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@Tamara54....
First, when the cell is formatted as General or Scientific, =T.DIST(-18.12, 499, TRUE) returns about 4.63E-57 on my computer and using Excel Online at onedrive.live.com.
If you see literally 0.00 on another computer, it is because the cell is formatted as Number with 2 decimal places, and 0.00 is just an illusion. On the other computer, confirm that =A1=0 returns FALSE(!), assuming the T.DIST formula is in A1.
Second, what makes you think that 5.13E-51 (rounded) and 4.63E-57 are wrong? What are you expecting, and why?
Finally, note that 5.13E-51 and 4.63E-57 are infinitesimally small numbers. They are approximately zero.
Even if T.DIST should return exactly zero with those parameters mathematically (but I doubt it!), most binary computer implementations are subject to the limitations and anomalies of (typically) 64-bit binary floating-point representation.
So, it is not unusual for the result of an Excel formula to be different from the mathematical formula. As a simple example, note that 10.1 - 10 = 0.1 returns FALSE(!). (LMK if you would like me to explain why.)
Generally, the work-around is: when you expect a calculation to be accurate to some number of decimal places, explicitly round to that number of decimal place -- and not to an arbitrary number of decimal places like 10.
For example, =ROUND(T.DIST(-16.84, 499, TRUE), 4), if you expect accuracy to 4 decimal places.
PS.... Literally T.DIST(-16.84, 499, TRUE) returns 5.13384546596352E-51, which rounds to 5.13385E-51, not 5.12902E-51.
So, either you posted the wrong example, or (more likely) the first parameter is not literally -16.84 as you wrote.
Obviously, when you ask a question about precision, it is important to show us the numerical inputs and results precisely.
For example, the first parameter might be -16.8400872802734, which rounds to -16.84. And T.DIST might return 5.12901956959532E-51, which rounds to 5.12902E-51.