Question

Rational numbers multiple choice. select all that apply

Answer 1

The first two numbers are rational, because they are rational numbers with a finite number of decimal digits.

The third number is also rational, because $\sqrt{169}=13$, which is integer, and thus rational as well.

We can't say that the fourth number is rational, because we don't know how the number continues. A decimal number is rational if its decimal digits are finitely many, or if they show some periodicity. This doesn't seem the case, so the number may be irrational.

The last number is rational, because it is a periodic decimal number, and as such it admits a fraction that generates it.