Dimensional Analysis, oooh!

Although the name can sound daunting, it's quite simple and follows basic Math 9 concepts like x/x=1

Dimensional Analysis:

ex. converting 100km/h into miles/hour

It's just like converting currencies in Chemistry, it is usually necessary to convert between units

There are FOUR SIMPLE STEPS to Dimensional Analysis, and once you have a lot of experience with this in the bag, you can skip steps!

1) Find a unit equality

2) Find the conversion factors

3) Apply the conversion factor

4) Cancel units

Sounds complicated? Here are a few examples to simplify it a bit, showing precisely how the though process works through these steps:

ex 1. How many miles are equal to 120 km?
Step 1-  1 mile = 1.6 km

Step 2- 1= 1 mile/ 1.6 km

Step 3- 120 km x 1 mile/1.6 km

Step 4- 75 miles

In Step 2, we can find that conversion factor because if we know that 1 mile= 1.6 km, then 1 mile/1.6 km must equal to 1 (just like 1/1= 1, 5/5=1)

As you can see, the 'km' isn't in the final answer, because it cancels out

Here is a slightly more complicated example (converting the top and bottom of the equation, weehoo!)

ex.2 Convert 150 kJ/h into J/s

Step 1- 1000 J = 1 kJ         3600= 1 h

Step 2- 1= 1000 J/ 1 kJ      1= 1 h/3600 s

Step 3- 150 kJ/ 1 h  x 1000J/ 1 kJ x  1 h/ 3600 s = 150 000 J/ 3600 s

Step 4- 41.7 J/s

In step 3, the 'kJ' is on the bottom (denominator) while the 'h' is on the top (numerator) because in order for the units to cancel out, it has to be opposite (ex. on the bottom if it is at the top, at the beginning) of what we are trying to convert it from.