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....#

_

#" "x=0.777777777777.....#

#9x=7#

#x=7/9#