To solve the problem of ordering the given numbers from least to greatest, we first need to understand each number's approximate value. The numbers in question are:
[tex]\[
\frac{1}{2}, -4, \sqrt{7}, -\frac{7}{4}, 3.3
\][/tex]
Let's approximate the values:
1. [tex]\(\frac{1}{2}\)[/tex] is simply [tex]\(0.5\)[/tex].
2. [tex]\(-4\)[/tex] is already in its simplest form as [tex]\(-4\)[/tex].
3. [tex]\(\sqrt{7}\)[/tex] is approximately [tex]\(2.6457513110645907\)[/tex].
4. [tex]\(-\frac{7}{4}\)[/tex] can be converted to a decimal, which is [tex]\(-1.75\)[/tex].
5. [tex]\(3.3\)[/tex] is already in its simplest form as [tex]\(3.3\)[/tex].
Now, let's list these numbers with their values for clarity:
- [tex]\(-4 = -4\)[/tex]
- [tex]\(-\frac{7}{4} = -1.75\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\sqrt{7} \approx 2.6457513110645907\)[/tex]
- [tex]\(3.3 = 3.3\)[/tex]
Next, arrange these values from least to greatest:
[tex]\[
-4, -1.75, 0.5, 2.6457513110645907, 3.3
\][/tex]
With this ordering, we see that the correct sequence of numbers from least to greatest is:
[tex]\[
-4, -\frac{7}{4}, \frac{1}{2}, \sqrt{7}, 3.3
\][/tex]
Now let's match this sequence with the given options:
- A. [tex]\(-4, -\frac{7}{4}, \frac{1}{2}, \sqrt{7}, 3.3\)[/tex]
- B. [tex]\(-4, -\frac{7}{4}, \frac{1}{2}, 3.3, \sqrt{7}\)[/tex]
- C. [tex]\(\frac{1}{2}, -\frac{7}{4}, 3.3, \sqrt{7}, -4\)[/tex]
- D. [tex]\(-\frac{7}{4}, -4, \frac{1}{2}, 3.3, \sqrt{7}\)[/tex]
The correct option is A:
[tex]\[
A. \(-4, -\frac{7}{4}, \frac{1}{2}, \sqrt{7}, 3.3\)
\][/tex]
