Question

classify each value as rational or irrational. value 0.034 1/2 classification select select select select

Explanation:

Step1: Recall rational - irrational definition

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. An irrational number cannot be written as such a fraction.

Step2: Analyze $\pi$

$\pi$ is a non - repeating, non - terminating decimal. It cannot be written as a fraction $\frac{p}{q}$ with $p,q\in\mathbb{Z}$ and $q
eq0$. So it is irrational.

Step3: Analyze $\frac{4}{5}$

$\frac{4}{5}$ is in the form of a fraction where $p = 4$ and $q = 5$ are integers and $q
eq0$. So it is rational.

Step4: Analyze $0.034$

$0.034=\frac{34}{1000}=\frac{17}{500}$, which is a fraction with integers in the numerator and denominator and non - zero denominator. So it is rational.

Step5: Analyze $\sqrt{2}$

$\sqrt{2}$ is a non - repeating, non - terminating decimal. It cannot be written as a fraction $\frac{p}{q}$ with $p,q\in\mathbb{Z}$ and $q
eq0$. So it is irrational.

Answer:

$\pi$: Irrational
$\frac{4}{5}$: Rational
$0.034$: Rational
$\sqrt{2}$: Irrational