Biomedical Engineering Reference
In-Depth Information
SOP No. QCS-016.00 Effective date: mm/dd/yyyy
Approved by:
The six significant figures in the initial and final weights produce a number (their difference)
with only three significant figures (but still with four decimal digits. The zero after the decimal
point, while important, is not a significant figure).
Suppose that the sample weight is now used in the calculation of a concentration by dividing it
by a volume of 20.32 mL. Despite the four significant figures in the volume, the resulting concentra-
tion should be reported to at most three significant figures, namely 0.00253 g/mL. In general, the
number of significant figures in a multiplication or division of quantities will be that of the quantity
with the least number of significant figures.
16.3.3.2.3 How to Manage Zeros
Perhaps the most confusing aspect of significant figures is how to deal with the digit zero (0). That
number is often used as a place holder to indicate the location of a decimal point. When used in this
manner, zero is not a significant figure. The only times that 0 is significant is when one or more of
them occur between nonzero digits or when one or more of them in a row is at the end of a string of
nonzero digits.
Consider the following examples:
The 0 is used only to highlight the occurrence of a decimal point following it. It is not a signifi-
cant figure.
0.0654
In this case, neither 0 is significant. They are not preceded by any nonzero digit
0.605
The 0 is again not significant, but the 0, since it occurs between two nonzero digits, is
significant
0.6005
The 0 is again not significant, but both the 0's are significant, since they occur between
two nonzero digits.
10.654
This time, the 0 to the left of the decimal point is significant. It occurs between two
nonzero digits.
10.0654
In this number, both the zeros are significant digits since there are nonzero digits both
before the first and after the second.
Now consider a number that is the result of an experimental measurement. Suppose the number
is reported as 3.16.
We can assume that the investigator was certain that the result was <3.17 and >3.15. With the
usual rules for rounding, we can indeed assume that the result was <3.165 and >3.155.
Suppose instead, one reports the number as
3.160
What shall we make of the terminal 0? The fact that the number is written as is an
indication that the investigator was certain that the result was <3.161 and >3.159.
(With rounding, <3.1605 and >3.1595.) A substantial decrease in the uncertainty of
the result and an increase in the precision of the measurement over the previous
representation.
If the number is reported as
3.1600 This is an indication that the investigator was certain that the number was 3.1599. (One
should be able to provide the limits assuming rounding rules.) An additional decrease in
the uncertainty. These zeros are certainly significant.
If one understands the above, one should be able to determine which zeros are significant in the
following number: 0.0010600.
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