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Taking the measure of unit qualifiers

June 25, 2015

Max The Magnificent-June 25, 2015

Recently, I was in an email conversation with one of the editors at Everyday Practical Electronics (EPE), which is the UK's premier electronics and computing hobbyist magazine. (There used to be two magazines -- Practical Electronics and Everyday Electronics -- but they merged many years ago; hence the EPE moniker.)

Anyway, my friend at EPE shared a "Letter to the Editor" with me, part of which read as follows:

It interests me that in your article you use the prefix "k" for kilo. I was always taught throughout school and university (albeit a long, long time ago!) that any prefix larger than the unit must be in uppercase and smaller in the lowercase; for example, Mm is megametre and mm is millimeter; likewise Dm is decametre whereas dm would be decimetere; therefore kilometer should be Km.

This is one of those perennial topics that keeps on coming back to haunt us. Let's start with the fact that the metric system of measurement was developed during the French Revolution and its use was legalized in the US in 1866. The International System of Units (SI, which stands for Système International d'Unités) is a modernized version of the original metric system.

Stop! It Hertz!
In the case of an SI unit that is derived from the proper name of a person, the first (often only) letter of its symbol must be in uppercase, while any other letters are in lowercase; for example V, A, W, F, H, and Hz, which stand for "volt," "amp," "watt," "farad," "henry," and "hertz," respectively. By comparison, when this type of SI unit is spelled out in English, it should always begin with a lowercase letter (volt, amp, watt, farad, henry, hertz, etc.), except when used at the beginning of a sentence or in capitalized material such as a title.

As an aside -- and just in case you were wondering -- the term volt is named after the Italian physicist Count Alessandro Giuseppe Antonio Anastastio Volta (1745–1827), who invented the electric battery in 1800. (Having said this, some people believe that an ancient copper-lined jar found in an Egyptian pyramid was in fact a primitive battery used for electroplating... but, there again, some people will believe anything. Who knows for sure?) Meanwhile, the terms amp and ampere are named after the French mathematician and physicist André-Marie Ampère (1775–1836), who formulated one of the basic laws of electromagnetism in 1820. An amp corresponds to approximately 6,250,000,000,000,000,000 electrons per second flowing past a given point in an electrical circuit.

But wait... there's more! The amount of power consumed by an electronic circuit is measured in watts, where the term watt is named after the Scottish inventor and engineer James Watt (1736–1819), whose improvements to the steam engine were fundamental to the changes brought by the Industrial Revolution. The term farad is named after the British scientist Michael Faraday (1791–1867), who constructed the first electric motor in 1821. The term henry is named after the American inventor Joseph Henry (1797–1878), who discovered inductance in 1832. And the term hertz is a unit of frequency, where one hertz equals one cycle -- or one oscillation -- per second. The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made many important scientific contributions to electromagnetism.

Little and large
Electronic engineers often work with very large or very small values of voltage, current, resistance, capacitance, inductance, and so forth. As an alternative to writing endless zeros, electrical quantities can be annotated with the qualifiers given in the table shown below.

For example, 15 MO (15 megaohms) means fifteen million ohms, 4 mA (4 milliamps) means four thousandths of an amp, and 20 fF (20 femtofarads) means a very small capacitance indeed.

Since I love trivia, there are several things worth noting about this table. In Britain, for example, the term billion traditionally used to mean "a million million" (10^12). However, for reasons unknown, the Americans decided that billion should mean "a thousand million" (10^9). In order to avoid the confusion that would otherwise ensue, most countries in the world (including Britain) have decided to go along with the Americans on this one.

The term giga (G) comes from the Greek gigas, meaning "giant"; the term mega (M) comes from the Greek mega, meaning "great" (hence the fact that Alexander the Great was known as Alexandros Megos in those days of yore); and the term kilo (k) comes from the Greek khiloi, meaning "thousand."

Personally, I agree with the writer of the letter in that I think it would make more sense for every qualifier larger than unity to be in uppercase, while every qualifier smaller than unity would be in lowercase. In fact, this is largely the way things are; for example we have mega = 10^6 = M, giga = 10^9 = G, tera = 10^12 = T, peta = 10^15 = P, exa = 10^18 = E, zetta = 10^21 = Z, and yotta = 10^24 = Y. Similarly, we have milli = 10^-3 = m, micro = 10^-6 = u or µ, nano = 10^-9 = n, pico = 10^-12 = p, femto = 10^-15 = f, atto = 10^-18 = a, zepto = 10^-21 = z, and yocto = 10^-24 = y.

So why do we use a lowercase 'k' for kilo? Well, one reason is that the uppercase 'K' is reserved for "Kelvin" -- the fundamental unit of temperature -- which was named for the great physicist and engineer Lord Kelvin, who was Professor of Natural Philosophy for over 50 years at Glasgow University.

It's also worth noting that the lowercase 'k' is not alone; currently, hecta (also spelled hecto) (h) and deca (also spelled deka) (da) are also lowercase. (In the not-so-distant past, the prefixes hecto, deca, deci, and centi were commonly used for everyday purposes; the use of centimeter (cm) is still common.) The reason I used the "currently" qualifier is that the system is updated and refined from time to time. Prior to 1960, the now-little-used deca had a confusing variety of prefixes, such as dk, D, and Da. Some old cooking books specified weights in decagrams (Dg), for example, but today's decagramophiles would use dag.

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