SL 1.6—Approximation and error
- Syllabus
- First assessment 2021
- Objective
- —
- Level
- SL
Approximation: accuracy, bounds and error
An approximation replaces an exact value with a nearby value that is easier to report or use. Its accuracy is part of the statement: rounding to a given unit defines an interval, while significant figures communicate relative precision.
Ifxisroundedtothenearestunitu,thenx−u/2≤exactvalue<x+u/2.
A length reported as 8.4 cm to the nearest 0.1 cm represents 8.35 ≤ L < 8.45. If the measured value is 8.37 cm, using 8.4 cm introduces an absolute error of 0.03 cm and a percentage error of about 0.36%. Keep full calculator precision until the final rounding.
The required precision depends on the context. A calculated result of 3.2 containers cannot be reported as 3.2 containers in practice: four whole containers are needed. Do not confuse a rounding bound with the exact value, and do not round intermediate values unnecessarily.