It is a count of all digits, excluding leading zeros before the decimal point.
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I assume you mean significant digits. All digits are significant. A zero between other digits is always significant.
Five significant digits. Remember that all non-zero digits are significant, and all zeros in-between significant digits are significant.
All numbers which are not "zero" are classed as significant digits. Therefore in the number 129 there will be three digits which are classed as significant.
The number 6,051.00 has six significant digits. The number 6,051 has only four significant digits.
Because all non-zero numbers are significant and any zeros in-between significant digits are significant, there are 6 significant digits in 10.0039.