(a) physical quantities have a numerical value and a unit

The idea

Every physical quantity is expressed as a numerical value multiplied by a unit. For example, a length might be 2.5 m, where 2.5 is the numerical value and m is the unit. Without a unit, a numerical value is meaningless in physics: stating that a speed is 5 tells you nothing unless you know whether it is 5 m s⁻¹, 5 km h⁻¹ or 5 cm s⁻¹. You must be able to identify the numerical value and unit in any given quantity, choose appropriate SI units, and convert between prefixes such as kilo (10³), milli (10⁻³) and micro (10⁻⁶). The seven SI base units include the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd).

What earns the marks

• States that a physical quantity consists of a numerical value and a unit, and that both are required for the quantity to be meaningful.
• Identifies the numerical value and the unit in a given expression, such as 9.81 m s⁻² having numerical value 9.81 and unit m s⁻².
• Converts between SI prefixes, for example 1 km = 10³ m, 1 mm = 10⁻³ m, and 1 μs = 10⁻⁶ s.
• Recognises the seven SI base units and distinguishes them from derived units such as the newton (N) or joule (J).

Common mistakes and how to put them right

• Writing a numerical answer without a unit.

  Put it right: To attach the correct SI unit to every physical quantity.

• Confusing prefixes, for example treating 1 mm as 10⁻⁶ m instead of 10⁻³ m.

  Put it right: Learn the prefix powers of ten systematically.

• Assuming all units are SI base units.

  Put it right: Derived units such as the newton and joule are combinations of base units and are equally valid in calculations.

Exam tips

• Always write the unit alongside your numerical answer, even in multiple-choice questions where units may be part of the options.
• Check prefix conversions carefully: write out the power of ten before substituting into an equation.
• Learn the seven SI base units and be ready to express derived units in terms of them.