Physics for Geologists, Second edition

6 Basic concepts
pascal (Pa) and siemens (S), the latter retaining its final 's' in the singular
because that is the name.
For very large and very small numbers of units there is a set of prefixes
(Table 1.4). The basic unit kilogram already has a prefix and it does not take
another. A thousand kilograms is one tonne (t), a unit of mass; or Mg. The
use of those in italics in Table 1.4 is discouraged, but centimetre (cm), hectare
(ha, 10 000 m2, land measurement) and hectopascal (hPa, meteorology) will
no doubt persist.
When these prefixes are used in combination with a basic or derived unit,
any exponent applies to both. So 1 km2 is lo6 m2 and 1 Fm2 is 10-l2 m2.
Numbers should be written with a space, not a comma,' separating groups
of three digits on either side of the decimal point, so 12 345.678 9, and with
a space between the number and any units (except perhaps the degree sym-
bol, "). Four-digit numbers may be written together, as 1234 and 1234.567 8.
A number between 1 and -1 must always have a zero before the decimal
point: 0.75, not ,75. The decimal point should be returned to mid-line, .;
only the limitations of the manual typewriter led to its being combined with
the full stop or period. The New Scientist has been using this for some years
now.
There are advantages, arising from the prefixes, in using what is called
the engineering notation of numbers, that is, giving the exponent of 10 to
a multiple of three (the practice used here), rather than the scientific notation.
So 10'' in scientific notation will be written 10 x lo9.
Distinctions and definitions
Average, mean, median
The word average has several meanings in shipping and science, but it usually
means the arithmetic mean, C x/n, where 1 x is the sum of n values of x.
It follows that the word mean is at least partly synonymous with 'average'.
The mean is usually written with a bar over the symbol, for example, 2,;.
The weighted average is the sum of the products of the quantity and the
weight, w, attached to it, divided by the sum of the weights, Cxw/ 1 w.
This is used, for example, in sedimentology for representing the results of
a sieve analysis, where w is the proportion of the sediment by weight retained
on sieve sized x.
The geometric mean of n positive quantities is the nth root of the product
of these quantities: (xl x x2 x x3 x . . . x xn)'ln. This is used in sedimentology
because size distribution of sediments is normalized by its use, becoming
more symmetrical when plotted as a frequency diagram. A linear size scale
2 If your country uses the comma as the decimal point, and the stop as the separator of
thousands, then you must follow your local customs.
Copyright 2002 by Richard E. Chapman