To solve this problem, we need to arrange the given numbers [tex]\(1 \frac{3}{4}, -1.5, -1.1, 1.03\)[/tex] in ascending order.
Step-by-step Solution:
1. Convert mixed numbers to improper fractions or decimals:
- The number [tex]\(1 \frac{3}{4}\)[/tex] can be converted to a decimal. Since [tex]\(\frac{3}{4} = 0.75\)[/tex], we have [tex]\(1 + 0.75 = 1.75\)[/tex].
- The other numbers are already in decimal form.
2. List the numbers for clarity:
- We have the following numbers to order: [tex]\(1.75, -1.5, -1.1, 1.03\)[/tex].
3. Rank the numbers in ascending order:
- First, identify the smallest negative number: [tex]\(-1.5\)[/tex].
- The next smallest negative number: [tex]\(-1.1\)[/tex].
- The next smallest positive number: [tex]\(1.03\)[/tex].
- The largest number: [tex]\(1.75\)[/tex].
4. Arrange the numbers in ascending order:
- The correct order is: [tex]\(-1.5, -1.1, 1.03, 1.75\)[/tex].
5. Match the given choices:
- Let's compare the ascending order [tex]\(-1.5, -1.1, 1.03, 1.75\)[/tex] with the choices provided:
- [tex]\(-1.5, -1.1, 1.03, 1 \frac{3}{4}\)[/tex]
- [tex]\(-1.1, -1.5, 1.03, 1 \frac{3}{4}\)[/tex]
- [tex]\(1 \frac{3}{4}, -1.5, -1.1, 1.03\)[/tex]
- [tex]\(1.03, -1.1, -1.5, 1 \frac{3}{4}\)[/tex]
6. Determine the correct choice:
- The first choice [tex]\(-1.5, -1.1, 1.03, 1 \frac{3}{4}\)[/tex] matches our ordered list of [tex]\(-1.5, -1.1, 1.03, 1.75\)[/tex].
Thus, the correct order for the given numbers is [tex]\(-1.5, -1.1, 1.03, 1.75\)[/tex], which corresponds to choice A:
[tex]\[
\boxed{-1.5, -1.1, 1.03, 1 \frac{3}{4}}
\][/tex]
