Should percentages be reported with decimal places? When presenting data using a percentage, is it a good thing to have decimal places, say 2 decimal places instead of rounding off to whole numbers?
For example, instead of 23.43%, you round off to 23%.
I am looking at this from the perspective of whether the 2 decimal places accuracy will make much difference since we are dealing with percentage and not raw data value.
 A: It depends on the size of the differences between classes. In most applications, saying the 73% prefer option A and 27% prefer option B is perfectly acceptable. But if you're dealing in an election where candidate X has 50.15% of votes and candidate Y has 49.86%, the decimal places are very much necessary.
Of course, you need to take care to make sure that all classes add up to 100%. In my electoral example above, they add up to 100.01%. In that case you might even consider adding a third decimal place.
A: Different organisations often have conflicting rules for the precision in reporting of results. Ultimately there is a trade-off between when seeing the extra digits is useful, versus cases where unnecessary and excessive precision "can swamp the reader, overcomplicate the story and obscure the message" — a subject explored by Tim Cole (2015) in a piece that I found gave a useful guide to "sensible" precision in reporting, and a comparison of leading style manuals. His advice on percentages was as follows:

Integers, or one decimal place for values under 10%. Values over 90% may need one decimal place if their complement is informative. Use two or more decimal places only if the range of values is less than 0.1%
Examples: 0.1%, 5.3%, 27%, 89%, 99.6%

By "complement" he is referring to cases where one might be interested in the "other lot", e.g. if I tell you 98% of patients in a trial got better, you may well be interested in the 2% who did not, and in that case another decimal place to distinguish whether that "2%" really means "2.4% or "1.6%" would actually be useful.
References
Cole, T. J. (2015). Too many digits: the presentation of numerical data. Archives of disease in childhood, 100(7), 608-609. http://dx.doi.org/10.1136/archdischild-2014-307149
A: This is a significant figures issue, and is dependent upon the precision of the numbers underlying the percentages. The technically correct number of significant figures is not dependent upon downstream use or the differences between percentage values.
If you're trying to express a percentage describing 5 items out of 7, it would be absurd to claim that it's 71.4285714285% - you simply don't have the precision to back up all those decimal places. When doing division, your answer should have as many significant figures and the fewest number of sig figs in your starting numbers. Here, you only have 1 significant figure, so the percentage should really just be 70%, not even 71%. If you had another example where you want to express 71428 items out of 100000, then you are justified in using more significant figures, all the way out to 71.428%.
Even if you have great precision, it's often preferable to truncate for human readability. Depending on your domain, adding those two extra decimal places may or may not make a difference. You should never over-report significant figures, but you may be justified in under-reporting them if your statistical precision is greater than what's needed for your application.
