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Unit Conversion


Many people have problems converting units from one type to another, commonly there are questions such as:

"If I change from millimetres to metres do I multiply or divide by 1000?"

With this method, you will no longer have to worry about this confusion. There are a couple of simple steps which I will describe with an example, we want to convert metres per second into kilometres per hour

1: Write down what you want to convert
V = 15m/s

2: Write down necessary conversions
1000m = 1km
3600 seconds = 1 hour

3: Multiply by 1
this is easiest shown by example but basically we have:
1000m = 1km
Therefore [math]1 = \frac{1km}{1000m}[/math]
and 3600 seconds = 1 hour [math]1 = \frac{1hr}{3600s}[/math]

we can substitute these 1's into our 15m/s which becomes:
[math]V = 15\frac{\frac{m\color{red}km}{\color{red}1000m}}{\frac{s\color{blue}hr}{\color{blue}3600s}}[/math]

because we have multiplied by 1, the result is unchanged only now we have a more complicated way to write it with more units and fractions which will soon be removed.

4: Cancel and multiply out
[math]V = 15\frac{3600km}{1000hr}[/math] which becomes
[math]V = 54\frac{km}{hr}[/math]


This method is simple and effective. It's only problem is that it takes more time but it is worth it if you often make simple mistakes in unit conversions.