Approximate values and error
Find the absolute and relative error, compare the accuracy of measurements and bound the error of a sum.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- Russia: grade 9
Guide
In the Russian programme, approximate values and absolute and relative errors are studied in grade 9 (algebra, the section on approximate calculations) and repeated at the advanced level in grade 10.
If x is the exact value and a the approximation, the absolute error Δ = |x − a| is the distance between them on the number line. The relative error is δ = Δ/|a|, usually written as a percent.
To compare how accurate measurements are, compare relative errors. When adding approximate numbers, the bounds of their errors add. Common slips: adding the numbers instead of subtracting, giving the absolute error as a percent, comparing accuracy by the absolute error.