Revision Notes on Measurement

Physical Quantities

Physical quantities are classified as base(or fundamental) quantities and derived quantities. 7 base quantities are chosen to form the base units.

Base Quantity Base Unit
mass kg
length m
time s
Current A
Temperature K
Amount of Substance mol
Luminous Intensity cd

 Any other physical quantities can be derived from these base quantities. These are called derived quantities.

Standard Prefixes

Prefixes are attached to a unit when dealing with very large or very small numbers.

Power Prefix Symbol
10-12 pico p
10-9 nano n
10-6 micro µ
10-3 milli m
10-2 centi c
10-1 deci d
103 kilo k
106 Mega M
109 Giga G
1012 Tera T

Homogeneity of A Physical Equation

A physical equation is said to be homogeneous if each of the terms, separated by plus, minus, equality or inequality signs has the same base units.

Uncertainty

Uncertainty in measurements is unavoidable and estimates the range within which the answer is likely to lie. This is usually expressed as an absolute uncertainty Δa, but can be given as a percentage uncertainty (Δa/a) x 100.
The normal way of expressing a measurement a, with its uncertainty, Δa, is a ± Δa. This means that the true value of the measurement is likely to lie in the range a – Δa to a + Δa.

Very frequently, the values of two or more quantities such as a and b are measured and then these are combined to determine another quantity Y. In that case, the absolute or percentage uncertainty of Y can be calculated as follows:

1. If Y = a + b or Y = a – b, then ΔY = Δa + Δb

2. If Y = ab or a/b , then ΔY/Y = Δa/a + Δb/b

3. If Y = apbq/cr, then ΔY/Y = pΔa/a + qΔb/b + rΔc/c

Error

An error is systematic if repeating the measurement under the same conditions yields readings with error of same magnitude and sign. Readings with systematic error change in a predictable manner depending on external conditions. Systematic error can be eliminated by making corrections for it if the cause of the systematic error is known, for example, the zero error of a micrometer can be determined and be subtracted from the observed reading, or the measuring instrument can be recalibrated.

An error is random if repeating the measurement under the same conditions yields readings with error of different magnitude and sign. Readings with random error spread over a certain range within which a mean value may be determined. Taking repeat readings and finding the mean is therefore a way of minimizing random error.

Accuracy and Precision

The accuracy of an experiment is a measure of how close a measured value is to the true value. It is a measure of the correctness of the result.

The precision of an experiment is a measure of how exact the result is without reference to what that the result means. It is a measure of how reproducible the results are, i.e. it is a measure of how small the uncertainty is.

Vectors and Scalars

A vector quantity has magnitude and direction.
A scalar quantity has magnitude only.