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.
[tex]0.167[/tex]
We can write [tex]0.167[/tex] as [tex]\frac{167}{100}[/tex] . Hence it is a rational number.
[tex]\frac{2}{9}[/tex] This number is already written as fraction. It is a rational number.
[tex]\pi[/tex] We can not write [tex]\pi[/tex] as a fraction because the equivalent decimal values of [tex]\pi[/tex] are non repeating and non terminating. Therefore [tex]\pi[/tex] is an irrational number. Remember that [tex]\frac{22}{7}[/tex] is just an approximation for [tex]\pi[/tex]. It isn't the actual value of [tex]\pi[/tex].
[tex]\sqrt225[/tex] is equivalent to 15. We can write 15 as a fraction like [tex]\frac{15}{1}[/tex]. Therefore [tex]\sqrt225[/tex] is a rational number.
