Should bin widths of histograms fall on “nice” round numbers? TLDR - I want to know if it's ok to use bin widths which are not nice round numbers (like integers or simple fractions are)
I have a set of data, for which I have calculated a recommended uniform
bin width using Scott's rule (I'm not interested in non-uniform widths), and the value is a recurring decimal. This means that the bars are placed in awkward positions along the axis, and they do not correspond to the tick marks. Furthermore, it feels a bit awkward to talk about "the data in the range 1.456 - 2.211". What is considered best practice?
EDIT
To clarify, my data relates to the weights of sample of animals, since a few people that commented mentioned the type of data is important. The weights range from 0 to around 5 lbs. The suggested bin width is 0.678etc lb.
 A: No, there's no need to fall on round numbers. However, categories may be important for description (e.g. age intervals). On the other side, what if you're constructing a histogram with a variable whose sample values are between 0.23 and 1.12? Here the round numbers are simply impossible.
Whether these bins make the histogram look good or horrible strongly depends on sample size; for instance, data from a bayesian MCMC are so numerous (generally > 1000) that you may well choose very small bins, way smaller than unity.
Try these lines in R:
hist(rnorm(10), breaks = seq(from = -3, to = 3, by = 1))
hist(rnorm(10), breaks = seq(from = -3, to = 3, by = 0.5))
hist(rnorm(10000), breaks= seq(from = -5, to = 5, by = 1))
hist(rnorm(10000), breaks= seq(from = -5, to = 5, by = 0.5))
hist(rnorm(10000), breaks= seq(from = -5, to = 5, by = 0.1))

Now compare how informative are them concerning the underlaying distribution of values (normal with mean 0 and sd 1).
hist(rnorm(10000), breaks= seq(from = -5, to = 5, by = 0.1), prob = TRUE)
curve(dnorm(x, 0, 1), from = -5, to = 5, add = TRUE, col = "red")

A: No clear yes/no answer, but points of consideration. 
Who is the audience? When possible, a graphic should show frequencies binned into scientifically relevant categories. The experts can then deduce the useful info they need from the graphic. These may or may not be nice, round numbers as you say. But as an example, we would like to depict age in 5 or 10 year intervals, BMI in 5 kg/m$^2$ intervals, US annual household income in \$10,000 or \$50,000 intervals, and so on. These intervals are informed by our prior research. By complying with previously set standards, results can be compared directly across different studies.
When finding scientifically relevant intervals is simply not possible, it is important to devote some discussion to why you chose the intervals you did choose. Using values empirically from a sample to divide the range into 5-10 evenly spaced bins is not inherently bad. Mentioning the method explicitly helps the reader appreciate the seemingly arbitrary breakpoints. But it is not a valid critique of analysis to simply say, "That's a strange number...".
If you want to strike a compromise, it is always acceptable to round the former numbers to a nice, round value. For instance, if the bin width is calculated to be 1.74 based on 10 bins of equal space, there is nothing wrong with setting the bin-width to 2 and obtaining potentially 9 bins spanning the range instead of 10. 
This process can drastically affect the appearance of multimodal data. Aliasing can completely mask the appearance of two or more nodes to make data appear unimodal, or vice versa. Often the point of a histogram is to depict the "shape" of the distribution. It is therefore always advisable to verify the appropriateness of a binned histogram by inspecting a kernel density smoothed 
 distribution plot. This is a type of "continuous histogram" and shows local frequency minima and maxima in data more precisely  than histograms.
