Metric prefixes are numerical

Part of my units pages

It’s well known that metric quantities are related by powers of 10, for example:

We can use these relationships to figure out the meaning of the prefixes “c”, “k” and “m” (taking care to distinguish between “m” standing for “metre”, and “m” standing for “milli”; which is definitely annoying!).

The first tells us that “c” (“centi”) is a hundredth:

100cm = 1m
100c  = 1
   c  = 1/100

The second tells us that “m” (“milli”) is a thousandth:

10mm = 1cm
10m  = 1c
10m  = 1/100
  m  = 1/1000

The third tells us that “k” (“kilo”) is a thousand:

1kN = 1000N
 k  = 1000

Notice that these are statements about numbers, not units. Indeed, in each case the units immediately cancelled-out!

This isn’t specific to metric units either: we can do the same with inches, pounds, etc.

There’s also nothing special about ten: there are convenient factors for many bases, e.g. 3Kim = 3072m