01. Measurement

Base and Derived Quantities

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

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

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

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.

Absolute uncertainty of a measurement of $x$ can be written as $\Delta x$. This means that true value of the measurement is likely to lie in the range $x-\Delta x$ to $x + \Delta x$.
Fractional uncertainty = $\dfrac{\Delta x}{x}$
Percentage uncertainty = $\dfrac{\Delta x}{x}\times100%$
If the values of two or more quantities such as $a$ and $b$ are measured and then these are combined to determine another quantity $Y$, the absolute or percentage uncertainty of $Y$ can be calculated as follows:
- If $Y = a\pm b$, then $\Delta Y = \Delta a+\Delta b$
- If $Y = ab$ or $Y = \frac{a}{b}$ , then $\frac{\Delta Y}{Y} =\frac{\Delta a}{a}+\frac{\Delta b}{b}$
- If $Y = a^n$ then $\frac{\Delta Y}{Y} = n\frac{\Delta a}{a}$

Systematic errors are errors that, upon repeating the measurement under the same conditions, yield readings with error of same magnitude and sign.
Random errors are errors that, upon repeating the measurement under the same conditions, yield readings with error of different magnitude and sign.

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.