Question

#3 0.\overline{2} e) rational f) irrational #6 \sqrt{16} k) rational l) irrational

Explanation:

Step1: Recall rational - number definition

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. A repeating decimal is rational.
For $0.\overline{2}$, let $x = 0.222\cdots$. Then $10x=2.222\cdots$. Subtracting $x$ from $10x$ gives $10x - x=2.222\cdots - 0.222\cdots$, so $9x = 2$, and $x=\frac{2}{9}$.

Step2: Evaluate $\sqrt{16}$

We know that $\sqrt{16}=4$ since $4\times4 = 16$. And $4=\frac{4}{1}$, which is a fraction of two integers.

Answer:

E. Rational
K. Rational