Let's break down the set of numbers and convert them into decimal values for easier comparison. The given set is:

$\{-415\%, -\sqrt{17}, -4.1, -4.08\}$

Step 1: Convert each value to decimal

1. $-415\%$: $-415\% = -415/100 = -4.15$

2. $-\sqrt{17}$: $\sqrt{17} \approx 4.1231, \quad \text{so} \quad -\sqrt{17} \approx -4.1231$

3. $-4.1$: Already in decimal form, $-4.1 = -4.1000$.

4. $-4.08$: Already in decimal form, $-4.08 = -4.0800$.

Step 2: Compare the decimal values

Now that we have all the numbers in decimal form, let's list them:

$\{-4.15, -4.1231, -4.1, -4.08\}$

From least to greatest:

$-4.15, -4.1231, -4.1, -4.08$

Step 3: Verify on the number line

Looking at the number line, which ranges from $-4.18$ to $-4.08$, we can plot the values:

• $-4.15$ is between $-4.16$ and $-4.14$.
• $-4.1231$ (which is $-\sqrt{17}$) is between $-4.12$ and $-4.10$, slightly to the left of $-4.1$.
• $-4.1$ is exactly on the mark at $-4.1$.
• $-4.08$ is exactly on the mark at $-4.08$.

Conclusion:

The correct order from least to greatest is:

$\boxed{-4.15, -\sqrt{17}, -4.1, -4.08}$

Would you like further clarification or details?

Here are 5 related questions to expand on this:

1. What is the square root of a number, and how is it calculated?
2. How can you convert percentages to decimal values?
3. What is the significance of number line intervals in plotting values?
4. How can we compare irrational numbers like square roots to decimals?
5. Why is it important to standardize units before comparing values?

Tip: When comparing irrational numbers like square roots, it's helpful to approximate their decimal values to make direct comparisons easier.