For A-level physics and equivalent courses you often need to work out areas or volumes, and express these in m2 and m3 when they have been given to you in other units, such as mm2 or cm3 (Mathskit, PHYSICS REVIEW Vol. 26, No. 4, pp. 30–32). For example, you might be given the diameter of a wire in mm and need to know its area in m2 for calculations involving stress. Or you might be told the volume of a container in cm3 and need to convert into m3. (Exam talkback on pp. 23–26 has other examples of area and volume calculations where you need to convert the units.) It is all too easy to get these conversions wrong and drop marks, so the aim of this Mathskit is to help you get it right every time.
You will be expected to convert from length measurements of mm or cm to m, and to convert areas and volumes into m2 and m3, respectively. A key point to bear in mind is that the prefixes (centi = 10–2, milli = 10–3 and so on) apply to the units of length, not directly to the units of area or volume. So, for example, you cannot just use a factor of 103 to convert between mm3 and m3. Do not try to remember all the conversions for areas and volumes based on cm and mm — there are too many, and it is easy to remember them wrongly. It is much safer to work directly from the units of length, and it only takes a few seconds.
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