1.1 Physical quantities

A measurement is written as number×unit, such as 3.0 m. The unit states the scale, while the number changes when the unit is changed.

Keep significant figures consistent with the measurement uncertainty and convert units before substituting into equations.

2.5 km is 2500 m; the physical distance is unchanged even though the numerical value differs.

A bare number is not a complete physical measurement, and adding quantities with incompatible units is meaningless.

Base quantities such as mass, length and time are defined independently; derived quantities such as speed, force and energy are built from them by equations.

Identify the quantity before choosing a formula, then check whether it is scalar or vector and whether the units match the physical meaning.

Speed is distance divided by time, so its SI unit is m s⁻¹; acceleration adds another factor of s⁻¹.

A derived quantity is not less fundamental as a measurement; its unit reveals how the underlying quantities combine.