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To solve this expression, I'll break down each part of the equation step-by-step for clarity. Here's the expression we need to evaluate:

\[
\sqrt{\left(\frac{915 - 0.1}{915^2}\right)^2 \times 2.5^2 + \left(\frac{0.1}{915 \times 6.9}\right)^2 \times 0.297^2}
\]

Let's go through each component:

1. **Calculate \(\frac{915 - 0.1}{915^2}\):**
   - First, \(915 - 0.1 = 914.9\).
   - Then, \(915^2 = 837225\).
   - So, \(\frac{915 - 0.1}{915^2} = \frac{914.9}{837225}\).

2. **Square the result from step 1 and multiply by \(2.5^2\):**
   - \(2.5^2 = 6.25\).
   - Square the fraction and then multiply by 6.25.

3. **Calculate \(\frac{0.1}{915 \times 6.9}\):**
   - First, calculate \(915 \times 6.9\).
   - Then, \(\frac{0.1}{915 \times 6.9}\).

4. **Square the result from step 3 and multiply by \(0.297^2\):**
   - \(0.297^2\) is another component.
   - Square the fraction and multiply by \(0.297^2\).

5. **Add the results from steps 2 and 4, then take the square root of the sum.**

I'll calculate each step for you.The result of the expression is approximately:

\[
0.0027
\]

Would you like further details on any specific steps, or do you have any questions?

Here are some related questions that might expand on this:

1. How does squaring affect fractions in expressions?
2. What is the importance of order of operations in complex expressions like this?
3. How can similar expressions be simplified before calculation?
4. What are common errors to avoid in handling such large denominators?
5. How does this type of expression apply in real-world contexts, such as physics or engineering?

**Tip:** Breaking down complex expressions step-by-step, especially with nested operations, can help prevent mistakes and improve accuracy in calculations.

Evaluate the expression \( \sqrt{\left( \frac{915 - 0.1}{915^2} \right)^2 \times 2.5^2 + \left( \frac{0.1}{915 \times 6.9} \right)^2 \times 0.297^2} \).

Learn how to evaluate a complex expression involving fractions, squares, and square roots. The expression \( \sqrt{\left( \frac{915 - 0.1}{915^2} \right)^2 \times 2.5^2 + \left( \frac{0.1}{915 \times 6.9} \right)^2 \times 0.297^2} \) is broken down into simple steps for clarity, covering algebraic concepts suitable for Grades 10-12.

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