Measurement and Practical Skills: Units, Errors and Data
Measurement and practical skills: reliable data
Physics measurements use SI units: metre, kilogram, second, ampere, kelvin, mole and candela, with derived units such as newton, joule, watt and ohm. Convert prefixes carefully: kilo = 10³, centi = 10⁻², milli = 10⁻³. Choose instruments to match the quantity: metre rule for length, vernier callipers or micrometer for small lengths, balance for mass, measuring cylinder for volume, thermometer for temperature, ammeter in series and voltmeter in parallel.
Accuracy means closeness to the true value; precision means closeness of repeated readings to one another. Random errors scatter readings and are reduced by repeating and averaging; systematic errors shift all readings in one direction, such as a zero error or incorrectly calibrated scale. Read scales at eye level to avoid parallax, and read the bottom of a meniscus for water. Record readings to the smallest division plus one estimated digit, and state uncertainty, often ± half the smallest division.
Present data in tables with units in headings. Plot graphs with labelled axes, suitable scales and a line of best fit; identify anomalous points and do not force the line through them. The gradient of a straight-line graph often gives the required quantity. State the conclusion in terms of the hypothesis and comment on reliability, sources of error and improvements.
Traps: mixing units in one calculation; quoting more significant figures than the instrument allows; calling a precise set of readings accurate when it is offset; and drawing a join-the-dots graph instead of a best-fit line.
Worked example: Readings 2.10, 2.20, 2.00 and 2.10 cm give a mean of 2.10 cm. If the smallest division is 0.1 cm, the uncertainty is about ±0.05 cm, so the percentage uncertainty is (0.05/2.10) × 100 ≈ 2.4%.