When I am writing an essay, do I spell out times? How would I write AM or PM?
How would I write that?
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The latest edition of the Chicago Manual of Style recommends am and pm, with or without periods. They used to be set in small caps, but that's falling out of favour. You shouldn't use these abbreviations with the words morning, afternoon, evening, night, or o’clock.
There is no need to spell out times in an essay, although you might in creative writing or prose.
The important thing is to pick a convention, and be consistent.
According to an article on About.com:
Dates, phone numbers, and time: Use numbers for dates:
My birthday is March 16.
He was born on Valentines Day, 1975.
And use numbers for phone numbers: The phone number for the school is 800-555-6262
And use numbers for time if using a.m. or p.m.:
The alarm will sound at 7 p.m.
I make my bed at 7 a.m. each morning.
But spell out times when using "o'clock" or when the a.m. or p.m. are omitted:
The alarm will sound at seven o'clock.
I make my bed at seven each morning.
The correct way to write a precise time when using the acronym of Ante or Post Meridiem is AM or PM in professional writing.
Sources: Common Errors in English Usage The time stamp on your email, mobile phone, digital clock, Microsoft Windows, etc.