Question

Multiply write your answer in scientific notation
( 3 x 10 to the power of -5 ) (3 x 10 to the power of 2)

Answer 1

To multiply numbers in scientific notation, you can follow these steps:

1. Multiply the coefficients (the numbers in front).
2. Add the exponents of the powers of ten.

Given the expression:

\[
(3 \times 10^{-5}) \times (3 \times 10^{2})
\]

1. **Multiply the coefficients**:
\[
3 \times 3 = 9
\]

2. **Add the exponents**:
\[
-5 + 2 = -3
\]

Putting it all together, we have:
\[
9 \times 10^{-3}
\]

Now, we need to express it in proper scientific notation. The coefficient \(9\) needs to be between \(1\) and \(10\). To do this, we can express \(9\) as \(9.0 \times 10^0\):

\[
9 \times 10^{-3} = 9.0 \times 10^0 \times 10^{-3} = 9.0 \times 10^{-3} = 0.9 \times 10^{-2}
\]

Thus, the final answer in proper scientific notation is:
\[
0.9 \times 10^{-2}
\]

But if we wish to keep the \(9\) as a coefficient, the simplest scientific notation result is:

\[
9 \times 10^{-3}
\]

So, the answer in scientific notation is:

\[
9 \times 10^{-3}
\]