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Fractional Quantifier Prefixes (sub-multiples of ten) Used in Chemistry for Units of Measure such as Mass, Moles, Volume, and Time

by Christian Daughton, Ph.D. - 2000

Prefix Ordinal Value in power of 10 # Molecules per ordinal molea Derivation
milli (m) one-thousandth 10-3 - Fr. milli: thousand
micro (µ) one-millionth 10-6 - Gr. mikros: small (Greek letter 'mu')
nano (n) one-billionth 10-9 - Lat. nanus: dwarf
pico (p) one-trillionth 10-12 - Sp. pico: small quantity
femto (f) one-quadrillionth 10-15 600,000,000   Nor. femten: fifteen
atto (a) one-quintillionth 10-18 600,000   Nor. atten: eighteen
zepto (z)b one-sextillionth 10-21 600   Lat. septa: seven
yocto (y)b one-septillionth 10-24 ~1 (0.6)   Lat. octa: eight

a  derived from Avogadro's number = 6.0221 X 1023

b  "zepto" and "yocto" were accepted as prefixes by the 19th Conférence Générale des Poids et Mesures in 1990 as permissible prefixes used to modify SI units. (SI is an abbreviation for Système International d'Unités.)  Zepto had already been in unofficial use for several years. Zepto was coined from septa by replacing the "s" and "a" (for consistency with other units); "seven" times the standard unit multiplicative increment, 10-3, yields 10-21. Likewise, yocto was coined from octa because "eight" times the multiplicative increment, 10-3, yields 10-24. The initial letters, "z" and "y" were selected so that future units could be named in reverse alphabetical order.

A Perspective on Prefixes and Magnitude

One mole of M&M candies would occupy more than 14.5 million cubic miles of space (a cube 244 miles on side) [this assumes closest possible packing by a cubed-shaped candy occupying 0.1 cm3, actual candies would occupy a significantly larger volume (from Chem. Eng. News 18 Feb 2002, page 120)]  This same volume is sufficient to cover the entire conterminous U.S. to a height of 17,000 feet.

One liter of coffee containing 1 millimole of caffeine (1 mmol/L, or 1 mM) would have nearly one SEXTILLION MOLECULES of caffeine.

One liter of solution whose analyte concentration is 1 zeptomolar (zM) would contain only about 600 MOLECULES of analyte. In contrast, the highly sensitive human nose can only detect concentrations down to about 1 picomolar (pM) - or 600 billion molecules per liter.

Detection of a chemical at a concentration of 1 part-per-billion (ppb; e.g., 1 µg/L) is similar to looking for one family among the world's entire population. In 1 nano second (ns), light travels a distance of only 1 FOOT.

One hydrogen atom has a mass of almost two yoctograms (yg).

Visual demonstration of "powers of 10" (demonstration of traveling from the edge of the universe [starting at a distance of 1023 meters from earth] down to the sub-atomic dimension of 10-16 meters — a total change of almost 40 "orders of magnitude" in scale)

How much is a part per million?
http://www.phthalates.org/pdfs/How_Much.pdf (American Chemistry Council) [PDF, 146 KB]
http://ace.orst.edu/info/extoxnet/tibs/partperm.htm (EXTOXNET: Extension Toxicology Network)

For perspective on the immense size of Avogadro's number (6.0221 × 1023, a number also referred to in chemistry shorthand as one mole or 1 mol), consider that a very rough estimate of the number of stars in the universe is 1021 (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970115.html); a more current number of known stars is 70 sextillion (70 × 1021) and exceeds by 10 fold the number of individual grains of sand from all the world's beaches and deserts [see: CNN.com 23 July 2003: http://www.cnn.com/2003/TECH/space/07/22/stars.survey/] This means that the number of known stars in the universe amounts to but a fraction of the number of atoms in merely 12.0 grams of carbon-12 (defined as Avogadro's number) or the number of molecules of any gas contained in the volume of 22.4 liters (at standard pressure and temperature).

For a discussion of statistical issues related to solutions of ultra-low concentrations, see the following reference:
C.E. Efstathiou "On the Sampling Variance of Ultra-Dilute Solutions," Talanta 2000, 52(4), 711-715.

Comprehensive Background and Information on SI

FootRule.com (unit conversions)

Google Conversions - help (e.g., 1000 femtograms = ? milligrams)

The NIST Reference on Constants, Units, and Uncertainty

The International System of Units (SI): NIST Special Publication 330 
  [PDF, size not available]

Interpretation of the SI for the United States and Federal Government Metric Conversion Policy


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