Work Out The Value Of $\left(6.31 \times 10^5\right) + \left(2.6 \times 10^4\right$\]. Give Your Answer In Standard Form.

When dealing with numbers in scientific notation, it's essential to understand the rules for adding and subtracting them. In this case, we're given two numbers in scientific notation: $\left(6.31 \times 10^5\right)$ and $\left(2.6 \times 10^4\right)$. Our goal is to find the value of their sum and express it in standard form.

What is Scientific Notation?

Scientific notation is a way of expressing numbers in the form $a \times 10^n$, where $a$ is a number between 1 and 10, and $n$ is an integer. This notation is useful for representing very large or very small numbers in a more compact and manageable form.

Understanding the Numbers in Scientific Notation

Let's take a closer look at the two numbers given in scientific notation:

• $\left(6.31 \times 10^5\right)$: This number represents a value between 1 and 10 multiplied by $10^5$. In this case, $a = 6.31$ and $n = 5$.
• $\left(2.6 \times 10^4\right)$: This number represents a value between 1 and 10 multiplied by $10^4$. In this case, $a = 2.6$ and $n = 4$.

Adding Numbers in Scientific Notation

When adding numbers in scientific notation, we need to follow a specific procedure:

1. Ensure the powers of 10 are the same: If the powers of 10 are different, we need to adjust the numbers so that they have the same power of 10.
2. Add the coefficients: Once the powers of 10 are the same, we can add the coefficients (the numbers in front of the powers of 10).
3. Express the result in standard form: After adding the coefficients, we need to express the result in standard form.

Applying the Procedure to the Given Numbers

Let's apply the procedure to the given numbers:

1. Ensure the powers of 10 are the same: We need to adjust the numbers so that they have the same power of 10. Since $10^5$ is larger than $10^4$, we can rewrite the second number as $\left(2.6 \times 10^4\right) = \left(0.026 \times 10^5\right)$.
2. Add the coefficients: Now that the powers of 10 are the same, we can add the coefficients: $6.31 + 0.026 = 6.336$.
3. Express the result in standard form: The result is $6.336 \times 10^5$.

Conclusion

In this article, we learned how to add numbers in scientific notation. We applied the procedure to the given numbers and found the value of their sum in standard form. By following the steps outlined in this article, you can confidently add numbers in scientific notation and express the result in standard form.

Final Answer

The final answer is $\boxed{6.336 \times 10^5}$.