Knowledge and use of the SI prefixes, values and standard form.

The idea

SI prefixes scale a unit by powers of ten. You must know their values and convert fluently between prefix form, ordinary decimal form and standard form. For example, 1 km = 1 × 10³ m, 1 mm = 1 × 10⁻³ m, 1 μs = 1 × 10⁻⁶ s and 1 nm = 1 × 10⁻⁹ m. To convert, multiply or divide by the prefix value: 2.5 km = 2.5 × 10³ m = 2500 m, and 4700 Ω = 4.7 × 10³ Ω = 4.7 kΩ. In calculations, convert all quantities to base units before substituting, then present the answer with a sensible prefix. Standard form a × 10ⁿ, where 1 ≤ a < 10, keeps very large and very small values readable and reduces place-value errors.

What earns the marks

• 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.

Common mistakes and how to put them right

• Confusing milli and micro, treating 1 mm as 1 × 10⁻⁶ m.

  Put it right 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.

  Put it right 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.

  Put it right by rewriting as 2.5 × 10⁴.

Exam tips

• 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.