The story of milli and micro
Struggles with units of measure have a long and somewhat sordid history. People have been measuring things (at least coarsely) since we learned how to talk. We have needed the assistance of units of measure in order to communicate distances (to sources of food or water), time (to plant and harvest crops), and weight (in trade) among others.
As societies grew (bearing in mind that communication was once slow and tedious), different people in different places invented units of measure in forms and scales on an "ad hoc" basis as convenient to their daily lives. Measures of length, time, and weight often differed from town to town, much less country to country. Meanwhile, different and odd units were invented for measuring things small (e.g., inches) vs. large (e.g., miles, furlongs). While being convenient for everyday life in simpler times, these traditional units of measurement made life messy when society became more industrialized. Traditional units complicated conversion between measures of big things and measures of small things.
As communications improved, and political units grew larger, commonality of measures improved -- but this clutter didn't really start clearing up in earnest until the 18th century. In 1790, French investigations into reform of weights and measures resulted in the development of the world's first "metric system." Over the years, this was improved and refined until in 1960 the "modernized metric system" (a.k.a., SI for Système International d'Unités) made its formal appearance. SI units brought a new, cleaner way of dealing with units of measurement and scale size. Base units for various measures would be interrelated in a simple way, and scaling of almost any unit would be done via a decimal (powers of ten) scheme (only time and angles were left out of this -- but that's another long story...). Note that while some countries have still not completely converted to SI units for daily life, SI is still the international standard for scientific endeavors.
In spite of the advantages of decimal units, the SI system would be clumsy in practical use if it went no further than this. For example, 1 Farad (the base unit of capacitance) is big, really too big to be convenient for most purposes. A common size for capacitors in BEAM robots is 2.2 x 10-7 Farad; a common size for capacitors in many other applications is 1 x 10-12 Farad. A basic decimal system would lead to mathematical messiness by forcing you to carry lots of digits and powers of ten around in various domains of study.
Fortunately the SI system accommodates both the desire for simpler math (via decimal units), as well as the need for measures scaled appropriately to a given task. This is done via unit prefixes based on powers of ten. Rather than carry the full numeric notation for a given power of ten, a "shorthand" notation is provided for units related to their base unit by powers of ten. Using this shorthand, then, you can describe small things via millimeters (thousandths' of a meter, mm), or large things via kilometers (thousands of meters, km), and not have to deal with difficult conversions between them.
Returning to our capacitance example, BEAMers can deal with capacitors sized in microfarads, and other electronics designers can work with capacitors sized in picofarads. Mind the powers of ten associated with this shorthand, and the math all works out cleanly.
At the same time, the SI system provides both a prefix if
you wish to spell out a unit name (e.g., microfarad),
and a symbol if you prefer to use the unit's symbol (e.g.,