To order the given set of rational numbers from least to greatest, let's carefully examine each number and compare them:
1. We have the numbers:
[tex]\[
-4.625, -5.2, -4 \frac{4}{5}, -4 \frac{8}{11}
\][/tex]
2. Convert the mixed numbers to improper fractions or decimals to facilitate comparison:
- [tex]\( -4 \frac{4}{5} = -4 + \frac{4}{5} = -4 + 0.8 = -4.8 \)[/tex]
- [tex]\( -4 \frac{8}{11} = -4 + \frac{8}{11} \approx -4 + 0.727 = -4.727 \)[/tex]
3. Now we have:
[tex]\[
-4.625, -5.2, -4.8, -4.727
\][/tex]
4. Arrange the numbers from least to greatest:
- The smallest number is [tex]\(-5.2\)[/tex]
- Next is [tex]\(-4.8\)[/tex]
- Then comes [tex]\(-4.727\)[/tex]
- Finally, [tex]\(-4.625\)[/tex]
So the correct order from least to greatest is:
[tex]\[
-5.2, -4.8, -4.727, -4.625
\][/tex]
Thus, the correct answer choice is:
b. [tex]\( -5.2, -4 \frac{4}{5}, -4.625, -4 \frac{8}{11} \)[/tex]
