Let's analyze the question from the uploaded image:

The problem asks to find the missing number in the list of numbers ordered from least to greatest. The given numbers are:

• $\frac{18}{5}$,
• $3.71$,
• a missing number,
• $\sqrt{17}$.

The options for the missing number are:

1. $4.5$
2. $3.8 \%$ (interpreted as 0.038)
3. $\frac{57}{15}$
4. $(3.9)^2$

Step 1: Evaluate all the given numbers

1. $\frac{18}{5} = 3.6$
2. $3.71$ is already in decimal form.
3. $\sqrt{17} \approx 4.123$ (square root of 17 to three decimal places).

Step 2: Analyze the possible missing numbers

• $4.5$: Already in decimal form.
• $3.8\%$: Written as a decimal, $3.8\% = 0.038$, which is very small.
• $\frac{57}{15} = 3.8$: Convert $\frac{57}{15}$ to a decimal, yielding $3.8$.
• $(3.9)^2 = 15.21$: Square of $3.9$ is much larger than the other values in the list.

Step 3: Order the numbers

The list in ascending order:

• $0.038$ (option 2: $3.8\%$),
• $3.6$ ($\frac{18}{5}$),
• $3.71$,
• $3.8$ (option 3: $\frac{57}{15}$),
• $4.123$ ($\sqrt{17}$),
• $4.5$ (option 1: $4.5$).

Since the missing number falls between $3.71$ and $\sqrt{17} \approx 4.123$, the only possible choice is:

$\frac{57}{15} = 3.8$.

Final Answer:

The missing number is $\frac{57}{15}$ (Option 3).

Would you like further clarification or help with any step?

Here are 5 related questions to expand your understanding:

1. How do you convert percentages into decimals or fractions?
2. How do you approximate square roots like $\sqrt{17}$ without a calculator?
3. What is the method for ordering fractions, decimals, and square roots on a number line?
4. How do you simplify and compare fractions like $\frac{18}{5}$ and $\frac{57}{15}$?
5. How does $(3.9)^2$ affect its position on the number line when squared?

Tip: Always compare numbers in the same format (either all as decimals or fractions) for an accurate comparison!