Finally, the estimated precision for the determination of the concentration of hydrochloric acid is
obtained using equation (2.12).
One important point to remember is that the absolute standard deviations for the unit processes are
constant, but the relative standard deviations will decrease with the magnitude of the sample and the
titre. In other words, within limits the larger the sample taken the better the precision of the results.
Significant Figures
Results are normally given to a certain number of significant figures. All the digits in a number that are
known with certainty plus the first that is uncertain, constitute the significant figures of the number. In
the case of a zero it is taken as significant when it is part of the number but not where it merely
indicates the magnitude. Thus a weight of 1.0421 g which is known within the limits of ± 0.0001 g has
five significant figures whilst one of 0.0421 g which is known within the same absolute limits has only
three. When a derived result is obtained from addition or subtraction of two numbers, its significant
figures are determined from the absolute uncertainties. Consider the numbers 155.5 ± 0.1 and 0.085 ±
0.001 which are added together to give 155.585. Uncertainty appears at the fourth digit, whence the
result should be rounded off to 155.6. If the derived result is a product or quotient of the two quantities,
the relative uncertainty of the least certain quantity dictates the significant figures. 0.085 has the
greatest relative uncertainty at 12 parts per thousand. The product 155.5 × 0.085 = 13.3275 has an
absolute deviation of 13.3275 × 0.012 = 0.16. Uncertainty thus appears in the third digit and the result is
rounded off to 13.3.
Limits of Detection
It is important in analysis at trace levels to establish the smallest concentration or absolute amount of an
analyte that can be detected. The problem is one of discerning a difference between the response given
by a 'blank' and that given by the sample, i.e. detecting a weak signal in the presence of background
noise. All measurements are subject to random errors, the distribution of which should produce a
normal error curve. The spread of replicate measurements from the blank and from the sample will
therefore overlap as the two signals approach each other in magnitude. It follows that the chances of
mistakenly identifying the analyte as present when it is not, or vice versa, eventually reach an
unacceptable level. The detection limit must therefore be defined in statistical terms and be related to
the probability of making a wrong decision.
Figure 2.4(a) shows normal error curves (B and S) with true means μB and μS for blank and sample
measurements respectively. It is assumed that for measurements made close to the limit of detection, the
standard