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} (598211)/(33000)=18.127606060\ldots \\ (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=(22)/(2)`

Third number

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

`25.4777=(254777)/(10000)`

Fourth number

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

`\begin{gathered} (213877)/(11100)=19.268198198198198\ldots \\ (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} (303488)/(24975)=12.15167167167\ldots \\ (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.