Unit conversion

A conversion factor links two units, like $1$ meter $= 100$ centimeters.
To change into a smaller unit you multiply (a meter is many centimeters), and to change into a larger unit you divide.

Some common factors are worth knowing.
For length, $1$ m $= 100$ cm $= 1000$ mm and $1$ km $= 1000$ m.
For time, $60$ seconds $= 1$ minute and $60$ minutes $= 1$ hour.
For volume, $1$ liter $= 1000$ milliliters.

Area and volume are the classic trap.
Since an area is a length times a length, you must square the conversion factor: because $1$ m $= 100$ cm, $1$ m² $= 100 \times 100 = 10{,}000$ cm².
For volume you cube it, so $1$ m³ $= 1{,}000{,}000$ cm³.

Angles convert between degrees and radians using $\pi \text{ radians} = 180^\circ$.
To go from degrees to radians, multiply by $\frac{\pi}{180}$; the other way, multiply by $\frac{180}{\pi}$.
For example, $60^\circ \times \frac{\pi}{180} = \frac{\pi}{3}$.

Very large numbers are easiest as powers of $10$.
One million is $10^6$, one billion is $10^9$, and one trillion is $10^{12}$.
So $2.8$ trillion is $2.8 \times 10^{12}$.

How many millimeters are in $45.6$ meters?
There are $1000$ millimeters in a meter, and millimeters are smaller, so multiply.
So $45.6 \times 1000 = 45{,}600$ millimeters.

Given that $1$ yard $= 3$ feet, how many square feet are in $1$ square yard?
Area means you square the conversion factor.
So $1 \text{ yd}^2 = 3^2 \text{ ft}^2 = 9$ square feet.

Convert $\frac{\pi}{4}$ radians to degrees.
To go from radians to degrees, multiply by $\frac{180}{\pi}$.
So $\frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45^\circ$.