1.2 SI units

The SI base units include kilogram (kg) for mass, metre (m) for length, second (s) for time, ampere (A), kelvin (K), mole (mol) and candela (cd).

Write symbols exactly, distinguish units from quantities and use the base set when checking an equation or converting a derived unit.

A force measured in newtons can be rewritten as kg m s⁻² using kg, m and s.

The symbol kg is already the base unit; prefixes such as g or ms do not replace the definition of the quantity.

Use the defining equation to express a derived unit in base units: N=kg m s⁻², J=kg m² s⁻² and W=kg m² s⁻³.

Treat unit algebra like algebra of powers, cancel common factors and check that the final dimensions match the quantity named.

Pressure is force/area, so Pa=N m⁻²=kg m⁻¹ s⁻².

A named unit such as joule is not dimensionless; replacing it with base units exposes the physical dimensions.

Every additive term in a valid equation must have the same dimensions, and both sides must match. Dimensions use base quantities such as [L], [T] and [M].

Do not use dimensional analysis to determine dimensionless numerical constants or prove an equation completely; it is a consistency test.

In s=ut+½at², both ut and at² have dimensions L, matching displacement s.

An equation can be dimensionally correct but physically wrong because of a missing factor or incorrect model.

Prefixes such as kilo (10³), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹) and pico (10⁻¹²) multiply the unit by a stated power of ten.

Convert the prefix before calculating, keep the exponent sign visible and distinguish a prefixed unit from a power of the base unit.

5.0 μm=5.0×10⁻⁶ m; 3.0 mm²=(3.0×10⁻³ m)²=9.0×10⁻⁶ m².

Squaring an area conversion squares the prefix factor too; converting 3 mm² as 3×10⁻³ m² is wrong.