Question

Simplify the following quotient. Write the answer in scientific notation.
StartFraction 2.4 times 10 Superscript negative 8 Over 8 times 10 Superscript negative 6 EndFraction
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Part 1
StartFraction 2.4 times 10 Superscript negative 8 Over 8 times 10 Superscript negative 6 EndFraction
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​(Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To simplify the quotient

\[
\frac{2.4 \times 10^{-8}}{8 \times 10^{-6}},
\]

we can follow these steps:

1. **Divide the coefficients**:
\[
\frac{2.4}{8} = 0.3.
\]

2. **Subtract the exponents of \(10\)**:
\[
10^{-8} \div 10^{-6} = 10^{-8 - (-6)} = 10^{-8 + 6} = 10^{-2}.
\]

3. **Combine the results**:
\[
0.3 \times 10^{-2}.
\]

4. **Convert to scientific notation**:
We know that \(0.3\) can be written as \(3.0 \times 10^{-1}\). Therefore,
\[
0.3 \times 10^{-2} = (3.0 \times 10^{-1}) \times 10^{-2} = 3.0 \times 10^{-1 - 2} = 3.0 \times 10^{-3}.
\]

Hence, the final answer in scientific notation is

\[
\boxed{3.0 \times 10^{-3}}.
\]