FHSST Biology/How to Change Units

How to Change Units
Firstly you obviously need some relationship between the two units that you wish to convert between. Let us demonstrate with a simple example. We will consider the case of converting millimeters (mm) to meters (m)&mdash;the SI unit of length. We know that there are 1000 mm in 1 m which we can write as

$$\begin{matrix}1000 \mbox{ mm} = 1 \mbox{ m}\end{matrix}$$.

Now multiplying both sides by

$$\frac{1}{1000\mbox{ mm}}$$

we get

$$\begin{matrix}\frac{1}{1000 \mbox{ mm}}1000 \mbox{ mm}=\frac{1}{1000 \mbox{ mm}}1 \mbox{ m}\end{matrix}$$,

which simply gives us

$$\begin{matrix}1=\frac{1 \mbox{ m}}{1000 \mbox{ mm}}\end{matrix}$$.

This is the conversion ratio from millimeters to meters. You can derive any conversion ratio in this way from a known relationship between two units. Let's use the conversion ratio we have just derived in an example:

Question: Express 3800 mm in meters.

Answer:

$$\begin{matrix}3800 \mbox{ mm} & = & 3800 \mbox{ mm} \times 1\\& = & 3800 \mbox{ mm} \times \frac{1\mbox{ m}}{1000 \mbox{ mm}}\\& = & 3.8 \mbox{ m}\\\end{matrix}$$.

Note that we wrote every unit in each step of the calculation. By writing them in and canceling them properly, we can check that we have the right units when we are finished. We started with mm and multiplied by $$\frac{\mbox{m}}{\mbox{mm}}$$

This canceled the mm leaving us with just m&mdash;the SI unit we wanted to end up with! If we wished to do the reverse and convert metres to millimeters, then we would need a conversion ratio with millimeters on the top and meters on the bottom.

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