Physics - I keep messing up my conversion factors! - MCAT

The only conversion you will have to do is of prefixes, e.g., micro-whatsis to kilo-whatsis. No kilograms to slugs, or liters to hogsheads, or meters to chains, or…

For those who have trouble converting units, I suggest the following method:

First, forget the conversion factors listed in whatever reference material you’re using. They’re correct, of course, but if you’re having trouble they’re what’re mixing you up. Instead, just think in terms of big and small, as shown here. Also, eschew multiplying by negative exponents — divide instead. Finally, think of the units as variables, and cancel as you would with variables.

An example problem will show the method best. Lets say you want to know the speed of light, c = 3×10^8 m/s, but in cm/ms.

Write down 3×10^8 m/s on the left. Write down the units you want, cm/ms, on the right. Now multiple and divide to get rid of the m and the s, and to get cm and ms in the right spots:

Code:

3x10^8 m x _____cm x _____s_ = _______cm       s        m         ms          ms

Now fill in the numbers, which you should know, just focusing on which unit is bigger, and remembering that it takes more of the smaller ones to make a big one:

Code:

3x10^8 m x 10^2_cm x ___1_s_ = _______cm       s      1 m    10^3 ms          ms

Check to ensure that the old units cancel out, that you wind up with the new units, that you have more of the smaller units in each fraction (the fractions must each equal 1); now do the math:

Code:

3x10^8 m x 10^2_cm x ___1_s_ = 3x10^7_cm       s      1 m    10^3 ms          ms

Finally, never use a squared or cubed conversion factor: use the normal conversion factor, and square or cube it at the end. As another example, find the density of osmium in kg/m^3:

Code:

22.4 g___ x ___1_kg x (____cm)^3 = _______kg_     cm^3        g    (    m )^3          m^3

Code:

22.4 g___ x ___1_kg x (100_cm)^3 = 3x10^7_kg_     cm^3   1000 g    (  1 m )^3          m^3

Code:

22.4 g___ x ___1_kg x 10^6_cm^3 = 2.24x10^4_kg_     cm^3   1000 g       1 m^3              m^3

Notice that we filled in the cm/m conversion, which we know well, and squared at the end. Notice also that there’s no need to use scientific notation for many numbers — the notation is a tool, not an end in itself.