To determine which of the given numbers is not a rational number, let's analyze each one in detail:
1. Number: [tex]\(-5 \frac{4}{11}\)[/tex]
We can express this as a single fraction:
[tex]\[
-5 + \frac{4}{11} = -5 + 0.363636363636... = -4.636363636363637
\][/tex]
This number is a terminating or repeating decimal, so it is rational.
2. Number: [tex]\(\sqrt{31}\)[/tex]
The square root of 31 is:
[tex]\[
\sqrt{31} \approx 5.5677643628300215
\][/tex]
Since 31 is not a perfect square, [tex]\(\sqrt{31}\)[/tex] is an irrational number.
3. Number: 7.608
This is a simple decimal number that does not repeat and terminates. Therefore, it is a rational number.
4. Number: [tex]\(18.4 \overline{6}\)[/tex]
The notation [tex]\(18.4 \overline{6}\)[/tex] represents a repeating decimal:
[tex]\[
18.4666666\ldots
\][/tex]
Repeating decimals are rational numbers because they can be expressed as a fraction.
Hence, among the given numbers:
- [tex]\(-5 \frac{4}{11} \approx -4.636363636363637\)[/tex]
- [tex]\(\sqrt{31} \approx 5.5677643628300215\)[/tex]
- [tex]\(7.608\)[/tex]
- [tex]\(18.4 \overline{6}\)[/tex]
The number that is not rational is [tex]\(\sqrt{31}\)[/tex].
