I am trying to illustrate the convergence of a sequence of iterates by means of the following plot:
In my discussion I would like to state the fact that 1) the function is monotonically decreasing and 2) the sequence of iterates converge at iteration 13 (as there is no further decrease in the function after this point as shown in sub-figure inside the plot). My concern, however, is that the y-axis label in this plot has too many significant figures. I would be very grateful for some advice on the following points:
a) whether the number of significant figures in the y-axis label should be reduced
b) whether doing a) compromises the aims of my disucssion
Many thanks.
The last three digits of the $y$ values are the only ones that carry any information that varies in the plot. I assume you have reason to believe they are correct. You certainly can't reduce the number of significant digits in the display. But you can consider changing the format.
I think you should display only those three digits on the $y$ axis, perhaps with format
...abc, with an indication in the text or caption that they are the digits that follow $47.26566$.