https://file.aiquickdraw.com/mathbot/file/1728859943883rajgddp4.jpg

From the uploaded image, I can read two mathematical problems related to scientific notation:

1. **Problem 11:**
   Calculate \( 2.1 \times 10^3 + 2.21 \times 10^2 \). Write your answer in scientific notation.

2. **Problem 12:**
   Calculate \( 8140 \times 10^5 - 6.68 \times 10^7 \). Write your answer in scientific notation.

Let's solve these one by one:

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### Problem 11: \( 2.1 \times 10^3 + 2.21 \times 10^2 \)

To add these numbers, we need them to have the same exponent. We can rewrite \( 2.21 \times 10^2 \) as \( 0.221 \times 10^3 \), so we can combine the terms:
\[
2.1 \times 10^3 + 0.221 \times 10^3 = (2.1 + 0.221) \times 10^3 = 2.321 \times 10^3
\]

Thus, the answer in scientific notation is:
\[
2.321 \times 10^3
\]

---

### Problem 12: \( 8140 \times 10^5 - 6.68 \times 10^7 \)

First, express both terms in the same exponent. We rewrite \( 8140 \times 10^5 \) as \( 8.14 \times 10^8 \), and the second term is already \( 6.68 \times 10^7 \), so we rewrite it as \( 0.668 \times 10^8 \).

Now, subtract the terms:
\[
8.14 \times 10^8 - 0.668 \times 10^8 = (8.14 - 0.668) \times 10^8 = 7.472 \times 10^8
\]

Thus, the answer in scientific notation is:
\[
7.472 \times 10^8
\]

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Would you like further details on any of these steps or explanations?

Here are some related questions you might explore:

1. How do you convert a number from standard form to scientific notation?
2. Why is it important to match exponents when adding or subtracting numbers in scientific notation?
3. What are the rules for multiplying and dividing numbers in scientific notation?
4. How can scientific notation help simplify very large or very small numbers?
5. What are common applications of scientific notation in fields like chemistry or astronomy?

**Tip:** Always ensure that numbers are expressed with the same powers of ten when performing addition or subtraction in scientific notation to avoid calculation errors.

Problem 11: Calculate 2.1 × 10^3 + 2.21 × 10^2. Problem 12: Calculate 8140 × 10^5 - 6.68 × 10^7.

Learn how to add and subtract numbers in scientific notation, including detailed solutions for the expressions 2.1 × 10^3 + 2.21 × 10^2 and 8140 × 10^5 - 6.68 × 10^7. Suitable for students in Grades 7-10.

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