What does the data represent? If it is a date-time in 2016, precise to the millisecond, the answer might be for converting it to a JMP date-time value. If it is a part number you should keep it as character data.
Is it a CSV file? Are you using text file import or Multiple File Import or Excel Import?
I'm not an Excel expert, but I think those values are string data in Excel.
Most programs (JMP included) use a double precision floating point representation that can't handle exact integers bigger than 2^53, which is smaller than those numbers.
You can make JMP use a format that will look like an integer, but least significant digits are not really there.
Format( "Fixed Dec", 18, 0 )
There are at most 15-16 significant digits in a double.
big integer values
Craige