Please check the sentence and let me know is it correct or not? My question is that "can we use since to tell the complete duration of time as well in this way?"
I have been doing it since 4:40 P.M. to 7:00 P.M.
Thanks in advance.
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This is not idiomatic.
Since always refers to a timespan extending from the named time to the current Reference Time (RT)—the time your sentence is talking about.
In your example, the main verb is in the present perfect, so RT is the present, now. You would use since only if the endpoint of the timespan is now, which need not (and indeed should not) be further specified:
I am very tired. I have been doing X since 4:40 pm.
If you used a past perfect here, the timespan would extend up to the RT you are talking about, and again would not be further specified:
I was very tired. I had been doing X since 4:40 pm.
If RT is present (now) and the endpoint of the timespan is in the past, you should use a simple past form, and the timespan should be defined using from ... to/until:
I am very tired. I did X from 4:40 pm to 7 pm (and then did something else).
If RT is past and the endpoint is some point before RT, you should use a past perfect, and again the timespan should be defined using from ... to/until:
I was very tired. I had done X from 4:40 pm until 7 pm (and had then done something else).