Question

Express the following decimal expression into rational number

${\displaystyle 17.2\overline{15}}$

Answer 1

Let x = 17.2151515……….  ..........(1)

10x = 172.151515………   ........(2)

100x = 17215.1515……..  ........(3)

(3) – (2)

⇒ 1000x – 10x

= 17215.1515……….. (−)

17215.1515……..

990x = 17043

x = ${\displaystyle \frac{17043}{990}}$

or

${\displaystyle \frac{5681}{330}}$