Question

Is 5.131131113.... a rational number or irrational number?

Answer 1

A number that can be expressed as $\frac{p}{q}$ , where $p,q$ are integers and $q\ne 0$, is called a rational number.

Irrational numbers:A number that cannot be expressed in the form $\frac{p}{q}$ , where $p,q$ are integers and $q\ne 0$, is called irrational number.

These numbers neither terminates nor repeat the particular number in the process of division is said to be a non terminating non repeating decimal expansion.

Here, $5.131131113\dots$ has non terminating non repeating decimal expansion.So it is an irrational number.