Recall and use multiples and sub-multiples of units, including giga (G),…

The idea

This criterion asks you to know the prefixes giga (G), mega (M), kilo (k), centi (c), milli (m), micro (μ) and nano (n), and to convert between a prefixed unit and the base unit. Learn the powers of ten: G = 10⁹, M = 10⁶, k = 10³, c = 10⁻², m = 10⁻³, μ = 10⁻⁶ and n = 10⁻⁹. To convert to the base unit, multiply by the power of ten, so 3 kΩ = 3 × 10³ Ω = 3000 Ω and 5 mA = 5 × 10⁻³ A = 0.005 A. To convert back, divide by the same factor. Check the direction of the conversion and keep the sign of the index.

What earns the marks

• Matches each prefix to its power of ten, such as kilo to 10³ and nano to 10⁻⁹.
• Converts a prefixed value to the base unit by multiplying by the correct power of ten, for example 4 kΩ to 4000 Ω.
• Converts a base-unit value to a prefixed unit by dividing by the correct power of ten, for example 0.002 A to 2 mA.
• Keeps the correct sign and magnitude of the index when converting, such as treating micro as 10⁻⁶ rather than 10⁶.

Common mistakes and how to put them right

• Reverses the direction of conversion.

  Put it right: Multiply by the power of ten to reach the base unit and divide to reach the prefixed unit.

• Confuses mega and milli because both begin with m.

  Put it right: Use capital M for 10⁶ and lower-case m for 10⁻³.

• Drops the negative sign on a sub-multiple index.

  Put it right: Keep micro as 10⁻⁶ and nano as 10⁻⁹.

• Treats centi as 10⁻³.

  Put it right: Use 10⁻² for centi and 10⁻³ for milli.

Exam tips

• Write the prefix as a power of ten first, then do the multiplication or division, so the direction is clear.
• Watch the capital or lower-case letter, because M and m mean very different factors.
• Estimate the size of the answer to check the conversion, since a kilo value should become a larger number in base units.
• Keep the negative index for sub-multiples such as milli, micro and nano rather than writing a positive power.