Determine the number of significant digits in the value 0.001001 .

According to the rules for determining significant figures, all non-zero digits are significant, and zeros between non-zero digits are also significant.

Leading zeros to the left of the first non-zero digit are not significant as they only indicate the position of the decimal point.

In the given number $0.001001$, the first three zeros are leading zeros and are not significant.

The digits $1001$ consist of two non-zero digits and two zeros between them, making all four of these digits significant.

Therefore, the number of significant digits in $0.001001$ is $4$.