Page 161 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

THE USE OF CALCULATORS AND MICROCOMPUTERS 4.7

zero is significant, but in the quantity 0.0025 kg the zeros are not significant
figures; they serve only to locate the decimal point and can be omitted by proper
choice of units, i.e. 2.5 g. The first two numbers contain five significant figures,
but 0.0025 contains only two significant figures.
Observed quantities should be recorded with one uncertain figure retained.
Thus in most analyses weights are determined to the nearest tenth of a
milligram, e.g. 2.1546 g. This means that the weight is less than 2.15478 and
more than 2.1545 g. A weight of 2.150 g would signify that it has been determined
to the nearest milligram, and that the weight is nearer to 2.150g than it is to
either 2.151 g or 2.149 g. The digits of a number which are needed to express
the precision of the measurement from which the number was derived are known
as significant figures.
There are a number of rules for computations with which the student should
be familiar.
1. Retain as many significant figures in a result or in any data as will give only
one uncertain figure. Thus a volume which is known to be between 20.5 mL
and 20.7 mL should be written as 20.6 mL, but not as 20.60mL, since the
latter would indicate that the value lies between 20.59 mL and 20.61 mL.
Also, if a weight, to the nearest 0.1 mg, is 5.2600 g, it should not be written
as 5.260g or 5.26g, since in the latter case an accuracy of a centigram is
indicated and in the former a milligram.
2. In rounding off quantities to the correct number of significant figures, add
one to the last figure retained if the following figure (which has been rejected)
is 5 or over. Thus the average of 0.2628,0.2623, and 0.2626 is 0.2626 (0.2625,).
3. In addition or subtraction, there should be in each number only as many
significant figures as there are in the least accurately known number. Thus the
addition

should be written

The sum or difference of two or more quantities cannot be more precise than
the quantity having the largest uncertainty.
4. In multiplication or division, retain in each factor one more significant figure
than is contained in the factor having the largest uncertainty. The percentage
precision of a product or quotient cannot be greater than the percentage
precision of the least precise factor entering into the calculation. Thus the
multiplication

should be carried out using the values

and the result expressed to three significant figures.
4.7 THE USE OF CALCULATORS AND MICROCOMPUTERS

The advent of reasonably priced hand-held calculators has replaced the use of
both logarithms and slide-rules for statistical calculat~ons. In addition to the