Significant Digits and Uncertainty - Page 1
Forum section: electronics / beginners

author: metrologist
author_rank: Super Contributor
timestamp: April 22, 2019, 10:11:59 pm
content: Hi All,I was looking at a specification and wondered if this is presented correctly:High Power: 32dBm ± 1dB; Total Uncertainty: 0.5dBLow Power: 12dBm ± 1.5dB; Total Uncertainty: 0.75dBI've forgotten if the number of significant digits or measurement resolution should all match?Thanks

author: metrologist
author_rank: Super Contributor
timestamp: April 22, 2019, 11:59:05 pm
content: I was reading this:Quotehttps://www.inorganicventures.com/significant-figures-and-uncertainty

author: David Cutcher CEG
author_rank: Contributor
timestamp: April 23, 2019, 12:14:37 am
content: I'm going to suggest that this is an editing problem, not a significant figure problem.David Cutcher "Certified Evil Genius"

author: sokoloff
author_rank: Super Contributor
timestamp: April 23, 2019, 12:35:27 am
content: 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.

author: David Cutcher CEG
author_rank: Contributor
timestamp: April 23, 2019, 12:43:37 am
content: 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 10299.5David Cutcher "Certified Evil Genius"

author: metrologist
author_rank: Super Contributor
timestamp: April 23, 2019, 01:02:53 am
content: Quote from: David Cutcher CEG on April 23, 2019, 12:43:37 amI 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).

author: metrologist
author_rank: Super Contributor
timestamp: April 23, 2019, 02:32:05 pm
content: 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?

author: Mr. Scram
author_rank: Super Contributor
timestamp: April 23, 2019, 02:36:05 pm
content: Quote from: sokoloff on April 23, 2019, 12:35:27 amI 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?

author: tggzzz
author_rank: Super Contributor
timestamp: April 23, 2019, 03:15:52 pm
content: Quote from: sokoloff on April 23, 2019, 12:35:27 amI have a voltage sources marked 10.0000V. Does that have 1 significant figure (not 6), and so could be anywhere between 9V and 11V?

author: metrologist
author_rank: Super Contributor
timestamp: April 23, 2019, 03:29:55 pm
content: From NIST SP811-2008Quote1.2E3 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.I've not found an explanation of what I'm looking for.

author: AndyC_772
author_rank: Super Contributor
timestamp: April 23, 2019, 03:32:45 pm
content: 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.

author: metrologist
author_rank: Super Contributor
timestamp: April 23, 2019, 04:31:16 pm
content: 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, soMU 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: 0.50dBLow Power: 12.0dBm ± 1.5dB; Total Uncertainty: 0.75dBOne 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)