To solve the expression $(1.08 \times 10^{-3}) \times (9.3 \times 10^{-3})$, we can multiply the coefficients and add the exponents for the powers of 10.

1. Multiply the coefficients:
   $1.08 \times 9.3 = 10.044$

2. Add the exponents:
   $(-3) + (-3) = -6$

3. Combine the results:
   $10.044 \times 10^{-6}$

This can be expressed as $1.0044 \times 10^{-5}$ after adjusting to proper scientific notation.

Final Answer:

$1.0044 \times 10^{-5}$

Would you like more details on any step?

Related Questions:

1. How do you convert a number to scientific notation?
2. What are the rules for multiplying exponents?
3. How do you multiply numbers with different exponents?
4. How does adjusting scientific notation work?
5. What is the significance of exponents in multiplication?

Tip: When multiplying numbers in scientific notation, remember to multiply the coefficients and add the exponents!