Introduction

Physics is fundamentally a quantitative science — its laws are stated as precise numerical relationships between measured quantities, not vague qualitative descriptions. Every measurement is, at its core, a comparison: when we say the length of a wire is $5\ \text{m}$, we are stating that the wire is five times as long as an internationally agreed reference length called the metre. The number ($5$) tells us 'how many' and the unit ($\text{m}$) tells us 'of what standard', and a measurement is meaningless without both parts stated together — '5' alone answers nothing, and 'metre' alone specifies no particular length.

We measure physical quantities constantly in everyday life — the size of objects, the volume of liquids, the amount of matter in something, the weight of vegetables or fruits, body temperature, the length of cloth — and each of these needs its own family of standard units, because different physical quantities are fundamentally different in kind (a length cannot meaningfully be compared to a mass). For example, to measure the mass of a fruit we compare it against standard mass units such as $1\ \text{kg}$ or $500\ \text{g}$; these agreed reference quantities are called units. A measured quantity is always expressed as a number followed by its unit, e.g. length in metre (m), time in seconds (s), mass in kilogram (kg).

For measurement to be useful across laboratories, industries and countries, the reference standard for each unit must be fixed, reproducible and internationally accepted — otherwise a 'kilogram' in one place could silently mean something different from a 'kilogram' elsewhere. This need for a single, self-consistent, universally accepted family of units is what led to the System International (SI) of units, and this chapter builds up from first principles: what counts as a fundamental quantity, how derived quantities and units are built from them, how measurements of length, mass and time are actually carried out in practice across scales from the atomic to the astronomical, how dimensional analysis lets us check and even derive physical relationships, and how to honestly quantify the uncertainty that is present in every real measurement.