Writing an uncertainty of the form $8.3\pm1.2$ using 'parenthesis' notation similar to $5.9722(6)$ It's common in the physical sciences to write dimensional quantities with their 1-sigma uncertainty range as, e.g.:
$$
M_\oplus=5.9722(6)\times10^{24} \; \mathrm{kg}
$$
However, I'm having a disagreement with a colleague over what to do in the situation where the number you're quoting only has 1 d.p. For example, I want to express $h = (8.3 \pm 1.2) \; \mathrm{m}$. I think I should do so like this:
$$
h = 8.3(12) \; \mathrm{m}
$$
She thinks I should do so like this:
$$
h = 8.3(1.2) \; \mathrm{m}
$$
Which of us is right, is this a matter of opinion and, most importantly, can you provide a reference to an authoritive style guide, etc. on the subject?
 A: Both forms are correct, but the uncertainty is rarely if ever reported in an abbreviated form in cases like that of your example. The first form is definitely ambiguous and can be easily mistaken. The second one is less ambiguous, but not well known (it's correct anyhow, see the Guide to the expression of uncertainty in measurement, §7.2.2, point 3).
Thus, you're both right, but, generally speaking, I'd avoid ambiguous forms.
A: When analyzing a reported value and trying to determine what is significant, all nonzero digits are significant, and it is only zeros that require some thought. We will use the terms “leading,” “trailing,” and “captive” for the zeros and will consider how to deal with them. Source: https://opentextbc.ca/chemistry/chapter/measurement-uncertainty-accuracy-and-precision/.

I agree with your friend, use 1.2, not your value. In cases where only the decimal-formatted number is available, it is prudent to assume that all trailing zeros are not significant.

The probabilities of a value lying within 1-sigma, 2-sigma and 3-sigma of the mean for a normal distribution.
The significance of various levels of $\sigma$, or confidence that result is real: 1 $\sigma$ 84.13%, 1.5 $\sigma$ 93.32%, 2 $\sigma$ 97.73%, 2.5 $\sigma$ 99.38%, 3 $\sigma$ 99.87%, 3.5 $\sigma$ 99.98%, 4 $\sigma$ 100%. Source: https://thecuriousastronomer.wordpress.com/2014/06/26/what-does-a-1-sigma-3-sigma-or-5-sigma-detection-mean/.
Note: When determining significant figures, be sure to pay attention to reported values and think about the measurement and significant figures in terms of what is reasonable or likely when evaluating whether the value makes sense. For example, the official January 2014 census reported the resident population of the US as 317,297,725. Do you think the US population was correctly determined to the reported nine significant figures, that is, to the exact number of people? People are constantly being born, dying, or moving into or out of the country, and assumptions are made to account for the large number of people who are not actually counted. Because of these uncertainties, it might be more reasonable to expect that we know the population to within perhaps a million or so, in which case the population should be reported as 3.17 × 10$^8$ people.
There are many fields where allowance and tolerance is a factor and Standards were created, currently the "ISO Guide to the Expression of Uncertainty in Measurement" (GUM) and the NIST TN 1297 (Section 7: Reporting Uncertainty) are what is followed.
Source: http://pages.physics.cornell.edu/p510/w/images/p510/b/b7/Lecture_3_S11.pdf
Different Types of Uncertainties


*

*Random/Statistical  (All)
Always  present  in a measurement.  It  is  caused  by  inherently unpredictable  fluctuations  in the readings  of  a measurement apparatus  or  in the  experimenter's  interpretation  of  the instrumental  reading.  Originates  in the  Poisson  distribution.   

*Systematic  (All) 
From  imperfect  calibration  of  measurement  instruments,  or imperfect  methods  of  observation,  or  interference  of  the environment  with  the  measurement  process.  Always  affect the  results  of  an  experiment  in a predictable  direction. e.g.  zero  setting  error  in  which  the  instrument  does  not  read zero  when  the  quantity  to  be  measured  is  zero 

*Theory  (e.g.  N15,  N17)
In  these  experiments  you  measure  the  muon  lifetime.  But  there are  corrections  to  the  capture  rate  for  muon  that  come  from theory. 
Different Types of Uncertainties
It  is common to  quote  these  uncertainties  separately: 
τ$_μ$=(2.19+/-0.05$_{stat.}$+/-0.01$_{syst.}$+/-0.02$_{th.}$) $μ$s 
Different notations  are used  for  uncertainties,  e.g. 
τ$_μ$=(2.19(5)$_{stat.}$+/-(1)$_{syst.}$+/-(2)$_{th.}$) $μ$s 
Meaning  of Measurement  Uncertainty
• If  we  measure  for example  a  voltage  V = 10.2 +/- 0.3 V, what  does  this  mean?
• In  general  there  are differences  in  different science disciplines.
• In physics, a  1-sigma  uncertainty  is  generally  used. If  the measurements  are normally  distributed  (Gaussian), this corresponds  to a  68% confidence  level  (CL)  interval.  Or that  32% of the  time the true  value  would  be outside  the quoted  uncertainty range. 
Semantics


*

*Accuracy  vs. Precision 
Accuracy  is the  degree  to which a measurement  agrees  with  the true  value.
Precision  is the  repeatability of the  measurement.

*Error vs. Uncertainty 
Error  is the  degree  to  which  a Measurement  agrees  with  the true  value.
Uncertainty  is an  interval  around  the  measurement  in  which  repeated measurements  will  fall. 
