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Nano the Dwarf - A Guide to Decimal Prefixes

You're probably familiar with the metric system of units. If you're a native of continental Europe, then it may be all you've ever known. If you're from certain other parts of the world, then you may have had to integrate it with the measurements which your parents and grandparents used. Maybe you have old reference books with those wonderfully archaic names which conjure up a far simpler way of life - a hogshead of ale, perhaps, or a peck of pickled peppers. There just doesn't seem to be as much colour to 500 grams of flour or a litre of petrol.

One innovation that the metric system introduced was the use of prefixes with the units, to keep the numbers manageable. Take the gram for example, the unit of mass. We can use grams for small jobs like cooking (100g of butter), but we use milligrams and micrograms for very small traces (50 milligrams of alcohol in the bloodstream), kilograms for heavier items (maybe your bathroom scales indicate 80kg), and there are prefixes for both smaller and larger scales of magnitude. The moon, for example has a mass of around 73.5 Yg, or yottagrams. It would make both arithmetic and communication more clumsy if we had to say and write 0.05g of alcohol, 80,000g on the scales, and 73,500,000,000,000,000,000,000,000g for the mass of the moon.

In the British imperial system, we just didn't have prefixes like this - we would use a completely new word for a unit on a different scale, and we had to use conversion charts to standardise the units if we needed to perform arithmetic.

So, where did these prefixes come from, and why are they so called?

Decimal System of Prefixes

The metric system was devised in France and standardised there in the 1790s, following the French Revolution. It became widely accepted from around the middle of the 19th Century, and at the end of that century a set of standard decimal multiplier prefixes was introduced. Greek names were used for the integral (large-scale) multipliers, and Latin for the fractional (small-scale) ones. These ranged from one thousandth through to ten thousand times, with one prefix for each factor of ten, hence it was known as a decimal system:

Milli-

Milli-, or one thousandth, derives from the Latin word for 'one thousand'; engineers might write it as 10-3. The prefix symbol is a lowercase m-, hence mg for milligrams and mA for milliamps.

According to the 1985 UK Weights and Measures Act, it is the only prefix legal for trade in the UK for all of metre, gram and litre.

Centi-

Centi-, or one hundredth, or 10-2, derives from the Latin for 'one hundred'. Its prefix is the lowercase c-, hence cm for centimetres, cl for centilitres. This is known as a non-millesimal prefix, as it is not in the set of prefixes which occur in steps of 1,000. (milli-, micro-, nano-, etc).

Centigrams and centilitres are only really used in Europe. The centilitre isn't legally recognised in the UK, neither is the centiare, the unit of area which is equivalent to one square metre.

Draughtsmen tend not to use the centimetre, as there's a risk it could be misinterpreted by a factor of ten in their drawings - they prefer to use millimetres instead.

Despite the names, centipedes do not have exactly 100 legs, neither do millipedes have 1,000. In any case, as these are fractional prefixes, it would presumably have been more accurate to name them hectopedes and kilopedes - we'll discuss those prefixes later.

Deci-

Deci-, or one tenth, or 10-1, derives from the Latin for 'ten'. Its prefix is the lowercase d, hence dg for decigrams, dm for decimetres.

Again, this prefix is rarely seen outside Europe. It is legal for UK trade only in terms of the decimetre, the square decimetre and the cubic decimetre, which is equivalent to the litre. In fact, even scientists can't agree on which volume unit is best; organic and inorganic chemists measure volume in litres, whereas physical chemists prefer the cubic decimetre.

It is however the most convenient and widely used prefix for the unit of sound intensity, the bel.

Deca-

Deca-, or ten times, derives from the Greek for 'ten'. It has a lowercase da- as its prefix, to distinguish it from deci-, but the uppercase D- was used until 1960. Like all prefixes which end in either 'o' or 'a', you can drop the final letter if you use it before a vowel, hence decametre, but decare. Of units with this prefix, only decares are legally acceptable in the UK. Before 1985, it was spelled as dekare in the UK.

In geometry, a decagon is a ten-sided figure.

Hecto-

Deriving from the Greek for 'one hundred', hecto- indicates 100 times the base unit. Its symbol is the lowercase h-, but the uppercase H- was used before 1960. Like the other non-millesimal prefixes in this section, it is little-used outside Europe. Like deca-, the final vowel of the prefix is omitted before a unit beginning with a vowel.

It is best known in the units hectare (ha), possibly the most widely-used land measurement unit, and the hectopascal (hPa), the unit of pressure which is identical to the millibar beloved of meteorologists.

Kilo-

Back to the millesimal units, kilo- derives from the Greek for 'one thousand', and indicates, naturally, 1,000 times, or 103. Its symbol is the lowercase k-, but this was uppercase before 1960. One of the most widely-used and useful of prefixes, you will find the kilogram (kg) as the SI unit of mass. For trade purposes, however, only the kilogram and kilometre (km) are legally acceptable in the UK. The prefix is shortened to kil- before a vowel, hence kilohm, the unit of resistance (kΩ).

In fact, the symbol is widely used on its own to indicate multiples of 1,000 - you might have a salary of £30k, pronounced just 'thirty K', for example.

