Style clarification for date superscripts, th, st and nd

I wanted to know, while writing dates such as 1st April or 2nd March; do we need to superscript the st and the nd as 1^st April and 2^nd March, or is it ok to write them without the superscript formatting. When to use superscript for dates and when not to use it?

I couldn't find any guidance regarding this in my style manual. Any guidance on this as per the Chicago or the Oxford Manual will be very helpful.

Thank you.

Solution 1:

The Chicago Manual of Style (15th edition) is quite clear in section 9.35: "The day of the month. When specific dates are expressed, cardinal numbers are used, although they may be pronounced as ordinals."

Solution 2:

The Chicago Manual of Style 2017 says in section 9.6:

The letters in ordinal numbers should not appear as superscripts (e.g., 122nd, not 122^nd).

According to Wikipedia, Bluebook and style guides by the Council of Science Editors, Microsoft, and Yahoo recommend the same.