Concept:
Rules for significant figures:
• Leading zeros are not significant.
• Zeros between non-zero digits are significant.
• Trailing zeros after a decimal point are significant.
• The power of \(10\) does not affect the number of significant figures.
Step 1: Count the significant figures.
In
\[
0.0010200
\]
the significant digits are
\[
1,\;0,\;2,\;0,\;0
\]
Hence,
\[
\boxed{5\text{ significant figures}}
\]
Step 2: Final conclusion.
The factor \(10^{5}\) does not change the count of significant figures.
Therefore, the correct option is \(\boxed{(B)}\).