### Author Topic: Significant Digits and Uncertainty  (Read 405 times)

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#### metrologist

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##### Significant Digits and Uncertainty
« on: April 23, 2019, 08:11:59 am »
Hi All,

I was looking at a specification and wondered if this is presented correctly:

High Power: 32dBm ± 1dB; Total Uncertainty: 0.5dB
Low Power: 12dBm ± 1.5dB; Total Uncertainty: 0.75dB

I've forgotten if the number of significant digits or measurement resolution should all match?

Thanks

#### metrologist

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##### Re: Significant Digits and Uncertainty
« Reply #1 on: April 23, 2019, 09:59:05 am »

Quote
A number reported as 10,300 is considered to have five significant figures.
...
If the number is reported as 10,300 ± 53, the number of significant figures is still 4 and the number reported this way is acceptable, but the 3 in the 53 is not significant.

https://www.inorganicventures.com/significant-figures-and-uncertainty

#### David Cutcher CEG

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##### Re: Significant Digits and Uncertainty
« Reply #2 on: April 23, 2019, 10:14:37 am »
I'm going to suggest that this is an editing problem, not a significant figure problem.
David Cutcher "Certified Evil Genius"

#### sokoloff

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##### Re: Significant Digits and Uncertainty
« Reply #3 on: April 23, 2019, 10:35:27 am »
I was taught significant figure rules aligned with this page’s rules: https://courses.lumenlearning.com/introchem/chapter/significant-figures/

Where 10300 would have 3 (not 5) significant figures.

#### David Cutcher CEG

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##### Re: Significant Digits and Uncertainty
« Reply #4 on: April 23, 2019, 10:43:37 am »
I agree.
Where 10300 has an accuracy of half of the last significant figure.  Which means range of accuracy is between 10350 and 10250, unless otherwise stated.
If it had 5 sig figs, the accuracy would be between  10300.5  and 10299.5
David Cutcher "Certified Evil Genius"

#### metrologist

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##### Re: Significant Digits and Uncertainty
« Reply #5 on: April 23, 2019, 11:02:53 am »
I agree.
Where 10300 has an accuracy of half of the last significant figure.  Which means range of accuracy is between 10350 and 10250, unless otherwise stated.
If it had 5 sig figs, the accuracy would be between  10300.5  and 10299.5
David Cutcher "Certified Evil Genius"

I don't recall seeing it presented that way. For example, if I had a DMM that read 10300mV, that would mean the reading can be interpreted from (10299 to 10301)mV and the measurement then must add in the tolerance, which could be anything the mfg states (and then consider uncertainty on top of that).

#### metrologist

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##### Re: Significant Digits and Uncertainty
« Reply #6 on: April 24, 2019, 12:32:05 am »
My question is not so much how to determine how many significant figures in a number, but rather does a specification make sense in the example, or if you specify a number like -10dBm±1.3dB, and then list MU as ±0.55dB.

Do the sig digits need to match or the resolution or neither? And can you even tell for the MU? Does that depend on other factors that might not be known, as I think it is a calculated figure from a number of variables?

#### Mr. Scram

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##### Re: Significant Digits and Uncertainty
« Reply #7 on: April 24, 2019, 12:36:05 am »
I was taught significant figure rules aligned with this page’s rules: https://courses.lumenlearning.com/introchem/chapter/significant-figures/

Where 10300 would have 3 (not 5) significant figures.
I was taught that trailing zeros do have significance. Otherwise you'd be able to denote anything but an exact number. 10.0000 volt is as accurate as 9.9997 and not suddenly a lot less accurate. What's the point of having a super accurate 8 digit meter and reference if the significance is ultimately only one digit?
« Last Edit: April 24, 2019, 12:38:53 am by Mr. Scram »

#### tggzzz

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##### Re: Significant Digits and Uncertainty
« Reply #8 on: April 24, 2019, 01:15:52 am »
I was taught significant figure rules aligned with this page’s rules: https://courses.lumenlearning.com/introchem/chapter/significant-figures/

Where 10300 would have 3 (not 5) significant figures.

I have a voltage sources marked 10.0000V. Does that have 1 significant figure (not 6), and so could be anywhere between 9V and 11V?
There are lies, damned lies, statistics - and ADC/DAC specs.
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#### metrologist

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##### Re: Significant Digits and Uncertainty
« Reply #9 on: April 24, 2019, 01:29:55 am »
From NIST SP811-2008

Quote
A digit is significant if it is required to express the numerical value of a quantity. In the expression
l = 1200 m, it is not possible to tell whether the last two zeroes are significant or only indicate the
magnitude of the numerical value of l.

1.2E3 is not the same as 1.200E3. So, yes all those zeros AFTER the decimal are significant.

I also really like the example about rounding and conversion, where 36ft converts to 11.0m, and further, 36ft rounded to the nearest inch also converts to 11.0m.

« Last Edit: April 24, 2019, 01:32:03 am by metrologist »

#### AndyC_772

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##### Re: Significant Digits and Uncertainty
« Reply #10 on: April 24, 2019, 01:32:45 am »
Imagine how you'd choose to write the value using scientific notation, and count the digits prior to the exponent.

If your voltage source is 1x10^1, then that's one significant figure.

If it's 1.00000x10^1, then that's six.

#### metrologist

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##### Re: Significant Digits and Uncertainty
« Reply #11 on: April 24, 2019, 02:31:16 am »
Here is what I think based on what I read here:

https://www.isobudgets.com/how-to-report-uncertainty-in-measurement/

"The good news is the rules for reporting uncertainty have become much clearer over the last 10 years; and, today, we are going to cover them all!"

It was a lot longer than 10 years ago last I even casually looked at this, so

MU should be expressed to two significant digits in the same units, but could be to a higher resolution, and not lower. Tolerance should be to the same resolution as the stated specification. So my OP should be:

High Power: 32dBm ± 1dB; Total Uncertainty: 0.50dB
Low Power: 12.0dBm ± 1.5dB; Total Uncertainty: 0.75dB

One of their examples for the Fluke meter seems to clarify my question, where they state:

0.0000000 (nominal value to 7 sig figures)
0.0000256 (measurement result to 7 sig figures, same resolution)
0.0000500 (tolerance is -0.0000000 to +0.0000500, 7 sig figures)
1.0E-5 (or 0.000010, two sig figures, at greater resolution than the tolerance, so I guess that means a MU of 1.0E-10 could still be valid)
« Last Edit: April 24, 2019, 02:33:22 am by metrologist »

Smf