Random Errors
Random errors can occur in measurements due to unpredictable and uncontrollable circumstances.
Systematic Errors
Systematic errors, on the other hand, are consistent and repeatable, leading to inaccuracies in the measurement process.
Absolute Uncertainty
Absolute uncertainty is the total range within which the true value of a measurement is expected to lie.
The formula for absolute uncertainty is:
x = (x ± e) units of measure
Significant Figures
Significant figures are important in indicating the precision of a measurement. For example, 79.40 cm could have a significant figure of 0.45, which would be rounded to 0.5 cm.
Sensitivity
Sensitivity refers to how much the measurement may vary. For instance, a sensitivity of 0.5 cm would mean that the measurement can vary by up to 5 mm.
Examples of Error Types
- Random Error Example: (60 ± 2)
- Systematic Error Example: (2332 ± 286)
When dealing with systematic errors, it is important to approximate the measurement to ensure that at least one figure is certain.
For instance:
- Incorrect: (2.85 ± 9.43)
- Correct: (2.85 ± 0.011)
Relative Uncertainty
Relative uncertainty is a measure of the uncertainty in a measurement relative to the size of the measurement itself.
The formula for relative uncertainty is:
e = (uncertainty / value) x 100%
Precision and Measurement
The precision of a measurement can be determined through the number of significant figures. For example, a measurement of (1000 ± 10) m is more precise than a measurement of (100.000 ± 10) m.
Conclusion
Understanding and accounting for random and systematic errors, absolute and relative uncertainties, as well as the significance of figures, are all crucial aspects of making accurate and reliable measurements in the field of physics.
