Question

What is the product of 8, point, 0, times, 10, squared8.0×10
2
and 7, point, 4, times, 10, squared7.4×10
2
expressed in scientific notation?

Answer 1

To find the product of \(8.0 \times 10^2\) and \(7.4 \times 10^2\), we can follow these steps:

1. Multiply the coefficients (the numbers in front).
2. Add the exponents of 10.

### Step 1: Multiply the coefficients

\[
8.0 \times 7.4 = 59.2
\]

### Step 2: Add the exponents of 10

\[
10^2 \times 10^2 = 10^{2+2} = 10^4
\]

### Combine the results

Now, we put it together:

\[
59.2 \times 10^4
\]

### Convert to Scientific Notation

In scientific notation, we want the coefficient to be a number between 1 and 10. To convert \(59.2\) into proper scientific notation:

\[
59.2 = 5.92 \times 10^1
\]

Now we can substitute back:

\[
59.2 \times 10^4 = 5.92 \times 10^1 \times 10^4 = 5.92 \times 10^{1 + 4} = 5.92 \times 10^5
\]

Thus, the product of \(8.0 \times 10^2\) and \(7.4 \times 10^2\) expressed in scientific notation is:

\[
\boxed{5.92 \times 10^5}
\]