What is .18 repeating as a fraction?

Question

13864 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-20T18:11:57

$x = 0 . ¯ ¯¯ ¯ 18 - - - - - - - - - - - - \to (1)$ $x=0.bar(18)------------->(1)$

$100 x = 18 . ¯ ¯¯ ¯ 18 - - - - - - - - - - - - \to (2)$ $100x=18.bar(18)------------->(2)$

Subtract them

$100 x - x = 18 . ¯ ¯¯ ¯ 18 - 0 . ¯ ¯¯ ¯ 18$ $100x-x=18.bar(18)-0.bar(18)$

$99 x = 18$ $99x=18$

$x = \frac{18}{99}$ $x=18/99$

$x = \frac{2}{11}$ $color(red)(x=2/11$