Unit conversion
This is another area where students make frequent errors.
The aim of this section is to show a very simple and foolproof method for comverting units.
A conversion factor is the ratio of two identical quantities expressed in different units.
The ratio is arranged to cancel out the units that are not desired and to introduce those that are.
As a trivial example, in the imperial system 1 foot = 12 inches. It is desired to convert 4.0 ft to inches.
The conversion factor is the ratio of two identical quantities (12 in / 1 ft), and it multiplies the quantity to be converted, 4 ft. The ratio is arranged this way up so that the ft cancel out and the units in remain.
A very common error is to use unit conversions the wrong way round.
This is a correct representation of the quantity, but not in the form required.
If the units are kept in the calculation as above it will be immediately obvious when a conversion factor has been applied incorrectly.
When units are raised to a power, so must the conversion factor.
For example a car tyre pressure is specified as 28 psi (pounds (force) per square inch. Convert this to Pa (Newtons per square metre). The conversion factors are 1 lbf (pound force) = 4.448 N, and 1 in = 2.54 cm.
for good measure the conversion from in to m has been done in 2 stages.