# Section 3.1 Measurements and their errors

Content in this section is a 'continuing study' for a student of physics.

A recall of the symbols and working knowledge of the specified fundamental (base) units of measurement is vital.

Likewise, practical work in the subject needs to be underpinned by an awareness of the nature of measurement errors and of their numerical treatment. The ability to carry through reasonable estimations is a skill that is required throughout the course and beyond.

This section deals with this essential 'core knowledge'.

 Useful background You should be able to: 3.1.1 Use of SI units and their prefixes Fundamental (base) units. Use of mass, length, time, amount of substance, temperature, electric current and their associated SI units. SI units derived. Knowledge and use of the SI prefixes, values and standard form. The fundamental unit of light intensity, the candela, is excluded. Students are not expected to recall definitions of the fundamental quantities. Dimensional analysis is not required. Students should be able to use the prefixes: T, G, M, k, c, m, μ, n, p and f. Students should be able to convert between different units of the same quantity, eg J and eV, J and kW h. Base and derived units Learning aid The physics alphabet Unit rules Learn the prefixes by singing them! Recall the units for physical quantities exactly.... correct case as well as letter. 3.1.2 Limitation of physical measurements Random and systematic errors. Uncertainty: Absolute, fractional and percentage uncertainties represent uncertainty in the final answer for a quantity. Represent uncertainty in a data point on a graph using error bars. Determine the uncertainties in the gradient and intercept of a straight-line graph. Individual points on the graph may or may not have associated error bars. Errors - a comprehensive discussion of them - originally circulated by AQA in 2001 - identify random and systematic errors and suggest ways to reduce or remove them. - understand the link between the number of significant figures in the value of a quantity and its associated uncertainty. - be able to combine uncertainties in cases where the measurements that give rise to the uncertainties are added, subtracted, multiplied, divided, or raised to powers. Combinations involving trigonometric or logarithmic functions will not be required. 3.1.3 Estimation of physical quantities Orders of magnitude. Estimation of approximate values of physical quantities. - be able to estimate approximate values of physical quantities to the nearest order of magnitude. - be able to use these estimates together with their knowledge of physics to produce further derived estimates also to the nearest order of magnitude.