# Metric Prefixes - from yotta to yocto

In introductory chemistry we use only a few of the most common metric prefixes, such as milli, centi, and kilo. Our various textbooks and lab manuals contain longer lists of prefixes, but few if any contain a complete list. There is no point of memorizing this, but it is nice to have a place to look them up. You will find prefixes from throughout the range as you read the scientific literature. In particular, the smaller prefixes such as nano, pico, femto, etc., are becoming increasingly common as analytical chemistry and biotechnology develop more sensitive methods.

To help you visualize the effect of these prefixes, there is a column "a sense of scale", which gives some examples of the magnitudes represented. Thanks to Greg Pearce, author of ChemFormula, for help developing these examples. Also, thanks to "Nansen" for calling attention to an error in an earlier version. (Please let me know of any other errors you find, or suggestions for additions.)

 prefix abbreviation (upper and lower case are important) meaning example a sense of scale (for some) Most are approximate. yotta Y 1024 yottagram, 1 Yg = 1024 g mass of water in Pacific Ocean ~ 1 Yg energy given off by the sun in 1 second ~ 400 YJ volume of earth ~ 1 YL mass of earth ~ 6000 Yg zetta Z 1021 zettameter, 1 Zm = 1021 m radius of Milky Way galaxy ~ 1 Zm volume of Pacific Ocean ~ 1 ZL world energy production per year, ~ 0.4 ZJ exa E 1018 exasecond, 1 Es = 1018 s age of universe ~ 0.4 Es (12 billion yr) peta P 1015 petameter, 1 Pm = 1015 m 1 light-year (distance light travels in one year) ~ 9.5 Pm The dinosaurs vanished ~ 2 Ps ago. tera T 1012 terameter, 1 Tm = 1012 m distance from sun to Jupiter ~ 0.8 Tm giga G 109 gigasecond, 1 Gs = 109 s human life expectancy ~ 1 century ~ 3 Gs 1 light-second (distance light travels in one second) ~ 0.3 Gm mega M 106 megasecond, 1 Ms = 106 s 1 Ms ~ 11.6 days kilo k 103 kilogram, 1 kg = 103 g hecto h 102 hectogram, 1 hg = 102 g deka (or deca) da 10 = 101 dekaliter, 1 daL = 101 L deci d 10-1 deciliter, 101 dL = 1 L centi c 10-2 centimeter, 102 cm = 1 m milli m 10-3 millimole, 103 mmol = 1 mol micro μ (Greek letter "mu") 10-6 microliter, 106 μL = 1 L 1 μL ~ a very tiny drop of water nano n 10-9 nanometer, 109 nm = 1 m radius of a chlorine atom in Cl2 ~ 0.1 nm or 100 pm pico p 10-12 picogram, 1012 pg = 1 g mass of bacterial cell ~ 1 pg femto f 10-15 femtometer, 1015 fm = 1 m radius of a proton ~ 1 fm atto a 10-18 attosecond, 1018 as = 1 s time for light to cross an atom ~ 1 as bond energy for one C=C double bond ~ 1 aJ zepto z 10-21 zeptomole, 1021 zmol = 1 mol 1 zmol ~ 600 atoms or molecules "A picture is worth about 1.7 zmol of words." yocto y 10-24 yoctogram, 1024 yg = 1 g 1.7 yg ~ mass of a proton or neutron

The prefix zepto became relevant in a Musings post on a very very tiny container -- which could fit in a box of volume 90 zeptoliters (zL). See What is it? (May 25, 2011).

For more about units, visit http://www.unc.edu/~rowlett/units/index.html. This site features a Dictionary of Units of Measurement, plus much more listed below the dictionary header, under "Commentary and Explanation". It is maintained by Dr. Russ Rowlett at the Center for Mathematics and Science Education, University of North Carolina at Chapel Hill.

One interesting thing I learned about from Rowlett was binary prefixes. Binary prefixes? You have probably heard words such as kilobyte, in the context of computers. What does it mean? It might seem to mean 1000 bytes, since kilo means 1000. But in the computer world it often means 1024 bytes. That is 210 -- a power of two very close to 1000. Now, in common usage it often does not matter whether the intent was 1000 bytes or 1024 bytes. But they are different numbers and sometimes it does matter. So, a new set of "binary prefixes", distinguished by "bi" in the name or "i" in the abbreviation, was introduced in 1998. By this new system, 1024 bytes would be properly called a kibibyte or KiB. (Sounds like something you would feed the dog.)

This new system of binary prefixes has been endorsed by the International Electrotechnical Commission (IEC) for use in electrical technology. See the NIST page at http://physics.nist.gov/cuu/Units/binary.html.

Whether these will catch on remains to be seen, but at least if you see such an unusual prefix you might want to be aware of this.

### Contributors

23:43, 21 Dec 2014

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This material is based upon work supported by the National Science Foundation under Grant Number 1246120