Question

Multiply and write your answer in scientific notation. Click Here for Help Video.



Be sure to write your answer with the multiplication
×
×





(
7
×
1
0
−
2
)
(7×10
−2
) ·
(
4
×
1
0
8
)
(4×10
8
)

Answer 1

To multiply the two expressions in scientific notation, you can multiply the coefficients and add the exponents. The given expressions are:

\[
(7 \times 10^{-2}) \cdot (4 \times 10^{8})
\]

1. **Multiply the coefficients**:
\[
7 \cdot 4 = 28
\]

2. **Add the exponents for the powers of ten**:
\[
-2 + 8 = 6
\]

Putting it all together, you get:

\[
28 \times 10^{6}
\]

3. **Convert to proper scientific notation**: In scientific notation, the coefficient should be between 1 and 10. To convert \(28\) into proper scientific notation, we rewrite it as:

\[
2.8 \times 10^{1}
\]

Now, combine this with \(10^{6}\):

\[
2.8 \times 10^{1} \times 10^{6}
\]

4. **Add the exponents again**:
\[
1 + 6 = 7
\]

So, the final result in scientific notation is:

\[
2.8 \times 10^{7}
\]

Thus,

\[
(7 \times 10^{-2}) \cdot (4 \times 10^{8}) = 2.8 \times 10^{7}
\]