There are more significant digits in this number than four. The leading zero before the decimal point is not deemed insignificant nor are any of the numbers proceeding it.
In 1600.00 the proceeding two zeros after 1600 are insignificant. However, 1600.001, all numbers are significant.
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The 1st four digits are significant
Four - zeros between significant digits are significant.
111.009 rounded to four significant digits is 111.0
One - the four. None of the trailing 0s are significant digits.
14.587020 has eight significant digits. If you were going to round it off to four, the answer would be 14.59