Unit conversions
A conversion factor is a fraction equal to 1, built from two equal quantities in different units. Since 1 km = 1000 m, both of these equal 1:
(1000 m / 1 km) and (1 km / 1000 m)
Multiplying by a conversion factor changes the units without changing the amount. Choose the version that cancels the unit you want to remove. This method is called dimensional analysis.
Common metric prefixes:
| Prefix | Symbol | Meaning |
|---|---|---|
| kilo | k | 1000 |
| centi | c | 1/100 |
| milli | m | 1/1000 |
Worked example: convert 2.5 km to centimeters
Go through meters, one step at a time.
2.5 km × (1000 m / 1 km) × (100 cm / 1 m) = 250 000 cm
Kilometers cancel in the first step and meters cancel in the second, leaving centimeters.
Common mistake
Using the conversion factor upside down. If the unwanted unit does not cancel, flip the fraction. Writing the units in every step makes this error easy to see.