Question

What is the product of 3, point, 8, times, 10, squared 3.8 × 10 to the power of 2 and 6.4 × 10 to the power of 6 expressed in scientific notation?

Answer 1

To calculate the product of \(3.8 \times 10^2\) and \(6.4 \times 10^6\), you can follow these steps:

1. **Multiply the coefficients**:
\[
3.8 \times 6.4 = 24.32
\]

2. **Add the exponents of the powers of ten**:
\[
10^2 \times 10^6 = 10^{(2 + 6)} = 10^8
\]

3. **Combine the results**:
\[
24.32 \times 10^8
\]

4. **Convert to scientific notation**: To express \(24.32\) in scientific notation, we rewrite it as \(2.432 \times 10^1\). Therefore:

\[
24.32 \times 10^8 = 2.432 \times 10^1 \times 10^8 = 2.432 \times 10^{(1 + 8)} = 2.432 \times 10^9
\]

So, the product of \(3.8 \times 10^2\) and \(6.4 \times 10^6\) expressed in scientific notation is:

\[
\boxed{2.432 \times 10^9}
\]