Question

Classify each number as rational or irrational.

Answer 1

$0.167\ -\ rational\\\\\dfrac{2}{9}\ -\ rational\\\\\pi\ -\ irrational\\\\\sqrt{225}=15\ -\ rational$

Answer 2

A number is rational if we can write that number as a fraction.

A number is irrational if we can not write as a fraction. This means if a number has non repeating and non terminating decimal values then it is an irrational number.

Now let us look at our given numbers one by one.

$0.167$

We can write $0.167$ as $\frac{167}{100}$ . Hence it is a rational number.

$\frac{2}{9}$ This number is already written as fraction. It is a rational number.

$\pi$ We can not write $\pi$ as a fraction because the equivalent   decimal values of  $\pi$ are  non repeating and non terminating. Therefore  $\pi$ is an irrational number. Remember that $\frac{22}{7}$ is just an approximation for $\pi$. It isn't the actual value of $\pi$.

$\sqrt225$ is equivalent to 15. We can write 15 as a fraction like $\frac{15}{1}$. Therefore $\sqrt225$ is a rational number.