Question

1. It was close to 1:15 a.m.

2. It was near 1:15 a.m.
3. It was about 1:15 a.m.
4. It was around 1:15 a.m.
5. It was roughly 1:15 a.m.
6. It was approximately 1:15 a.m.
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Are they all grammatical and do they have the same meaning?

Answer 1

All are correct and they all have the same meaning. We would not say "near 1:15 A.M.", though, although it is correct. Near usually connotes physical distance, as in that town is near the river, etc.