Types of Error
- Systematic error — a consistent, reproducible bias, e.g. always using an assumed value of g = 10 m/s² instead of the true 9.8 m/s² in a calculation like . Every result is shifted the same way.
- Random error — unpredictable fluctuation from one reading to the next.
- Variability in repeated readings isn't always due to only one cause — it can come from measurement error, real variation in the quantity itself, or both, so "I or II" (rather than a single definite cause) is often the most correct general answer.
Reading Error and Instrument Precision
Reading error is conventionally half the smallest division on an instrument's scale.
Worked example: a speedometer marked 0, 20, 40, 60, 80 km/h with 5 subdivisions between marks: smallest division = 20/5 = 4 km/h, so reading error = ±4/2 = ±2 km/h.
Choosing the Right Instrument
| Instrument | Typical precision | Best for |
|---|---|---|
| Meter rule | 1 mm (coarsest — biggest calibration error) | Long lengths (tens of cm+) |
| Vernier caliper | 0.02 mm | Medium objects (a phone, a small block) |
| Micrometer screw gauge | 0.01 mm (finest) | Very small objects/thin wires (typically 0-25 mm range) |
Worked example: measuring a phone (~14-15 cm long) — a micrometer's jaw range is too small (0-25 mm) and a meter rule's 1 mm divisions are too coarse, so the vernier caliper is the most accurate practical choice.
Percentage Error vs Relative Error
Relative error (a plain fraction); percentage error . Dividing the percentage error by 100% recovers the relative error.
Error Propagation Rules
- For : the relative error in y equals the relative error in x (a power-rule result).
- For a product like P×V: relative errors add — .
Pressure & the Fortin Barometer
The SI unit of pressure is the Pascal. Atmospheric pressure is measured with a Fortin barometer; the Boyle's law apparatus in the teaching lab uses a Bourdon gauge.
Why This Matters for Your Exams
Whenever a question asks "which instrument is most accurate/has the biggest error," compare the smallest scale division of each instrument listed — smaller division always means smaller (better) reading error.