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Question
Write the following rational numbers in `bb(p/q)` form.
\[\ce{0.\overset{\bullet}{6}}\]
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Solution
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`
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