A student is researching astronomical distances and particle sizes for a science project. The student writes down the following measurements: the diameter of an atom as 0.0000000001 m, the wavelength of visible light as 0.0000005 m, the distance from Earth to the Moon as 384 000 000 m, and the mass of a proton as 0.0000000000000000000000000017 kg. Explain how using SI prefixes makes these measurements easier to work with, and convert two of the measurements above into appropriate SI prefix form.

AQA A-Level Physics (7408) — 3.1.1 Use of SI Units and Their Prefixes · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

Using SI prefixes removes long strings of zeros, making numbers shorter, easier to read and compare.

Each prefix represents a power of ten: for example, nano (n) = 10⁻⁹, pico (p) = 10⁻¹², mega (M) = 10⁶.

The diameter of an atom 0.0000000001 m = 1×10⁻¹⁰ m = 0.1 nm (or 100 pm).

The wavelength of visible light 0.0000005 m = 5×10⁻⁷ m = 500 nm.

The distance Earth–Moon 384 000 000 m = 3.84×10⁸ m = 384 Mm (or 384 000 km).

Examiner tips

  • Use the command word ‘Explain’ – give a short reason then give two conversions.
  • Show the power‑of‑ten form before converting to a prefix.
  • Include the unit with the prefix (e.g. nm, Mm).

Common mistakes

  • Writing 0.1 pm instead of 0.1 nm for the atom diameter.
  • Using the wrong prefix (e.g. µm for 500 nm).

Mark scheme (5 marks)

  1. SI prefixes replace many zeros, making measurements shorter / easier to read and compare
  2. Each prefix represents a specific power of ten (e.g. nano = 10⁻⁹, mega = 10⁶)
  3. Correct conversion of diameter of atom: 0.0000000001 m = 0.1 nm or 100 pm (accept 10⁻¹ nm)
  4. Correct conversion of wavelength of visible light: 0.0000005 m = 500 nm
  5. Correct conversion of Earth–Moon distance: 384 000 000 m = 384 Mm or 384 000 km (accept 3.84 × 10⁵ km)

Key terms in this question

prefix

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