Page 37 - Geochemistry of Oil Field Waters

26 ANALYSIS OF OILFIELD WATERS

decimal point but preceding other digits are not significant. These zeros only
indicate the pbsition of the decimal point.
(d) Final zeros in a whole number may or may not be significant.
A good measure of the significance of one or more zeros before or after
another digit is to determine whether the zeros can be dropped by expressing
the number in exponential form. If they can, the zeros are not significant.
For example, no zeros can be dropped when expressing a weight of 100.08 g
in exponential form; therefore, the zeros are significant. However, a weight
of 0.0008 g can be expressed in exponential form as 8 x g, and the
zeros are not significant. Significant figures reflect the limits of the particular
method of analysis. It must be decided beforehand whether this number of
significant digits is sufficient for interpretation purposes. If not, there is little
that can be done within the limits of normal laboratory operations to im-
prove these values. If more significant figures are needed, a further improve-
ment in method or selection of another method will be required to produce
an increase in significant figures.
Once the number of significant figures is established for a type of analysis,
data resulting from such analyses are reduced according to set rules for
rounding off.

Ro unding-o ff numbers
Rounding off of numbers is a necessary operation in all analytical areas. It
is automatically applied by the limits of measurement of every instrument
and all glassware. However, it is often applied in chemical calculations in-
correctly by blind rule or prematurely, and in these instances can seriously
affect the final results. Rounding off should normally be applied only as
follows.

Round ing-o ff rules
(a) If the figure following those to be retained is less than 5, the figure is
dropped, and the retained figures are kept unchanged. As an example,
11.443 is rounded off to 11.44.
(b) If the figure following those to be retained is greater than 5, the figure
is dropped, and the last retained figure is raised by 1. As an example, 11.446
is rounded off to 11.45.
(c) When the figure following those to be retained is 5, and there are no
figures other than zeros beyond the 5, the figure is dropped, and the last
place figure retained is increased by 1 if it is an odd number, or it is kept
unchanged if an even number. As an example, 11.435 is rounded off to
11.44, while 11.425 is rounded off to 11.42.

Rounding-off single arithmetic operations
(a) Addition: when adding a series of numbers, the sum should be
rounded off to the same number of decimal places as the addend with the