# 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 mole^{a
} |
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 10

^{23}

* ^{b}* "zepto"
and "yocto" were accepted as prefixes by the 19

^{th}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 cm^{3}, 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 10^{23} 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 × 10^{23}, 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 10^{21} (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970115.html);
a more current number of known stars is 70 sextillion (70 ×
10^{21}) 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)

http://www.footrule.com/index.htm

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

http://www.google.com/help/calculator.html

The NIST Reference on Constants, Units, and Uncertainty

http://physics.nist.gov/cuu/Units/index.html

The International System of Units (SI): NIST Special Publication
330

http://physics.nist.gov/Pubs/SP330/sp330.pdf [PDF,
size not available]

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

http://ts.nist.gov/ts/htdocs/200/202/pub814.htm