To solve the problem [tex]\(\left(6.31 \times 10^6\right)+\left(5.25 \times 10^6\right)\)[/tex], follow these steps:
1. Identify the given values: We have two numbers in scientific notation:
[tex]\[
a = 6.31 \times 10^6
\][/tex]
[tex]\[
b = 5.25 \times 10^6
\][/tex]
2. Add the numbers directly since the exponents (both are [tex]\(10^6\)[/tex]) are the same. This means we simply add the coefficients (6.31 and 5.25):
[tex]\[
a + b = 6.31 \times 10^6 + 5.25 \times 10^6
\][/tex]
[tex]\[
= (6.31 + 5.25) \times 10^6
\][/tex]
3. Calculate the sum of the coefficients:
[tex]\[
6.31 + 5.25 = 11.56
\][/tex]
4. Combine the result with the common exponent:
[tex]\[
(6.31 + 5.25) \times 10^6 = 11.56 \times 10^6
\][/tex]
5. Convert the result to proper scientific notation:
Scientific notation requires that the coefficient (the number before the exponent) is between 1 and 10. Here, 11.56 needs to be adjusted:
[tex]\[
11.56 \times 10^6 = 1.156 \times 10^7
\][/tex]
6. Round to two significant figures:
[tex]\[
1.156 \times 10^7 \approx 1.16 \times 10^7
\][/tex]
Hence, the result of [tex]\(\left(6.31 \times 10^6\right)+\left(5.25 \times 10^6\right)\)[/tex] in scientific notation is:
[tex]\[
1.16 \times 10^7
\][/tex]
So, [tex]\(\left(6.31 \times 10^6\right)+\left(5.25 \times 10^6\right) = 1.16 \times 10^7\)[/tex].
