# Understanding ILAC policy P14:12/2010 6.3 part a)

4

#### 426Hemi

I need help understanding ILAC policy P14:12/2010 6.3 part a), it states:

6.3 The numerical value of the expanded uncertainty shall be given to, at most, two significant figures. Further the following applies:
a) The numerical value of the measurement result shall in the final statement be rounded to the least significant figure in the value of the expanded uncertainty assigned to the measurement result.

Can someone explain this requirement, maybe in the form of "ILAC For Dummies", and provide a few examples.

I asked A2LA and have yet to get an answer.

D

#### dv8shane

WIki http://en.wikipedia.org/wiki/Significant_figures. So if you are reporting say % uncertainty and had a resolution of 3 significant figures you would round up per the GUM the least significant digit of the first 2 significant digits. Example measurement uncertainty before rounding 1.234 % This would round to 1.3% expressed with 2 significant figures. Ex 2 Measured value 10 V uncertainty 1.14 uV/V +/- 1.00 uV, This would be expressed as 1.2 uV/V +/- 1.0 uV

4

#### 426Hemi

Thanks for the examples. I interpret it as the measured result and the unc should be rounded to the same resolution. Here is an example of how my purchased software formats the calibration data for a balance with 1 g resolution: Nominal Value (standard mass) = 1000.0 g, As Found (DUT measured or displayed value) = 1000 g, Unc = 0.58 g. Does the Unc look correct or should it be 580 mg, 0.6 g, or 1 g? Thanks.

#### Hershal

##### Metrologist-Auditor
Staff member
Super Moderator
The other point to remember is P14 is in revision and discussion today may not work a few weeks from now. Personally, I would not stress that much at this time.

#### stefanhg

##### Involved In Discussions
Hi,

The correct uncertainty with two significant places is: 0.58 g or 58*10^1 mg

The correct uncertainty with one significant place is: 0.6 g or 6*10^2 mg

D

#### dv8shane

Hi,

The correct uncertainty with two significant places is: 0.58 g or 58*10^1 mg

The correct uncertainty with one significant place is: 0.6 g or 6*10^2 mg
I would disagree as the measured value is stated as 1000 not 1000.0, and the ? 0.58 would cause the display to go up or down by 1. You could not resolve the measurement by any less. Therefore the uncertainty would be ? 1 least significant digit.

#### stefanhg

##### Involved In Discussions
I would disagree as the measured value is stated as 1000 not 1000.0, and the ? 0.58 would cause the display to go up or down by 1. You could not resolve the measurement by any less. Therefore the uncertainty would be ? 1 least significant digit.
Hi,

According to official regulations and guidelines (GUM, Supplement 1 to the GUM, EA-4/02) the numerical values of the measurement results should be rounded to be consistent with their uncertainties.
This means, you can report the measured result with less or the same decimal places as the uncertainty, but never with more decimal places.

What you suggest is the opposite of the prescriptions in the standard - you are rounding the uncertainty by using as reference the measured value.
This is totally wrong, because the uncertainty is the defining parameter in the rounding procedure.

The complete result in this example should be: (1000 ? 0.58) g or (1000 ? 0.6) g

D

#### dv8shane

Hi,

According to official regulations and guidelines (GUM, Supplement 1 to the GUM, EA-4/02) the numerical values of the measurement results should be rounded to be consistent with their uncertainties.
This means, you can report the measured result with less or the same decimal places as the uncertainty, but never with more decimal places.
In this case the measurement result is limited to ? 1 significant figure. As the measurand can only be resolved to this how can you you claim less? The example quoted would be OK if you could resolve the measurement to 0.6 but you can not.

P

#### Pezikon

Hi,

According to official regulations and guidelines (GUM, Supplement 1 to the GUM, EA-4/02) the numerical values of the measurement results should be rounded to be consistent with their uncertainties.
This means, you can report the measured result with less or the same decimal places as the uncertainty, but never with more decimal places.

What you suggest is the opposite of the prescriptions in the standard - you are rounding the uncertainty by using as reference the measured value.
This is totally wrong, because the uncertainty is the defining parameter in the rounding procedure.

The complete result in this example should be: (1000 ? 0.58) g or (1000 ? 0.6) g
You are quoting section 7.2.6 of the GUM. The example given in that paragraph shows a situation where the measurement result has more precision than the uncertainty. As the example follows, the measurement result is rounded to match the precision of the uncertainty.
I would argue that 7.2.6 doesn't specifically address a situation where the measurement result has less precision than the uncertainty. What I consider to be "consistent" is when the precision of the measurement result and uncertainty match. Look in any guide on measurement uncertainty and it will be written that measurement uncertainty should be expressed as, at most, two sig-figs. It is necessary that the measurement result and reported uncertainty have the same precision for the sake of significance arithmetic.
Using significant figures rules, the result is rounded to the position of the least significant digit in the most uncertain of the numbers when adding or subtracting. For example:
1000. + 0.58 = 1000.
1000. - 0.6 = 1000.
1000. + 1. = 1001.
For the result to show no impact of uncertainty is to suggest that there is no uncertainty, which is erroneous. Considering uncertainties are the result of statistical calculations and sig-fig rules are used for scientific and statistical calculations, it should go without saying that significance arithmetic is extremely relevant here.
You said, "...you can report the measured result with less or the same decimal places as the uncertainty..." I would have to disagree with the "less decimal places" part.

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