Question

Simplify the expression. Write the answer in scientific notation.
left parenthesis 0.1 times 10 cubed right parenthesis left parenthesis 2 times 10 Superscript negative 9 right parenthesis
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Part 1
left parenthesis 0.1 times 10 cubed right parenthesis left parenthesis 2 times 10 Superscript negative 9 right parenthesisequals
  
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​(Simplify your answer. Use scientific notation. Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To simplify the expression \( (0.1 \times 10^3) \times (2 \times 10^{-9}) \), follow these steps:

1. **Multiply the coefficients**:
\[
0.1 \times 2 = 0.2
\]

2. **Add the exponents of 10**:
\[
10^3 \times 10^{-9} = 10^{3 + (-9)} = 10^{-6}
\]

3. **Combine the results**:
\[
0.2 \times 10^{-6}
\]

4. **Convert to scientific notation**: Scientific notation requires that the coefficient is between 1 and 10. To convert \( 0.2 \) to scientific notation:
\[
0.2 = 2.0 \times 10^{-1}
\]

Now, plugging that into our expression:
\[
(2.0 \times 10^{-1}) \times 10^{-6} = 2.0 \times 10^{-1 - 6} = 2.0 \times 10^{-7}
\]

So, the final answer in scientific notation is:

\[
\boxed{2.0 \times 10^{-7}}
\]