To simplify the expression [tex]\( 0.3 \left(8.2 \times 10^{-3}\right) \)[/tex] and write the answer using scientific notation, follow these steps:
1. Multiply the numerical values:
Multiply [tex]\( 0.3 \)[/tex] by [tex]\( 8.2 \)[/tex]:
[tex]\[
0.3 \times 8.2 = 2.46
\][/tex]
2. Account for the power of ten:
Multiply the result by [tex]\( 10^{-3} \)[/tex]:
[tex]\[
2.46 \times 10^{-3}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
2.46 \times 10^{-3}
\][/tex]
Comparing this result with the given options:
- A. [tex]\( 7.38 \times 10^{-4} \)[/tex] - This is incorrect.
- B. 0.00246 - This is not in scientific notation, although it is mathematically correct.
- C. 0.000738 - This is incorrect.
- D. [tex]\( 2.46 \times 10^{-3} \)[/tex] - This is correct.
Therefore, the correct answer is:
[tex]\[
\boxed{2.46 \times 10^{-3}}
\][/tex]
