To place the numbers given on the number line in ascending order, it's useful to consider their decimal representations. Let's first list the provided numbers for clarity: [tex]\(1 \frac{3}{4}, 1.5, -1.1, 1.03\)[/tex].
We need to convert any fractions to decimal form. The number [tex]\(1 \frac{3}{4}\)[/tex] can be converted to its decimal form:
[tex]\[1 \frac{3}{4} = 1 + \frac{3}{4} = 1 + 0.75 = 1.75.\][/tex]
We now have the decimal versions of all numbers:
[tex]\[1 \frac{3}{4} = 1.75, \, 1.5, \, -1.1, \, 1.03.\][/tex]
Next, we will arrange these numbers in ascending order (from the smallest to the largest):
1. [tex]\(-1.1\)[/tex]
2. [tex]\(1.03\)[/tex]
3. [tex]\(1.5\)[/tex]
4. [tex]\(1.75\)[/tex]
So, the correct order of the numbers is:
[tex]\[-1.1, \, 1.03, \, 1.5, \, 1.75.\][/tex]
Therefore, the correctly ordered indices should be:
[tex]\[-1.1, \, 1.03, \, 1.5, \, 1 \frac{3}{4}.\][/tex]
From the given multiple choice options, the correct choice that matches this order is:
[tex]\[
\boxed{-1.1, \, 1.03, \, 1.5, \, 1 \frac{3}{4}}
\][/tex]
