QCS-016 - Quality Operations Procedures for Pharmaceutical, API, and Biotechnology - page 86

SOP No. QCS-016.00 Effective date: mm/dd/yyyy
Approved by:

16.3.3.2.4 Integers: A Special Case
For quantities that are restricted to occurring in discrete, indivisible units, the number of significant
figures is infinite. We generally assume that integers always have as many significant figures as are
necessary when used in a calculation. For example, in the calculation of the perimeter of a square
(four times the length of a side), we can assume that the number 4 used in the calculation has as
many significant figures as the length measurement. One exception to this rule is Avogadro's num-
ber which, while an integer, has not been known to the requisite 23 significant figures.
The astute student will recognize that numbers such as pi, while not an integer, can be repre-
sented to as many significant figures as may be required in any given computation (e.g., the calcula-
tion of the volume of a sphere from its radius, using V = (4/3) × pi × r 3 ). Indeed, in this formula, the
4, the two 3s and the pi are all known to an infinite number of significant figures. All of the uncer-
tainty in the volume V is due only to the uncertainty in the radius r . The number of significant fig-
ures in V is fixed by those in r .

16.3.3.2.5 Significant Figures and Scientific Notation
Scientific notation (i.e., writing numbers in the form y.yyy × 10 n ) simplifies the use of significant
figures considerably. The issue of using zeros as place holders for decimal points can be made to
disappear. The multiplier (y.yyy) has exactly the number of significant figures as are justified. This
may involve a number of trailing zeros. For example, 6.02214 × 10 23 has six significant figures.
While scientific notation goes a long way toward solving the significant figure problem, it is not
always easy to follow, particularly when additions and subtractions are involved. Consider, for
example, the following two buret readings whose difference is the net volume.

Final volume

3.105 × 10 1 mL

Initial volume 3.2 × 10 −1 mL

In normal numeric representation, that subtraction is represented as follows:

Final volume 31.05 mL

Initial volume 0.32 mL

As the last example shows, in the laboratory course, scientific notation will not always be the best
way to handle simple computations—particularly the addition and subtraction of numbers.

16.4 reason for revision
First time issued for your company, affiliates, and contract manufacturers.