What conventions did the Jews use to express time in Jesus' day? I was reading Acts and I came across Acts 2:15 which reads "These men are not drunk, as you suppose. It's only nine in the morning!"(NIV, 1984).

But I realized that in the Apostolic times,  they did not use the a.m. and p.m. way of time telling. So, after a brief search, I found that in early translations, it is "For these are not drunken, as ye suppose, seeing it is but the third hour of the day" (KJB, Cambridge ed.)

I know we live by grace and anything we do which is not of faith is a sin. I like using the old way of time telling. But when I communicate, I try to be helpful in order not to confuse people and use the am, pm time. I think this old timing is the standard in countries like Ethiopia and some Greek, Indian and Russian churches.
The NIV has simply translated the Jewish reckoning into a time that moderns would understand more readily. 

Briefly, hours were reckoned from sunrise - the third hour of the day would be about three hours after sunrise.   Depending on the time of year, that is usually around 9 or 10am in the morning.

As to the concerns about translating units, one should realize there is nothing sacred about the units.  Translating units is merely a helpful aid to the reader who is otherwise unaccustomed to the system.

It would be the equivalent of going from the German Er fahrt funf kilometer to He drove three miles. Literally, the sentence says 5km, but in changing units as well, the reader gains more clarity. 

There is nothing any more sacred about units in which a thing is measured than in the sylables with which a word is pronounced. 

People who are baptized in the name of Jesu, Yeshua, iousous (Greek), or "der Herr" are not going to Hell because the syllables G and sus were not uttered. 

Unlike Islam, Christianity does not believe there is anything sacred about original languages. Units of measure would be no different- whilest the KJV will speak of homers and ephaths, modern translations are totally okay with kilos and liters. 

(As an American, however, quarts are clearly holier than liters. How else do you explain our refusal to do what everyone else is doing!)