GLP 9

**Good Laboratory Practice**

**for**

**Rounding Expanded Uncertainties and Calibration Values**

A calibration is not complete until the expanded uncertainty associated
with the calibration is determined and reported. Each Standard Operating
Procedure (SOP) includes information regarding the calculation of
uncertainties. The expanded uncer­tainty is generally reported with
approximately a 95 % confidence interval. The confidence interval is
determined by multiplying a coverage factor (usually 2) times the root
sum square of properly combined Type A and Type B evaluated components
according to the ISO/IEC Guide to the Expression of Uncertainty in
Measurement (GUM).

The steps for reporting corrections and uncertainties are as follows:

> 1\. Round the uncertainty to two significant figures.
>
> 2\. Round the correction/error to the last figure affected by the
> uncertainty.
>
> 3\. Report the rounded correction and uncertainty.

Zeros, which follow a decimal point, when there are only zeros ahead of
the decimal point, are not considered significant figures.

[Rounding Rules]{.underline}

Use the following rules to round measurement data, consistent with its
significance:

> 1\. When the digit next beyond the one to be retained is less than
> five, keep the retained figure unchanged. For example: 2.541 becomes
> 2.5 to two significant figures.
>
> 2\. When the digit next beyond the one to be retained is greater than
> five, increase the retained figure by one. For example: 2.453 becomes
> 2.5 to two significant figures.
>
> 3\. When the digit next beyond the one to be retained is exactly five,
> and the retained digit is even, leave it unchanged; conversely if the
> digit is odd, increase the retained figure by one (even/odd rounding).
> Thus, 3.450 becomes 3.4 but 3.550 becomes 3.6 to two significant
> figures.
>
> Note: Even/odd rounding of numbers provides a more balanced
> distribution of results. Use of computer spreadsheets to reduce data
> typically follows the practice of rounding up.

4.  When two or more figures are to the right of the last figure to be
    retained, consider them as a group in rounding deci­sions. Thus, in
    2.4(501), the group (501) is considered to be greater than 5 while
    for 2.5(499), (499) is considered to be less than 5.

Several examples to illustrate the proper method of reporting
corrections and uncertainties follow.

Example 1

Suppose the correction for a weight is computed to be 1.3578 mg and the
uncertainty is 0.5775 mg. First, round the uncertainty to two
significant figures, that is, 0.58 mg. Then state the correction as 1.36
mg. Notice that the uncertainty and the correction express the same
number of decimal places. Report the correction as 1.36 mg ± 0.58 mg.

Example 2

The volume of a given flask is computed to be 2000.714431 mL and the
uncertainty is 0.084024 mL. First, round the uncertainty to two
significant figures, that is, 0.084 mL. (Do not count the first zero
after the decimal point.) Round the calculated volume to the same number
of decimal places as the uncertainty statement, that is, 2000.714 mL.
Report the volume as 2000.714 mL ± 0.084 mL.

Example 3

The correction for a weight is computed to be 4.3415 mg and the
uncertainty is 2.0478 mg. First, round the uncertainty to two
significant figures, that is, 2.0 mg. (Notice that two significant
figures are shown. The zero is a significant figure since it follows a
non‑zero number.) Then, round the correction to the same number of
decimal places as the uncer­tainty statement, that is, 4.3 mg. Report the
correction as 4.3 mg ± 2.0 mg.

Example 4

The correction for a weight is computed to be 285.41 mg and the
uncertainty is 102.98 mg. Because this uncertainty is a large number, we
first convert both values to the next larger commonly reported unit
(i.e., 0.28541 g and 0.10298 g respectively). First, round the
uncertainty to 0.10 g. (The first nonzero digit (1) is the first
significant figure and the remaining digits are rounded to the nearest
number following the first nonzero digit.) Then, round the correction to
the point where the rounding occurred in the uncertainty statement.
Round the correction to 0.29 g. Report the correction as 0.29 g ± 0.10
g.

Example 5

The correction for a weight is computed to be 285.41 mg and the
uncertainty is 33.4875 mg. First, round the uncertainty to two
significant figures, that is 33 mg. Then, round the correction to the
same number of decimal places as the uncertainty statement, that is, 285
mg. Report the correction as 285 mg ± 33 mg.

Example 6

The length of a calibrated interval is computed to be 9.9994558 ft and
the uncertainty is 0.0035617 in. First, make sure both values are
reported in the same unit (i.e., convert the uncertainty to ft,
0.000296808 ft.) Then, round the value to two significant figures, that
is, 0.00030 ft. Then, round the length of the interval to the same
number of decimal places as the uncertainty value, that is, 9.99946 ft.
Report the length of the interval as 9.99946 ft ± 0.00030 ft.

Rather than stating the uncertainty value with each correction, it is
also proper to place the correction values in a column headed by the
words \"Correction\" or \"Error,\" etc., and place the uncertainties
(without plus or minus signs) in a column headed \"Expanded
Uncertainty\".