# Prefix factors

Dealing with very large or very small numbers can be awkward. To make life easier we can factor our quantities into multiples of some convenient magnitude. This approach is taken by scientific notation, and floating-point arithmetic. Linguistically, we can group a magnitude with a unit, by prefixing the unit’s name.

## All your bases

### Ten

In the metric and SI systems, it’s common to prefix the base unit of a dimension with a power-of-ten magnitude, like “centi”, “kilo”, “milli”, etc. to mean hundredth, thousand, thousandth, etc. Hence “three centimetres” is “three hundredth” metres; “five kilopascals” is “five thousand” pascals, etc.

There’s no reason we can’t do the same for any other quantity too; e.g. it’s perfectly correct (if a little unorthodox) to say that there are 100 centifeet in 1 foot and 1000 pounds in 1 kilopound. A listener might find it strange, but they could figure out what you meant.

Likewise, there’s no need to restrict ourselves to powers of ten when factoring quantities of metric/SI units.

## Two

The prefices
for powers of 2 are derived from the power-of-ten names, where
“kibi” is 2^{10} (symbol “Ki”; roughly a thousand), “mibi” is
2^{20} (symbol “Mi”; roughly a million), etc. These are used
almost exclusively for data sizes and rates, like an SSD with a 1TiB
capacity (one tibibyte, or 2^{40} bytes). Yet it’s perfectly
correct (if a little unorthodox) to say that 1Mim = 1,048,576m or that
there are one thousand and twenty four gallons in one kibigallon.

### Twelve

The prefix “dozen” refers to twelve, “gross” is a dozen dozen (144), and a “great gross” is a dozen gross (1728).

### Sixty

I’m not aware of any sexagesimal prefices (powers of 60), but they
would be useful e.g. for abbreviating times to begin with, and maybe
spreading their highly composite nature into other areas. The existing
system of “minutes”, “seconds”, “thirds”, etc. is useful for
*dividing* by 60, although it would be preferable to use it in
prefix rather than postfix position for consistency (e.g. “minutearc”
rather than “arcminute”). Metric
prefices traditionally used Latin for smaller parts (e.g. “centi” and
“milli”) and Greek for larger parts (e.g. “kilo” and “mega”). The
minutes/seconds/thirds system likewise uses Latin for the smaller parts,
so we should use Greek for our sexagesimal multiples: “prota” would be
sixties, “defter” would be three thousand six hundreds, “trito” would be
two hundred and sixteen thousands, and so on.