How do you find the repeating decimal 0.7 with 7 repeated as a fraction?

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Answer 1 · 2017-01-14T08:57:25

$7/9$

$x=0.777777777777.....$

since only one digit recurs multiply by $10$

$10x=7.77777777777777....$

now subtract the two eqns. to eliminate the recurring digits

$10x=7.77777777777777....$

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$" "x=0.777777777777.....$

$9x=7$

$x=7/9$