Question

Write the following rational numbers in `bb(p/q)` form.

\[\ce{0.\overset{\bullet}{6}}\]

Answer 1

Let x = 0.666.... = \[\ce{0.\overset{\bullet}{6}}\]

∴ 10x = 6.666... = \[\ce{0.\overset{\bullet}{6}}\]

∴ 10x − x = \[\ce{6.\overset{\bullet}{6} - 0.\overset{\bullet}{6}}\]

∴ 9x = 6

∴ x = `6/9`

∴ x =`2/3` 

∴  \[\ce{0.\overset{\bullet}{6}}\] = `2/3`