Nanograms per Gram

Date: 06/08/2001 at 00:53:11
From: Weston Becker
Subject: Mathematical symbols/terminology

I am studying some water quality data and have a few questions. 

First, I understand that if something is a unit is given with a "/" 
sign then it means "per," e.g. "2 mg/L" means "two milligrams per 
liter." However, sometimes I see units that say something like 
"2 ng g-1" (the (-1) portion of this is an exponent). Please explain 
to me what this phrase is saying. 

This may be two questions really: what is the relation between "ng" 
and "g" (per?), and then what does the "-1" exponent mean? 

Thank you for your help!.

Date: 06/08/2001 at 08:41:04
From: Doctor Peterson
Subject: Re: Mathematical symbols/terminology

Hi, Weston.

The exponent -1 means the same thing as the "/", on analogy with 
ordinary algebra, where

    b^-1 = 1/b

and

    a * b^-1 = a/b

(using our convention of "*" for multiplication and "^" for 
exponents).

So "2 ng g^-1" means 2 ng/g, or 2 nanograms of something per gram of 
something else.

You can read about metric symbol conventions, including this one, 
here:

  Using Abbreviations or Symbols - How Many? A Dictionary of Units 
  of Measurement - Russ Rowlett
  http://www.unc.edu/~rowlett/units/symbol.html   

  Rules and Style Conventions for Printing and Using Units - 
  NIST Guide to SI Units
  http://physics.nist.gov/Pubs/SP811/sec06.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/