounded measurement.
- Choose bounds that produce an extreme calculated value.
Key ideas
For usual rounding of positive measurements, use half the rounding unit on each side.
Positive values truncated to one decimal place keep the stated lower endpoint.
For positive measurements, use opposite bounds; the denominator lower bound must be strictly positive.
Keep intermediate bounds exact. An upper bound may not be attained.
Worked examples
Example 1
Distance is 120 km to the nearest km; time is 2.4 hours to the nearest 0.1 hour. Find the speed upper bound.
Use the distance upper bound and time lower bound.
Answer
Example 2
A length is 4.7 cm to the nearest 0.1 cm. Write the interval.
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
State an error interval or calculate a bound from rounded positive measurements.
AO2 · Reasoning
Justify which bounds give the greatest or least possible calculated value.
AO3 · Problem solving
Decide whether a claim remains valid given measurement uncertainty.
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
Do not use the denominator upper bound for an upper quotient bound. Rounding and truncation give different intervals.
Try it yourself
Attempt each question before opening its answer.
Check 1: A length is 4.7 cm to the nearest 0.1 cm. Write its error interval.
Answer: 4.65 ≤ length < 4.75 cm
Half of 0.1 cm is 0.05 cm.
Check 2: A square has side 3.0 cm to the nearest 0.1 cm. Find the lower bound of its area.
Answer: 8.7025 cm²
The side can be 2.95 cm; 2.95² = 8.7025.
Explain it in your own words
- Write an error interval for a measurement of 8.0 cm to the nearest 0.1 cm.
- Explain which boundaries give the upper bound of a positive quotient.
- Explain why an upper bound need not be an attained value.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All higher 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.