Unit Conversion
Unit conversion is rewriting a measurement in a different unit by multiplying by a ratio equal to one, such as 100 cm per 1 m.
Definition
Unit conversion means changing a measurement from one unit to another without changing the amount; the plant is the same height whether you say $8.5\ \text{cm}$ or $85\ \text{mm}$. It works by multiplying by a conversion factor, a fraction equal to one such as $\frac{1000\ \text{mL}}{1\ \text{L}}$, arranged so the unwanted unit cancels and the wanted unit remains; within the metric system the factors are powers of ten, and between systems they are fixed constants. Multi-step conversions chain factors, compound units such as m/s to km/h need a factor for each component, and squared or cubed units need the factor raised to the same power. Because a conversion factor is exact, the result keeps the significant figures of the original measurement.
Example
A ramp measured as $150\ \text{cm}$ is $1.5\ \text{m}$, since $100\ \text{cm} = 1\ \text{m}$. Converting $0.35\ \text{L}$ of water: $0.35\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 350\ \text{mL}$, which is also $350\ \text{cm}^3$ and, at $1.00\ \text{g/cm}^3$, $350\ \text{g}$. A cart speed of $2.40\ \text{m/s}$ becomes $2.40\ \frac{\text{m}}{\text{s}} \times \frac{1\ \text{km}}{1000\ \text{m}} \times \frac{3600\ \text{s}}{1\ \text{h}} = 8.64\ \text{km/h}$, and $2.5\ \text{m}^3$ becomes $2.5\ \text{m}^3 \times \left(\frac{100\ \text{cm}}{1\ \text{m}}\right)^3 \times \frac{1\ \text{L}}{1000\ \text{cm}^3} = 2500\ \text{L}$.
Key Insight
Ask whether the answer should be a bigger or smaller number: meters are bigger than centimeters, so the number of meters should be smaller. Writing the units in every step and canceling them like factors catches almost every conversion mistake before it happens. A conversion factor is exactly one, so it can never change the physics, only the label, and a converted value with a different number of significant figures from the original was converted wrong.