Question

Classify the numbers as rational or irrational : $7.478478$

Answer 1

$7.478478=7.\overline{478}$

It is a non-terminating & repeating decimal therefore, it is a $\text{rational}$ number.

Note:

A decimal number can either be terminating and other is non-terminating.

When a decimal digit is terminating than it is a rational number.

When a decimal digit is non-terminating then again there are two cases:

1. First when decimal digits are non-terminating and recurring then it is a rational number.

2. Other case is when decimal digits are non-terminating and non-recurring then it is irrational.