Prefixes
Simple Explanation
SI prefixes are small words (or symbols) added in front of a unit to represent it multiplied by a power of ten — for example, "kilo" means × 1000, and "milli" means × 0.001. They let very large or very small quantities be written with manageable numbers.
Why Do We Need It?
Prefixes avoid writing out long strings of zeros — a wavelength of light is far easier to read as 500 nanometres than as 0.0000005 metres.
Worked Example
Convert between a prefixed unit and the base unit
A capacitor is rated at 4.7 microfarads (μF). Express this value in farads (F), the base SI unit.
Why Does This Work?
Because each prefix is defined as an exact power of ten, converting a prefixed unit into its base unit is always just multiplying by that power of ten — no other adjustment is needed.
Real-Life Example
Reading a food nutrition label
A nutrition label lists vitamin content in micrograms (μg) and mineral content in milligrams (mg).
Using the right prefix for each nutrient keeps the numbers on the label small and readable, instead of listing amounts as tiny fractions of a gram.
Practice
A distance is 5 kilometres (km). Express this in metres.
EasyA signal has a wavelength of 650 nanometres (nm). Express this in metres, in scientific notation. (Enter just the coefficient, e.g. for 6.5 × 10⁻⁷, enter 6.5.)
MediumCommon mistake
Confusing similar-looking prefixes — especially "milli" (× 10⁻³) with "micro" (× 10⁻⁶), or "mega" (× 10⁶) with "milli" — a single mixed-up prefix changes an answer by a factor of a thousand or more.
Quick Review
- Common prefixes: giga (10⁹), mega (10⁶), kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹).
- A prefix always means "multiply the base unit by this power of ten."
- Always double-check which prefix is meant — mixing up milli and micro is a common error.