Let's break down the expression step-by-step.

We are asked to evaluate:

$\frac{90 \, \text{million km}}{110 \, \text{light years}} \times 206265$

Step 1: Convert quantities to consistent units.

• 1 light year = $9.461 \times 10^{12} \, \text{km}$

Thus, $110 \, \text{light years}$ becomes:

$110 \times 9.461 \times 10^{12} = 1.04071 \times 10^{15} \, \text{km}$

Step 2: Compute the fraction.

$\frac{90 \times 10^6}{1.04071 \times 10^{15}} = \frac{9.0 \times 10^7}{1.04071 \times 10^{15}} \approx 8.644 \times 10^{-8}$

Step 3: Multiply by 206265.

$8.644 \times 10^{-8} \times 206265 \approx 0.0178$

Final Answer:

$\frac{90 \, \text{million km}}{110 \, \text{light years}} \times 206265 \approx 0.0178$

Let me know if you need further clarifications or explanations!

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Here are 5 follow-up questions:

1. What is the significance of the number 206265 in astronomical calculations?
2. How is the parsec related to light years and astronomical units?
3. What are other units used to measure astronomical distances?
4. How do we convert kilometers into astronomical units (AU)?
5. Can you derive the conversion factor between arcseconds and degrees?

Tip: Astronomers often use 206265 to convert radians into arcseconds, since $1 \, \text{radian} = 206265 \, \text{arcseconds}$.