Measurements and uncertainties: precision and accuracy, random and systematic errors, absolute, fractional and percentage uncertainty, and combining uncertainties in sums, products and powers.

What this dot point is asking

OCR wants you to distinguish precision from accuracy and random from systematic error, express an uncertainty in absolute, fractional and percentage form, and combine uncertainties correctly when quantities are added, multiplied, divided or raised to a power.

The answer

Precision and accuracy

Random and systematic errors

Quantifying uncertainty

The percentage uncertainty is the most useful form because the rules for combining uncertainties through a calculation are stated in terms of percentages.

Combining uncertainties

Examples in context

In a Young modulus experiment the extension is small, so its percentage uncertainty dominates and is reduced by using a long wire and a travelling microscope. In radioactivity counting, random fluctuations follow a statistical spread, so longer counts give a smaller percentage uncertainty. Calibrating an ammeter against a known standard removes a systematic offset that repeating readings never could. Examiners reward quoting a result to a sensible number of significant figures consistent with its uncertainty.

Try this

Q1. Distinguish between precision and accuracy. [2 marks]

• Cue. Precision is the closeness of repeated readings to each other; accuracy is closeness of the mean to the true value.

Q2. A length is $(2.00 \pm 0.05)\ \text{m}$. State its percentage uncertainty. [1 mark]

• Cue. $\frac{0.05}{2.00} \times 100 = 2.5\%$.

Q3. A quantity $Q = ab^2$. The percentage uncertainties are $3\%$ in $a$ and $2\%$ in $b$. Find the percentage uncertainty in $Q$. [2 marks]

• Cue. $3 + (2 \times 2) = 3 + 4 = 7\%$.