If I have a date written: Saturday 16 December is it correct ?
Or does the grammar oblige me to add the number suffix to 16 making 16th as in: Saturday 16th December ?
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It is a matter of house style. Some publications will have the style explicitly set out in a standards document. For example, both the Guardian and Wikipedia standardise on not writing the number suffix in dates.
If you are writing for a magazine/etc. copy what other material in that organ does (or, trust subeditors to shape your words into their house style).
If you are in full control, pick a standard, and stick to it.
If you are writing dialogue, consider writing the exact words the person would say, in full -- so that the reader, or an actor, will say the words you had in mind.
The third of March
This is nothing to do with grammar but rather a matter of typography, and one on which practice varies. I prefer the unadorned date, 16 December, and I think that is what might now be generally found in the UK.
About a decade ago, I read a news of reporting a lot youths in U. K. made mistakes of writing 1th 2th and 3th as suffixes of dates which were embarrassing the Education Department. As to avoid such happenings in future, the educators suggested to omit the suffixes which was accepted by related department and later not only dates but also the abbreviations of Mr, Dr and Ms are with no full stop
Adding the suffix is the right way to write dates its always 3rd March or 2nd December .