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### 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?

```

```
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.

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/
```
Associated Topics:
Middle School Terms/Units of Measurement

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