Students should be able to use the prefixes: T,G, M, k, c, m, μ, n, p, f,…

The idea

Each prefix represents a power of ten: 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. To convert, multiply or divide by the appropriate power of ten, or use a known equivalence such as 1 eV = 1.60 × 10⁻¹⁹ J and 1 kW h = 3.6 × 10⁶ J. For example, 2.5 GJ = 2.5 × 10⁹ J, and 500 nm = 500 × 10⁻⁹ m = 5.0 × 10⁻⁷ m. Always check that the converted value is sensible and that the unit matches the quantity.

What earns the marks

• 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.

Common mistakes and how to put them right

• Reversing the direction of a conversion, for example multiplying by 10⁶ when converting from μF to F.

  Put it right: Multiply by 10⁻⁶ as micro means 10⁻⁶.

• Confusing the prefix m (milli, 10⁻³) with the unit symbol m for metre.

  Put it right: Read the context and write units unambiguously.

• Using 1 eV = 1.60 × 10¹⁹ J instead of 1.60 × 10⁻¹⁹ J.

  Put it right: Remember that the electronvolt is much smaller than the joule.

• Forgetting that 1 kW h equals 3.6 × 10⁶ J rather than 1000 J.

  Put it right: Convert kilowatts to watts and hours to seconds before multiplying.

Exam tips

• 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.