To solve the given operation [tex]\(\left(6.0 \times 10^5\right) \times \left(4.0 \times 10^6\right)\)[/tex] and express the result in correct scientific notation, follow these steps:
1. Multiply the coefficients:
The coefficients are the numbers in front of the powers of 10. Multiply [tex]\(6.0\)[/tex] and [tex]\(4.0\)[/tex]:
[tex]\[
6.0 \times 4.0 = 24.0
\][/tex]
2. Add the exponents:
The exponents are the powers of 10. Add the exponents [tex]\(5\)[/tex] and [tex]\(6\)[/tex]:
[tex]\[
5 + 6 = 11
\][/tex]
3. Combine the results:
Place the product of the coefficients and the sum of the exponents together:
[tex]\[
24.0 \times 10^{11}
\][/tex]
4. Adjust the coefficient to be between 1 and 10:
Since [tex]\(24.0\)[/tex] is not between 1 and 10, we need to adjust it. Divide [tex]\(24.0\)[/tex] by [tex]\(10\)[/tex], which gives us [tex]\(2.4\)[/tex], and increase the exponent by 1 to maintain the equality:
[tex]\[
24.0 \times 10^{11} = 2.4 \times 10^{12}
\][/tex]
Therefore, the answer in correct scientific notation is:
[tex]\[
2.4 \times 10^{12}
\][/tex]
