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The problem is asking to "Select all the pairs where the second number is about 20 times greater than the first number." Let's analyze the given pairs:

1. **Option A**: \( 9 \cdot 10^5 \) and \( 2 \cdot 10^7 \)

   The ratio is:
   \[
   \frac{2 \cdot 10^7}{9 \cdot 10^5} = \frac{2}{9} \cdot 10^2 \approx 0.22 \cdot 100 = 22.2
   \]
   This is approximately 20.

2. **Option B**: \( 5 \cdot 10^6 \) and \( 10^7 \)

   The ratio is:
   \[
   \frac{10^7}{5 \cdot 10^6} = \frac{1}{5} \cdot 10^1 = 2
   \]
   This is not close to 20.

3. **Option C**: \( 10^8 \) and \( 2 \cdot 10^{10} \)

   The ratio is:
   \[
   \frac{2 \cdot 10^{10}}{10^8} = 2 \cdot 10^2 = 200
   \]
   This is far larger than 20.

4. **Option D**: \( 3 \cdot 10^9 \) and \( 6 \cdot 10^{10} \)

   The ratio is:
   \[
   \frac{6 \cdot 10^{10}}{3 \cdot 10^9} = 2 \cdot 10^1 = 20
   \]
   This is exactly 20.

5. **Option E**: \( 4 \cdot 10^7 \) and \( 2 \cdot 10^9 \)

   The ratio is:
   \[
   \frac{2 \cdot 10^9}{4 \cdot 10^7} = \frac{2}{4} \cdot 10^2 = 0.5 \cdot 100 = 50
   \]
   This is much larger than 20.

### Conclusion:
The correct pairs are **A** and **D**, as they satisfy the condition of the second number being about 20 times greater than the first number.

Would you like more details or have any questions?

### Follow-up questions:
1. How do we calculate the ratio between two numbers using scientific notation?
2. Why does multiplying powers of 10 simplify when dividing numbers?
3. How do different bases affect the ratio in this kind of problem?
4. What are some common mistakes when interpreting ratios between large numbers?
5. Could logarithms help verify ratios in scientific notation?

### Tip:
Always break down complex ratios involving powers of 10 by first simplifying the coefficients and then handling the exponents separately.

Select all the pairs where the second number is about 20 times greater than the first number.

Analyze pairs of numbers in scientific notation and calculate the ratio between them. Learn how to identify which pairs have a second number about 20 times greater than the first. This problem is suitable for Grade 8 students.

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