Question

Write 0. 15 overbar as a fraction in simplest form.

Answer 1

Let x = 0.\overline{15} = 0.151515...

Then 100x = 15.\overline{15}. Subtracting,
100x − x = 15.\overline{15} − 0.\overline{15} ⇒ 99x = 15 ⇒ x = 15/99 = 5/33.

So 0.\overline{15} = 5/33.