Use of SI units and their prefixes — AQA A-Level Physics

This topic introduces the International System of Units (SI), which provides a consistent framework for all physical measurements. You will learn the seven SI base units, the derived units formed from them, and the prefixes that scale units by powers of ten, from pico (10^-12) to tera (10^12). Mastery of unit conversion is essential because every calculation in A-Level Physics depends on using consistent SI units.

Understanding SI units and prefixes is fundamental to practical work, data analysis, and problem-solving across all areas of physics, including mechanics, electricity, and waves. It also underpins correct use of standard form and significant figures, which are assessed throughout the AQA specification. This topic often appears in exam questions as a standalone conversion task or as a required step within longer calculations.

• →The seven SI base units are: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
• →Derived units are combinations of base units, such as newton (N = kg m s^-2), joule (J = kg m^2 s^-2), and watt (W = kg m^2 s^-3).
• →Prefixes are powers-of-ten multipliers: tera (10^12), giga (10^9), mega (10^6), kilo (10^3), centi (10^-2), milli (10^-3), micro (10^-6), nano (10^-9), pico (10^-12).
• →When converting units with powers, the prefix conversion factor must also be raised to that power (e.g., 1 cm^2 = 10^-4 m^2, 1 cm^3 = 10^-6 m^3).
• →Standard form (a x 10^n, where 1 <= a < 10) is used to express very large or very small quantities clearly and to avoid errors in calculation.

• State that fundamental units are the independently defined SI units from which all other units are derived.
• List the seven base quantities and their SI units: mass (kg), length (m), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol) and luminous intensity (cd).
• Distinguish base units from derived units, giving examples such as m s⁻¹ for speed and kg m s⁻² for force.
• Use base units to check the homogeneity of a physical equation by substituting units for each quantity.
• Recognise that prefixes such as kilo, milli and micro modify a base unit without changing its fundamental character.
• Select the correct base quantity and unit for a given physical context, such as using kelvin for thermodynamic temperature.
• Convert prefixed values to base units before substitution, for example 50 mA to 0.050 A and 20 °C to 293 K where absolute temperature is required.
• Derive the unit of a calculated quantity from its defining equation, for example C = A s from Q = I t.
• Present answers with the correct unit symbol, including negative or positive indices where needed, such as m s⁻¹ or kg m⁻³.
• Check that both sides of an equation have the same base units when validating a relationship.
• State the defining equation for the quantity before substituting units.
• Replace each symbol with its SI base unit, not with a named derived unit.
• Collect repeated base units into powers, for example m × m = m².
• Cancel units that appear on both sides of a division.
• Compare the derived combination with the named SI unit to confirm it is correct.
• Use negative indices for units in a denominator, for example m s⁻¹ rather than m/s.
• Recall the value of each required prefix as a power of ten.
• Convert from prefix form to base units by multiplying by the prefix value.
• Convert from base units to prefix form by dividing by the prefix value.
• Write numbers in standard form with the coefficient between 1 and 10.
• Apply the correct power of ten when raising a prefixed unit to a power, for example 1 cm² = 1 × 10⁻⁴ m².
• Keep units consistent throughout a calculation before combining quantities.
• Recall and apply the prefix values T = 10¹², G = 10⁹, M = 10⁶, k = 10³, c = 10⁻², m = 10⁻³, μ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹² and f = 10⁻¹⁵.
• Convert a value from one prefixed unit to another by adjusting the power of ten, for example from MHz to Hz or from pF to F.
• Convert between joules and electronvolts using 1 eV = 1.60 × 10⁻¹⁹ J, choosing multiplication or division correctly.
• Convert between joules and kilowatt hours using 1 kW h = 3.6 × 10⁶ J, including values given in MJ or GJ.
• Present converted values in standard form with an appropriate number of significant figures and the correct unit.

• 💡Learn the seven base quantities and their units as a fixed list so you can recall them without a data sheet.
• 💡When asked to show a unit is derived, substitute the defining equation and cancel to base units rather than quoting the named unit alone.
• 💡In dimensional checks, treat numerical factors and pure numbers as dimensionless and compare only the unit combinations.
• 💡Write units with correct spacing and index notation, for example kg m s⁻², so the examiner can follow your reasoning.
• 💡Write down the equation, rearrange it, then substitute values with units so errors in unit handling are visible.
• 💡Convert all data to base units at the start of a calculation and state the conversion briefly.
• 💡Give final answers to an appropriate number of significant figures and include the unit; a missing unit can lose credit.
• 💡Use standard unit symbols and spacing, for example N m⁻¹ rather than N/m, to avoid ambiguity.
• 💡Write the defining equation first, then substitute units line by line so the examiner can follow your reasoning.
• 💡Keep negative indices rather than fractions, as this makes cancellation clearer and matches the expected notation.
• 💡Check the final combination against the named unit; if it does not match, re-examine which equation you used.
• 💡Convert every quantity to base SI units before substituting into an equation, then convert the final answer back if a prefix is requested.
• 💡Show the conversion factor explicitly, for example × 10⁻³, so method marks are visible.
• 💡Check the sign and size of the power of ten against the physical scale of the quantity.
• 💡Write the prefix as a power of ten immediately above the value before doing any arithmetic, so the conversion factor is visible and less likely to be inverted.
• 💡For energy conversions, set out the equivalence as a ratio and cancel units explicitly to confirm the final unit.
• 💡Give answers in standard form when the power of ten is large or small, and keep the same number of significant figures as the data unless told otherwise.
• 💡Always write down the prefix as a power of ten before substituting into an equation. This reduces errors and makes your method clear to the examiner.
• 💡Check that your final answer has the correct SI unit and is in standard form if the question asks for it. Marks are often awarded for correct unit and standard form.
• 💡When converting squared or cubed units, apply the power to both the numerical factor and the prefix. For example, 1 mm^3 = (10^-3)^3 m^3 = 10^-9 m^3.

• Treating the newton or joule as a fundamental unit; correct this by expressing each in base units, for example N = kg m s⁻² and J = kg m² s⁻².
• Writing the unit of mass as gram rather than kilogram; the SI base unit of mass is the kilogram, and gram is a prefixed form.
• Omitting the ampere or kelvin from the list of base units; both are fundamental, with the kelvin used for thermodynamic temperature.
• Confusing amount of substance with mass; amount of substance is measured in moles, while mass is measured in kilograms.
• Substituting a value in centimetres or milliamperes directly into an equation; convert to metres or amperes first so the result is in coherent SI units.
• Using degrees Celsius in the ideal gas equation instead of thermodynamic temperature in kelvin; add 273 to convert.
• Writing the unit of amount of substance as grams or as a number without a unit; the correct unit is the mole, mol.
• Leaving a calculated answer without a unit or with an inconsistent unit; always attach the unit derived from the equation.
• Substituting a named derived unit such as N into a defining equation instead of its base-unit equivalent; correct by expanding N to kg m s⁻² first.
• Forgetting to square a unit when a quantity is squared, for example writing kg m s⁻² for kinetic energy; correct by squaring every factor, giving kg m² s⁻².
• Treating the mole or kelvin as if it were dimensionless; correct by including mol or K wherever the defining equation contains amount of substance or temperature.
• Confusing milli and micro, treating 1 mm as 1 × 10⁻⁶ m; correct by learning 1 mm = 1 × 10⁻³ m and 1 μm = 1 × 10⁻⁶ m.
• Squaring or cubing only the number and not the prefix value, for example treating 1 cm³ as 1 × 10⁻² m³; correct by cubing the whole conversion, giving 1 × 10⁻⁶ m³.
• Writing standard form with a coefficient outside the range 1 to 10, such as 25 × 10³; correct by rewriting as 2.5 × 10⁴.
• Reversing the direction of a conversion, for example multiplying by 10⁶ when converting from μF to F; the correction is to multiply by 10⁻⁶ as micro means 10⁻⁶.
• Confusing the prefix m (milli, 10⁻³) with the unit symbol m for metre; the correction is to read the context and write units unambiguously.
• Using 1 eV = 1.60 × 10¹⁹ J instead of 1.60 × 10⁻¹⁹ J; the correction is to remember that the electronvolt is much smaller than the joule.
• Forgetting that 1 kW h equals 3.6 × 10⁶ J rather than 1000 J; the correction is to convert kilowatts to watts and hours to seconds before multiplying.
• Students often think that prefixes change the physical quantity itself, but they only change the scale of the unit. For example, 1 km and 1000 m represent the same length.
• Students frequently forget to square or cube the prefix conversion factor when dealing with area or volume. For example, 1 m^2 = 10^4 cm^2, not 100 cm^2.
• Students sometimes confuse 'micro' (10^-6) with 'milli' (10^-3) or 'nano' (10^-9), leading to answers that are out by factors of 1000 or more.

1. 1Day 1: Learn the seven SI base units and their symbols. Test yourself by writing them from memory.
2. 2Day 2: Memorise the common prefixes and their powers of ten. Create flashcards for tera, giga, mega, kilo, centi, milli, micro, nano, and pico.
3. 3Day 3: Practise converting between prefixed units and base units, including squared and cubed units. Use textbook or online questions.
4. 4Day 4: Apply unit conversions to derived units (e.g., N, J, W) and check consistency in equations.
5. 5Day 5-7: Complete past paper questions on this topic and review any errors. Focus on standard form and significant figures.

• 📋Multiple-choice questions asking for the correct conversion between prefixed and base units. Advice: eliminate options by writing the prefix as a power of ten.
• 📋Short-answer calculations requiring you to convert units before substituting into an equation. Advice: always show your conversion step clearly.
• 📋Structured questions asking you to express a quantity in SI base units or standard form. Advice: check the number of significant figures required and include units.
• 📋Practical-based questions where you must identify the appropriate unit for a measurement or convert experimental data. Advice: pay attention to the context and use the correct prefix for the scale of the measurement.