Question

Express the following in the form of p/q 0.6666...

Answer 1

$0.6666... = 0.6 bar \\ let \: 0.6bar \: be \: x. \\ x = 0.6bar \\ (multiplying \: 10 \: on \: both \: the \: sides \: ) \\ x \times 10 = 0.6bar \: \times 10 \\ 10x = 6.6bar \\ 10x = 6 + 0.6bar \\ 10x = 6 + x \\ 10x - x = 6 \\ 9x = 6 \\ x = 6 \: upon \: 9 \\ x = 2 \: upon \: 3$
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