#### Answer

There are 6 significant digits.

#### Work Step by Step

To find the number of significant digits in the measurement $32.0070~g$, we follow the rules on page 162 of the book.
We use rule #1: all non-zero digits are significant. Thus "3,2,7" are significant.
We also use rule #2: all zeros between significant digits are significant; thus, we have here 2 zeros which are significant.
We also use rule #4: all zeros to the right of a significant digit and decimal point are significant; that is, we have here 1 zero which is significant.
Thus, there are 6 significant digits.