The idea
Use half of the rounding increment, not half of the displayed measurement. A length of 8.4 cm to the nearest 0.1 cm has an uncertainty interval extending 0.05 cm each way. When dividing positive measurements, a largest possible quotient uses the numerator’s upper bound and the denominator’s lower bound.
Worked example
A length is recorded as 12 cm to the nearest centimetre. State its bounds.
- The rounding increment is 1 cm, so half the increment is 0.5 cm.
- Lower bound = 12 − 0.5 = 11.5 cm.
- Upper bound = 12 + 0.5 = 12.5 cm, so 11.5 ≤ length < 12.5 cm.
A mistake to avoid
An upper bound is a boundary, not necessarily an attainable maximum. Include the correct inequality when stating the interval.
Check your understanding
A mass is 3.6 kg to the nearest 0.1 kg. Give its rounding interval.
Show the explanation
3.55 kg ≤ mass < 3.65 kg.
Explore the lesson
This guide connects to Estimation, Bounds and Accuracy in the IGCSE Mathematics course. The first two published lessons per subject are free previews; further interactive lessons require an account.