Express 0.007777777..... In rational number?

Question

1804 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-25T07:38:22

#7/900#

#" let "x=0.007777777....#

since only one digit recurs multiply by #10#

#10x=0.07color(red)(777...)#

#color(white)(aa)x=0.00color(red)(77777..)#

subtract, the digits in red cancel

#:.9x=0.07#

#=>x=0.07/9xx100/100#

#x=7/900#