Although I do very well in chemistry I never really understood converting units.

Question

Perform each of the following conversions.
A. 8.43cm to millimeters
B. 2.41x10^2cm to meters
C. 294.5nm to cm
D. 1.445x10^4m to kilometers
E. 235.3m to millimeters
F. 903.3nm to micrometers

Answer 1

A factor converts any unit to any other unit. The factor used depends upon which unit you have and which unit you want.
For example. A.
There are 10 mm to 1 cm so the conversion factor is 10mm/1cm or you can write it the other way as 1 cm/10mm.
8.43 cm x factor = ? mm
Now we decide which of the factors to use.

So we can write it one of two ways.
8.43 cm x (10mm/1 cm) = ?. You note if we write it this way the cm units cancel (those are the units we don't want to keep) and the only unit left is mm is the unit we want to keep.

The other way of writing it is
8.43cm x (1 cm/10mm) = ?
Note that this way no unit cancels and we end up with an answer of ? cm^2/mm which is not what we want.

So of the two ways to write the factor you always use the one in which the unit you are changing from gets canceled and the unit you want to convert to is the only unit left.