Express 0.5 as a common fraction.

Let x=0.5=0.55. Then 10x=5.5, and so 10x-x=9x=5 x=59.

jmc

number theory junior

Problem

Express

0. \overline{5}

as a common fraction.

Solution

Let

x = 0. \overline{5} = 0.5 \overline{5}

. Then

10 x = 5. \overline{5}

, and so

10 x - x = 9 x = 5 ⟹ x = \frac{5}{9}

Final answer

\frac{5}{9}