Question

Which of the numbers given are rational?Select all that apply:018.127600121025.4777019.26819812.15167

Answer 1

A rational number is a number that is the form p/q where p and q are integers, and q is not equal to 0.

$\text{Rational number: }\frac{\text{ integer}}{\text{ integer not equal to 0}}$

So, in this case, we have:

First number

We can rewrite this number as the division of two integers like this:

$\begin{gathered} \frac{598211}{33000}=18.127606060\ldots \\ \frac{598211}{33000}=18.127\bar{6}\bar{0} \end{gathered}$

Second number

We can rewrite this number as the division of two integers like this:

$\sqrt[]{121}=11=\frac{22}{2}$

Third number

We can rewrite this number as the division of two integers like this:

$25.4777=\frac{254777}{10000}$

Fourth number

We can rewrite this number as the division of two integers like this:

$\begin{gathered} \frac{213877}{11100}=19.268198198198198\ldots \\ \frac{213877}{11100}=19.268\bar{1}\bar{9}\bar{8} \end{gathered}$

Fifth number

We can rewrite this number as the division of two integers like this:

$\begin{gathered} \frac{303488}{24975}=12.15167167167\ldots \\ \frac{303488}{24975}=12.15\bar{1}\bar{6}\bar{7} \end{gathered}$

Therefore, all given numbers are rational because they can be expressed in the form p/q where p and q are integers, and q is different from zero.