https://file.aiquickdraw.com/mathbot/file/1726920863179ljf4qbuq.jpg

The given expression is:

\[
\frac{0.509 \times 67.9^2}{\sqrt{95.99}}
\]

We are asked to estimate the value using approximations to 1 significant figure. Let's break it down:

### Step 1: Approximate each term to 1 significant figure.
- \( 0.509 \approx 0.5 \)
- \( 67.9 \approx 70 \)
- \( 95.99 \approx 100 \)

### Step 2: Substitute the approximated values into the expression.
\[
\frac{0.5 \times 70^2}{\sqrt{100}} = \frac{0.5 \times 4900}{10}
\]

### Step 3: Simplify the expression.
\[
\frac{0.5 \times 4900}{10} = \frac{2450}{10} = 245
\]

### Final Approximation
The estimated value is approximately **245**.

Would you like further details or have any other questions?

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Here are 5 related questions to extend this problem:
1. How would the answer change if we used 2 significant figures instead of 1?
2. What is the effect of approximating the square root of 95.99?
3. How can you calculate this expression without approximations?
4. Why is it important to round consistently when estimating with significant figures?
5. Can you find an example where significant figures greatly affect the final answer?

**Tip:** When approximating numbers to 1 significant figure, rounding up or down can significantly affect your result, so always double-check your rounding!

Using approximations to 1 significant figure, estimate the value of (0.509 * 67.9^2) / √95.99.

Learn how to estimate the value of the expression (0.509 * 67.9^2) / √95.99 using approximations to 1 significant figure. This problem covers key concepts such as approximations, significant figures, and square roots, suitable for students in Grades 9-11.

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