Measurement

Measurement tells us “how much” of a physical quantity there is. To compare results, we use standard units and careful methods so that results are trustworthy.

Key quantities and SI units

• Length: metre (m)
• Time: second (s)
• Mass: kilogram (kg)
• Temperature: kelvin (K) or degree Celsius (°C)
• Volume: cubic metre (m³) or litre (L)

Choosing and using instruments

• Use a suitable instrument: ruler or tape (length), measuring cylinder (volume), balance (mass), thermometer (temperature), stopwatch (time).
• Resolution: the smallest change an instrument can reliably show. Match your recorded decimal places to this resolution.
• Place your eye level with the scale to avoid parallax error (a wrong reading because of viewing angle).
• Check for zero error. If an instrument does not read zero when nothing is measured, correct for it.

Accuracy, precision, repeats

• True value: the value you would get with a perfect measurement.
• Accuracy: how close your result is to the true value (think of darts landing near the bullseye).
• Precision: how close your repeated results are to each other (darts tightly grouped, even if not at the bullseye).
• Repeatability: same method, same person, same equipment → similar results.
• Reproducibility: different person, method, or equipment → similar results.
• Validity: the experiment actually tests the question by controlling other variables.

Errors and uncertainty

• Random errors: unpredictable changes (e.g. reaction time). Reduce by repeating and averaging.
• Systematic errors: results are shifted the same way each time (e.g. zero error). Reduce by calibration or correction.

For repeats, estimate uncertainty using half the range:

$$\text{uncertainty} \approx \frac{\text{max} - \text{min}}{2}$$

Mean (average): $$\bar{x} = \frac{x_1 + x_2 + x_3 + \dots}{n}$$

Percentage uncertainty: $$\%\,\text{uncertainty} = \frac{\text{uncertainty}}{\text{mean}}\times 100\%$$

Significant figures

• Write measurements to match the instrument’s resolution.
• For calculated answers, use the same number of significant figures as the least in your data.

Common misconceptions

• Precise results are not always accurate; you can be consistently wrong.
• More decimals do not guarantee a better result; quality depends on the instrument and method.
• A valid experiment must control other variables, not just take many readings.