Question

scientific notation of (6x10^-4)x(3x10^12)

Answer 1

To multiply the numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten.

Given:
\[
(6 \times 10^{-4}) \times (3 \times 10^{12})
\]

1. **Multiply the coefficients:**
\[
6 \times 3 = 18
\]

2. **Add the exponents:**
\[
-4 + 12 = 8
\]

Now, combine these results:
\[
18 \times 10^{8}
\]

However, the coefficient 18 is not between 1 and 10, so we need to express it in proper scientific notation. This can be done by rewriting 18 as \(1.8 \times 10^{1}\):

\[
18 \times 10^8 = 1.8 \times 10^{1} \times 10^8
\]

Now, add the exponents:
\[
1.8 \times 10^{1 + 8} = 1.8 \times 10^{9}
\]

Thus, the final result in scientific notation is:
\[
\boxed{1.8 \times 10^{9}}
\]