Topic 2 of 5
Prefixes and physical scales
A prefix changes the size of a unit. Milli means one thousandth, so a millimetre is one thousandth of a metre.
The numerical value can change while the physical quantity stays the same. See quantities and units if that distinction is unfamiliar.
Powers of ten make very large and small numbers easier to write. 103 = 1000, while 10-3 = 1 / 1000 = 0.001. A negative exponent means a fraction here; it does not mean a negative length or current.
| Prefix | Symbol | Factor |
|---|---|---|
| nano | n | 10-9 |
| micro | ยต | 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 |
Capital letters matter: mA means milliamperes, but MA means megaamperes. The prefix kilo is lower-case k; the upper-case K is the unit kelvin.
Worked examples
Convert by replacing the prefixed unit
- Millimetres to metres: 1 mm = 0.001 m, so 3.2 mm = 3.2 x 0.001 m = 0.0032 m.
- Milliamperes to amperes: 1 mA = 0.001 A, so 250 mA = 250 x 0.001 A = 0.250 A.
- Metres to millimetres: 1 m = 1000 mm, so 0.0045 m = 0.0045 x 1000 mm = 4.5 mm.
Check the direction: expressing a length in a smaller unit needs a larger number of those units. There are 1000 millimetres in each metre.
Area and volume need more than one conversion
A square measuring 1 cm along each side has an area of 1 cm2. Each side is 0.01 m, so convert both dimensions when calculating its area.
The same reasoning applies to a cube: 1 cm3 = (0.01 m)3 = 0.000001 m3. Apply the length conversion to all three dimensions.
Does the size of the answer make sense?
An order of magnitude gives the approximate scale of a quantity as a power of ten. For example, 100 m is 1 m. The objects below vary in size; these values are useful reference scales, not exact measurements of every example.
| Object and dimension | Approximate scale |
|---|---|
| Diameter of an atom | 10-10 m |
| Width of a bacterium | 10-6 m |
| Width of a human hair | 10-4 m |
| Diameter of a coin | 10-2 m |
| Height of a person | 100 m |
| Diameter of Earth | 107 m |
If a calculation gives 0.02 m for the width of a human hair, pause: 0.02 m is 2 cm, about the width of a small coin. A hair is much thinner, with a width of roughly 10-4 m. Check the original reading and conversion before accepting the answer.