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Let's go through each of the scientific notation problems and solve them step by step.

### Problem 1:
\[
(2 \times 10^3) + (5 \times 10^5)
\]
- Rewrite both numbers with the same exponent (convert \(10^3\) to \(10^5\)):
  \[
  2 \times 10^3 = 0.02 \times 10^5
  \]
- Now, add:
  \[
  0.02 \times 10^5 + 5 \times 10^5 = (0.02 + 5) \times 10^5 = 5.02 \times 10^5
  \]
- **Answer**: \(5.02 \times 10^5\)

### Problem 2:
\[
(4 \times 10^8) - (9 \times 10^7)
\]
- Rewrite both numbers with the same exponent (convert \(10^7\) to \(10^8\)):
  \[
  9 \times 10^7 = 0.9 \times 10^8
  \]
- Now, subtract:
  \[
  4 \times 10^8 - 0.9 \times 10^8 = (4 - 0.9) \times 10^8 = 3.1 \times 10^8
  \]
- **Answer**: \(3.1 \times 10^8\)

### Problem 3:
\[
(8 \times 10^9) - (3 \times 10^7)
\]
- Rewrite both numbers with the same exponent (convert \(10^7\) to \(10^9\)):
  \[
  3 \times 10^7 = 0.03 \times 10^9
  \]
- Now, subtract:
  \[
  8 \times 10^9 - 0.03 \times 10^9 = (8 - 0.03) \times 10^9 = 7.97 \times 10^9
  \]
- **Answer**: \(7.97 \times 10^9\)

### Problem 4:
\[
(5 \times 10^7) + (1 \times 10^6)
\]
- Rewrite both numbers with the same exponent (convert \(10^6\) to \(10^7\)):
  \[
  1 \times 10^6 = 0.1 \times 10^7
  \]
- Now, add:
  \[
  5 \times 10^7 + 0.1 \times 10^7 = (5 + 0.1) \times 10^7 = 5.1 \times 10^7
  \]
- **Answer**: \(5.1 \times 10^7\)

### Problem 5:
\[
(4 \times 10^2) + (7 \times 10^3)
\]
- Rewrite both numbers with the same exponent (convert \(10^2\) to \(10^3\)):
  \[
  4 \times 10^2 = 0.4 \times 10^3
  \]
- Now, add:
  \[
  0.4 \times 10^3 + 7 \times 10^3 = (0.4 + 7) \times 10^3 = 7.4 \times 10^3
  \]
- **Answer**: \(7.4 \times 10^3\)

### Problem 6:
\[
(9 \times 10^5) - (6 \times 10^4)
\]
- Rewrite both numbers with the same exponent (convert \(10^4\) to \(10^5\)):
  \[
  6 \times 10^4 = 0.6 \times 10^5
  \]
- Now, subtract:
  \[
  9 \times 10^5 - 0.6 \times 10^5 = (9 - 0.6) \times 10^5 = 8.4 \times 10^5
  \]
- **Answer**: \(8.4 \times 10^5\)

### Problem 7:
\[
(1 \times 10^6) - (8 \times 10^4)
\]
- Rewrite both numbers with the same exponent (convert \(10^4\) to \(10^6\)):
  \[
  8 \times 10^4 = 0.08 \times 10^6
  \]
- Now, subtract:
  \[
  1 \times 10^6 - 0.08 \times 10^6 = (1 - 0.08) \times 10^6 = 0.92 \times 10^6
  \]
- **Answer**: \(0.92 \times 10^6\)

### Problem 8:
\[
(5 \times 10^9) + (3 \times 10^8)
\]
- Rewrite both numbers with the same exponent (convert \(10^8\) to \(10^9\)):
  \[
  3 \times 10^8 = 0.3 \times 10^9
  \]
- Now, add:
  \[
  5 \times 10^9 + 0.3 \times 10^9 = (5 + 0.3) \times 10^9 = 5.3 \times 10^9
  \]
- **Answer**: \(5.3 \times 10^9\)

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### Relative Questions:
1. How do you convert between different powers of 10?
2. What is the general rule for adding and subtracting numbers in scientific notation?
3. Why do we need to convert exponents before adding or subtracting in scientific notation?
4. What happens when numbers have negative exponents in scientific notation?
5. How can scientific notation be applied to real-world measurements?

### Tip:
Always ensure that both numbers have the same exponent before adding or subtracting them in scientific notation to maintain consistency in calculations.

Simplify and express each problem in scientific notation.

Learn how to simplify and solve addition and subtraction problems using scientific notation. This worksheet includes multiple problems with step-by-step solutions, demonstrating key mathematical concepts like aligning exponents and adjusting coefficients. Suitable for students in Grades 6-8.

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