(e) prefixes and their symbols to indicate decimal submultiples or…

The idea

The prefix pico, symbol p, means 10⁻¹² of the base unit. It is used for very small quantities, such as a picosecond (1 ps = 1 × 10⁻¹² s) or a picometre (1 pm = 1 × 10⁻¹² m). To convert a value in picometres to metres, multiply by 10⁻¹²; to convert metres to picometres, divide by 10⁻¹², which is the same as multiplying by 10¹². For example, 250 pm = 250 × 10⁻¹² m = 2.5 × 10⁻¹⁰ m. In calculations, replace the prefix with its power of ten before substituting into an equation.

What earns the marks

• State that pico (p) represents a factor of 10⁻¹².
• Convert a value given with the pico prefix into the base unit by multiplying by 10⁻¹².
• Convert a base-unit value into pico units by multiplying by 10¹².
• Use the correct symbol p and avoid confusing it with other prefixes such as n or μ.

Common mistakes and how to put them right

• Confusing pico with nano.

  Put it right: Pico is 10⁻¹² while nano is 10⁻⁹, so a picometre is one thousandth of a nanometre.

• Multiplying by 10¹² when converting from picometres to metres.

  Put it right: Multiply by 10⁻¹² to go from pm to m, and multiply by 10¹² to go from m to pm.

• Writing the prefix as a separate unit, such as 'p m' instead of 'pm'.

  Put it right: The prefix and unit symbol form one symbol, for example pm or ps.

Exam tips

• Replace the prefix with its power of ten immediately, before doing any other arithmetic.
• Check the direction of the conversion by asking whether the numerical value should become larger or smaller.
• Keep the prefix symbol attached to the unit symbol, for example write pm rather than p m.