Question

Write 0.1 (the "1" with a horizontal line on top) as a fraction.

Answer 1

0.\overline{1} = 0.111... . Let x = 0.111... . Then 10x = 1.111... . Subtract: 10x − x = 1.111... − 0.111... = 1, so 9x = 1 and x = 1/9.

Thus 0.\overline{1} = 1/9.