Question

(8.03 times 10 power -8) times (2.56 times 10 power -2

Answer 1

To multiply the two numbers in scientific notation, we can use the following steps:

1. **Multiply the coefficients**: Multiply the numbers in front of the powers of ten.
2. **Add the exponents**: Add the exponents of ten together.

Here are the calculations for the expression \((8.03 \times 10^{-8}) \times (2.56 \times 10^{-2})\):

1. **Multiply the coefficients**:
\[
8.03 \times 2.56 = 20.5588
\]

2. **Add the exponents**:
\[
-8 + (-2) = -10
\]

Putting it together, we get:
\[
20.5588 \times 10^{-10}
\]

Next, we can express this in proper scientific notation. The coefficient \(20.5588\) should be between 1 and 10, so we adjust it:

\[
20.5588 = 2.05588 \times 10^1
\]

Now, incorporating the exponent:
\[
2.05588 \times 10^{1} \times 10^{-10} = 2.05588 \times 10^{-9}
\]

Thus, the final result is:
\[
2.05588 \times 10^{-9}
\]