It has also been adopted by computer scientists in the kilobyte (kB); this, however, is often used to mean 210, or 1,024 bytes1, rather than 1,000. This also applies to other larger-scale prefixes such as gigabytes and terabytes. A whole new set of binary prefixes has recently been created to rectify this inaccuracy, and, strictly speaking, we should now be saying one kibibyte (1 KiB) when we mean 1,024 bytes.

Myria-

A prefix which has all but disappeared these days, myria- indicates ten thousand, or 104 times, hence units such as myriagram and myriare. It derives from the Greek word for that number, a word which they also used to mean 'countless'. Myria- was never part of the SI system, and for the record, its symbol was My-.

The SI System

By 1960, measurements had become a lot more standardised, and a number of prefixes were created to cover millesimal multipliers at either end of the scale.

Micro-

They finally decided to ditch the convention of Latin roots for fractional prefixes when they got to one millionth, or 10-6. No Latin word could evidently capture this degree of smallness, so they simply switched to Greek. Micro- means 'small' in Greek, and the prefix indicates one millionth of a unit, or 10-6. Its symbol is the Greek letter μ (mu), which didn't impress a number of scientists, most notably American pharmacists, who mutinied and instead use mcg for microgram. Some others prefer the symbol u-, which looks not unlike μ, if you squint a bit.

The micrometre, μm, is commonly used in precision engineering, and is sometimes referred to as a micron.

Nano-

Carrying on with the Greek theme, a suitable word was needed for one billionth or 10-9 - they had already used the word for small. A bit of imagination produced the prefix nano- which derives from the Greek word for 'dwarf'. The symbol is n-.

It's used in microscopic measurements like nanolitres. Scientists can cool caesium atoms to temperatures measured in nanokelvin - less than one millionth of a degree above absolute zero - the kind of conditions which would make Newcastle United supporters think twice about wearing a shirt.

Pico-

Even the Greeks had no good word for something which was one thousand times smaller than a billionth, or 10-12 times. This time the metrologists raided Spanish for the prefix pico-, meaning 'small' in that language. The symbol is p-, and it's commonly used in units such as picofarads pF, for rating small electrical capacitors. Cable capacitance is often specified in picofarads per foot.

Atomic radii of the elements can be measured in picometres (pm). You might expect a length of 10-10 metres to be written as 100 picometres or 0.1 nanometres, but in fact physicists like to use a separate non-SI unit for this, the angstrom, symbol Å.

Mega-

At the other end of the scale, prefixes were created for larger-scale numbers. Mega- derives from the Greek for 'great', and indicates one million or 106 times the unit. The symbol is the uppercase M- (don't confuse it with the lowercase m- meaning milli-), and we use it in units such as megametres2 and megatonnes3. If you're into predicting the impact of a nuclear strike, then you might measure the effects in megadeaths - each being the death of a million people. Megacorpse is a jolly alternative, coined in 1953 by Dr Herman Kahn.

Giga-

Giga-, from the Greek for 'giant', is the prefix used for one billion, or 109 times. The symbol is an uppercase G-, and common examples include gigohms (GΩ) and gigahertz (GHz): a measure of clock frequency in large computer processors.

Tera-

After 'great' and 'giant', metrologists were rapidly running out of suitable words in the Greek language, and the tera- prefix derives from the word for 'monster'. It denotes one trillion, or 1012 times the base unit, and its symbol is the uppercase T-.

The average distance from the sun of the outer planets of our solar system can be measured in terametres (Tm). Laser technology often uses this prefix, in the forms of terahertz and teravolts.

Every few years, the boffins meet in France and agree any changes and additions to this set. This Researcher hasn't been invited to any such conventions, and can only imagine the sight of bearded academics arguing over the new word to be used for the next astronomically large number, while feasting on radians of pizza and decilitres of orange juice. Still, it's probably quite a big deal in the world of measurements when this happens, and a number of important additions have been made since 1960.

In 1964, the 12th Conférence Générale des Poids et Mesures4 or CGPM identified the need for two smaller scale multipliers, and this time they looked to the Danish language for inspiration:

Femto-

Femto- comes from the Danish for 'fifteen', and indicates the fraction 10-15, or 0.000000000000001 of a unit. Its symbol is the lowercase f-.

The unit one femtometre (1 fm) used to be named the fermi, after the physicist Enrico Fermi (1901-1954), who built the first nuclear reactor.

Atto-

Similarly 'atto-' comes from the Danish for 'eighteen', and indicates the fraction 10-18 times. Its symbol is the lowercase a-. This is getting really quite small: according to New Scientist, 'an attonewton is to the weight of a feather as the weight of a feather is to the weight of the Hoover dam'. An electron orbits a hydrogen atom in just 24 attoseconds: don't blink or you'll miss it.

Peta-

The 15th CGPM in 1975 rectified the units, so to speak, by creating two equivalent prefixes for large-scale multipliers.

Peta- derives from the Greek root 'pent-', meaning 'five', and indicates that this multiplier, 1015, is the base unit multiplied by 1,000 raised to the power of five. Its symbol is the uppercase P-.

