By definition:
- Rational numbers are those numbers that can be written as simple fractions. A fraction has this form:
[tex]\begin{gathered} \frac{a}{b} \\ \end{gathered}[/tex]
Where "a" is the numerator and "b" is the denominator. Both are Integers, and:
[tex]b\ne0[/tex]
- Irrational numbers cannot be written as simple fractions.
Then, knowing those definitions, you can identify that:
1. The number:
[tex]-\sqrt[]{25}=-5[/tex]
Since -5 is an Integer, it can be written as:
[tex]=\frac{-5}{1}[/tex]
Therefore, it is a Rational Number.
2. You can identify that the second number is a Repeating Decimal because the line over the decimal digits indicates that its digits are periodic.
By definition, Repeating Decimals are Rational Numbers.
3. Notice that the next number is:
[tex]-\sqrt[]{10}\approx-3.162278[/tex]
Since it cannot be written as a simple fraction, it is not a Rational Number.
4. For the number:
[tex]-\frac{18}{5}[/tex]
You can identify that it is a fraction whose numerator and denominator and Integers. Then, it is a Rational Number.
5. Notice that the last number is:
[tex]18\pi[/tex]
By definition, π is an Irrational Number.
Therefore, the answer is:
