Question

Calculate the product below and give your answer in scientific notation.
\[ \large{\left(8\times 10^{-3} \right) \times \left(0.0002 \right) =\ ?} \]

Answer 1

To find the product \( \left(8 \times 10^{-3}\right) \times \left(0.0002\right) \), we can first express \(0.0002\) in scientific notation.

We know that:
\[
0.0002 = 2 \times 10^{-4}
\]

Now we can substitute this into our problem:
\[
\left(8 \times 10^{-3}\right) \times \left(2 \times 10^{-4}\right)
\]

Next, we can rearrange the expression using the associative and commutative properties of multiplication:
\[
(8 \times 2) \times (10^{-3} \times 10^{-4})
\]

Calculating \(8 \times 2\):
\[
8 \times 2 = 16
\]

Now we can handle the powers of ten:
\[
10^{-3} \times 10^{-4} = 10^{-3 + (-4)} = 10^{-7}
\]

Putting it all together:
\[
16 \times 10^{-7}
\]

Finally, to express \(16\) in scientific notation, we can write it as \(1.6 \times 10^1\):
\[
16 \times 10^{-7} = 1.6 \times 10^1 \times 10^{-7} = 1.6 \times 10^{1 - 7} = 1.6 \times 10^{-6}
\]

So, the final answer in scientific notation is:
\[
\boxed{1.6 \times 10^{-6}}
\]