To solve the problem [tex]\(\frac{2 \times 10^4 + 6 \times 10^5}{3.1 \times 10^3}\)[/tex], let's walk through the steps in detail.
1. Calculate the numerator:
[tex]\[
2 \times 10^4 + 6 \times 10^5
\][/tex]
Breaking down the calculation:
[tex]\[
2 \times 10^4 = 20,000 \quad \text{and} \quad 6 \times 10^5 = 600,000
\][/tex]
Adding these values together:
[tex]\[
20,000 + 600,000 = 620,000
\][/tex]
Therefore, the numerator is [tex]\(620,000\)[/tex].
2. Calculate the denominator:
[tex]\[
3.1 \times 10^3
\][/tex]
Converting it to a numerical value:
[tex]\[
3.1 \times 10^3 = 3,100
\][/tex]
Therefore, the denominator is [tex]\(3,100\)[/tex].
3. Perform the division:
[tex]\[
\frac{620,000}{3,100}
\][/tex]
Carrying out the division:
[tex]\[
\frac{620,000}{3,100} = 200
\][/tex]
4. Convert the result to standard form:
The result is [tex]\(200\)[/tex]. We express this in standard form, which is a way of writing numbers that are too big or too small conveniently.
Standard form follows the structure [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex].
For [tex]\(200\)[/tex], we can write:
[tex]\[
200 = 2.00 \times 10^2
\][/tex]
Hence, the result given in standard form is:
[tex]\[
2.00 \times 10^2
\][/tex]
Therefore, the final answer to the problem [tex]\(\frac{2 \times 10^4 + 6 \times 10^5}{3.1 \times 10^3}\)[/tex] in standard form is [tex]\(\boxed{2.00 \times 10^2}\)[/tex].