Visible light is in the petahertz range of frequencies, and you can measure the amount of carbon in the atmosphere in petagrams. Very big lasers can now generate petawatts of power, but only for periods of femtoseconds.

Exa-

Exa- derives from the Greek root 'hex-', meaning 'six', and indicates that this multiplier, 1018, is the base unit multiplied by 1,000 raised to the power of six. Its symbol is the uppercase E-.

One exametre is approximately the distance from the Earth to the Hyades star cluster in the constellation Taurus.

Extreme Measures

The most recent addition of prefixes occurred in 1990, at the Comité International des Poids et Mesures5 (CIPM) convention. The further we go with these prefixes, the less likely we are to find physical examples which use them. Advances in technology may one day give us zettabyte (ZB) memory chips, but it may not stop Microsoft Windows from hogging most of it.

Zepto-

Zepto- is from the Latin root 'sept-', meaning 'seven', indicating that this multiplier, 10-21, is the base unit divided by 1,000 raised to the power of seven. Its symbol is the lowercase z-.

It has one useful application in the zeptomole, which is Avogadro's number divided by 10 -21, ie just over 602 molecules of a substance - a far easier figure for chemists to work with.

Yocto-

Yocto- is from the Latin root 'octo-', meaning 'eight', with a letter Y jauntily attached to the front. It indicates that this multiplier, 10-24, is the base unit divided by 1,000 raised to the power of eight. Its symbol is the lowercase y-.

Zetta-

Zetta-, like zepto- derives from the Latin for 'seven'. There is a risk that the two could be confused, but as they are at the opposite ends of the scale, this would seem unlikely. It multiplies the base unit by 1021 times, ie 1,000 to the power of seven, and its symbol is the uppercase Z-.

Our galaxy, the Milky Way is just under one zettametre in diameter.

Yotta-

Similarly yotta- is very similar to yocto-. It's the largest scale prefix at the time of writing, 1024, or 1,0008 times the base unit. Its symbol is the uppercase Y-. It isn't quite high enough a millesimal prefix to render the mass of the Earth in grams6, but the boffins will presumably rectify this at their next gathering. It isn't clear what naming system they might turn to if this happens; maybe if one of them was a Douglas Adams fan they might successfully plead the case for the marvilitre or the vogogram - only time will tell.

A Brief History Of Time Prefixes

Among all measurable items, time stands out as being the one which has resisted all attempts to decimalise it. For now, we are happy to keep working with 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, etc, but we do make good use of decimal prefixes to indicate very small fractions of a second. A blink of an eye could be 50 milliseconds, light travels a distance of one mile in 5.4 microseconds, and particularly short bursts of activity - in lasers and the like - can be measured in nanoseconds.

In fact, some hardliners have also adopted the integral multipliers too, and if you move in the right scientific circles you may well meet, among others, kiloseconds, exadays and gigayears. For the record, we can measure the time elapsed since the Big Bang in petaseconds.

One area where prefixes are universally absent is money7. We seem to prefer the sound of 'one million pounds' to 'one megapound'. It could be because we only have relatively small denominations of banknotes, or maybe we just enjoy the image of large numbers of them swirling around, or piled up in neatly stacked wads.

And Finally

From time to time, people circulate joke e-mails with inventive uses for these prefixes. We'll leave you with a few examples:

• 10 cards = one decacards,

• One trillion pins = one terrapin,

• 1,000 whales = one killer whale,

• One trillion microphones = one megaphone,

• 1021 piccolos = one gigolo, and

• 2,000 mockingbirds = two kilomockingbirds.

1 Because computer memories are nearly always a power of 2 in size.
2 The speed of light is approximately 300 megametres per second (Mms-1).
3 Although in widespread use for the TNT-equivalent mass of nuclear warheads and the like, the megatonne is frowned upon, and we should strictly use the teragram.
4 General Conference on Weights and Measures.
5 International Committee of Weights and Measures.
6 The mass of the Earth is about 6,000 Yg (yottagrams).
7 Except in the implied sense of £30K, as mentioned earlier.

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Entry Data
Entry ID: A29779159 (Edited)

Edited by:
U151503 - Gnomon - Future Guide Editor - towels at the ready

Date: 24   January   2008

 Referenced Guide Entries Alcohol Computers The Solar System Greece Pizza - Not Just Italian Astronomical Units Real Ale The European Union Newcastle-upon-Tyne, Tyne and Wear, UK France Speak-Your-Weight Machines The Sun The Moon Units of Measurement How a Nuclear Plant Works Earth Warheads Lasers The Big Bang Galaxies Scale How to Recover a Crashed Windows PC Bread Flour Time and Date The Mole (Chemistry) Email - an Introduction Douglas Adams - His Life and Worlds John Kettley - Weatherman (and people mentioned in the same song) Carbon and its Inorganic Compounds Atoms and Atomic Structure Growing a Beard How Many Seconds Are There In A Minute? Constellations: Taurus 'the Bull' Kibibytes and Yobibits - A Guide to Binary Prefixes

 Related BBC Pages BBC Science & Nature BBC Technology News: The Perfect Weight UK and the Metric System BBC Food - Converter BBC Learning - Maths Video: Was Metric System British?

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