Actually there are three established rules on counting how many significant figures are in a number:
Rule 1: Positive integers are always significant.
Rule 2: Any zeros between two significant digits are always significant.
Rule 3: A final zero or trailing zeros after the decimal point are always significant.
Since the given number is 10.0010 g, the two 1’s is under Rule 1, the three 0’s between the two 1’s is under Rule 2, and the zero after the last 1 is under Rule 3. Therefore all the digits are significant.
Answer: So the number of significant figures in the measurement is 6.