Question

Write the following rational numbers in $\frac{p}{q}$ form.
(i) $0.\overline{6}$

Answer 1

We have $0.\overline{6}=0.666...$
Let x = 0.6666.... = $0.\overline{6}$ ------ (1)

10x = 6.666.... = $6.\overline{6}$ ----------(2)

Subtracting equation (1) from (2), we get:

10x $-$ x = $6.\overline{6}-0.\overline{6}$
Or, 9x = 6
x= $\frac{6}{9}=\frac{2}{3}$

So, $0.\overline{6}=\frac{2}{3}$