$\"\"$

The decimal number is $\"\"$ .

Rewrite the number as $\"\"$ .

$\"\"$ .

After the first term, the series is in the form of geometric series.

Here first term $\"\"$ and common ratio $\"\"$ .

Since $\"\"$ , the series is converges.

The sum of infinite series in a geometric series is $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

The rational number is $\"\"$ .