Prefixes & Unit Conversions
Prefixes & Unit Conversions
- A is a power of ten written in front of a unit, so that very big and very small numbers stay short.
- The safe method for every conversion: replace the prefix with its power of ten first, then do the arithmetic.
The prefixes
| Prefix | Symbol | Multiplier |
|---|---|---|
| pico | p | 10⁻¹² |
| nano | n | 10⁻⁹ |
| micro | μ | 10⁻⁶ |
| milli | m | 10⁻³ |
| centi | c | 10⁻² |
| deci | d | 10⁻¹ |
| kilo | k | 10³ |
| mega | M | 10⁶ |
| giga | G | 10⁹ |
| tera | T | 10¹² |
Worked example
Smallest case: one prefix to another
Express 43 dJ in mJ.
- Replace the prefix: .
- Rewrite in the target prefix: .
Answer
(9702/12/O/N/21 Q2)
Common mistake
The two most-confused pairs: milli (m, 10⁻³) vs micro (μ, 10⁻⁶), and deci (d, 10⁻¹) vs centi (c, 10⁻²). Confusing milli and micro makes the answer wrong by a factor of 1000.
Squared and cubed units
- When a prefixed unit is squared or cubed, the power of ten is squared or cubed with it.
- The reason: cm² means (cm)², and the prefix is part of the unit. The picture below shows it as an area.
- Same idea in three dimensions: .
Worked example
One change: a compound unit
Convert 0.25 kN mm⁻² to N m⁻².
- The kilonewton: .
- The squared prefix: , so .
- Combine: .
Answer
(9702/12/M/J/25 Q2)
Worked example
One change: a density
Convert 1.0 g cm⁻³ (the density of water) to kg m⁻³.
- Mass: .
- Cubed prefix: .
- Divide: , so the density is .
Answer
When you square cm, the “centi” is squared too: 1 cm² = 10⁻⁴ m², not 10⁻² m². Forgetting this loses the mark.
Common mistake
Converting the number but not cubing the length: writing 1 cm³ = 10⁻² m³ (instead of 10⁻⁶) makes a density answer wrong by a factor of 10⁴.