- use the positive difference
Worked example
A length is measured as 8.4 cm, but the actual length is 8.1 cm. Find the absolute error.
Step by step
- Find the positive difference.
Final answer
0.3 cm
Absolute error is a size: It tells you the size of the mistake, not whether the measurement was above or below the actual value.
- use the true/reference value in the denominator
Worked example
Use absolute error 0.3 and actual value 8.1 to find the relative error.
Step by step
- Substitute into the formula.
Final answer
Relative error ≈ 0.0370
Denominator trap: Relative error compares the error with the actual value, not the measured value.
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Why relative error matters: A 0.5 cm error might be tiny for a 5 m object but large for a 1 cm object. Relative error tells you how important the error is compared with the size of the measurement.
| Situation | Absolute error | Relative effect |
|---|---|---|
| Length about 100 cm | 0.5 cm | small |
| Length about 1 cm | 0.5 cm | very large |
Quick interpretation
Which measurement is more accurate if both have absolute error 0.2, but one actual value is 2 and the other is 20?
Step by step
- Relative error for 2 is 0.2/2 = 0.1.
- Relative error for 20 is 0.2/20 = 0.01.
Final answer
The measurement with actual value 20 is more accurate because its relative error is smaller.
Turning it into a percentage: If you multiply the relative error by 100, you get percentage error. That full topic comes next.
Worked example
A relative error is 0.04. What percentage is this?
Step by step
- Multiply by 100%.
Final answer
4%
Decimal or percent?: Read the question carefully. Some questions want relative error as a decimal, others want percentage error.