Write \(0.\mathop 2\limits^ \bullet \mathop 4\limits^ \bullet \) as a geometric sequence and find

(i)  the first term

(ii)  the common ratio

(iii)  Hence write down \(0.\mathop 2\limits^ \bullet \mathop 4\limits^ \bullet \) as a fraction in its simplest form

By considering the limiting sum of a suitable infinite series, express 0.2\(\dot{7}\dot{2}\) as a fraction in its simplest form.

Using the limiting sum of G.P. \({\rm{0}}{\rm{.0\dot 7}}\) as a fraction is?

Using the limiting sum of a G.P. \({\rm{0}}{\rm{.\dot 1\dot 2}}\) as a fraction is?

Using the limiting sum of a G.P. \(0.\dot 1\dot 3\dot 5\) as a fraction is?

Using the limiting sum of a G.P. \(1.00\dot 4\) as a fraction is?

Using the limiting sum of a G.P. \(2.9\dot 6\dot 0\) as a fraction is?

Using the limiting sum of a GP \(0.\dot 1\dot 2\dot 5\) as a fraction is?

Using the limiting sum of a geometric progression, express \(0.0\dot 5\) as a fraction in its simplest form.