If the uncertainty in an experimentally determined quantity, x = 2.233597 is 0.003, then you round off the value of x to obtain, x = 2.234. Supposing the estimation of the uncertainty lead a value, 0.003498, then how do you obtain the final value of x?
The reference "Guide to the expression of uncertainty in measurement" (https://www.bipm.org/en/publications/guides/gum.html) recommends to report 2 significant digits on the uncertainty.
In your example 0.0035, and you round off the value at the same level 2.2336.
The question about the required number of significant figures in the uncertainty stement is not as straightforward as presented above. In fact, the Guide to the expression of uncertainty in measurement (Clause 7.2.6) recommends reporting "to at most two significant digits", not two significant digits necessarily. This is quite understandable since the uncertainty estimates are often very approximate and the relative uncertainty in the uncertainty estimate itself may as large as 20–30 %. Under these circumstances, there is little sense in citing the uncertainty such as 0.78 mg/l (the standard uncertainty in mass concentration) with two figures; a single figure (0.8 mg/l) is appropriate in this and similar cases. A rule, which is good to follow, is
The uncertainty of the measurement is expressed by two significant digits if the leading digit in the uncertainty equals 1 or 2, and by one significant digit if the leading digit equals 3 or more.
The measured quantity value should be rounded so that the last decimal digit corresponds to the last digit of the uncertainty. This useful rule has long been formulated in the metrological community.
Dr. Rouvim Kadis,
The recommendation of ASTM International (http://www.galvanizeit.com/uploads/ASTM-E-29-yr-13.pdf) is similar to what you have suggested. The difference is that the uncertainty is rounded off to the first significant digit if it is 2 or above (instead of 3 or above); viz.
"Round test results to the place of the first significant digit in the standard deviation if the digit is two or higher, to the next place if it is a one."
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